This paper discusses how to enhance often time-consuming RBM training processes based on the commonly used Gibbs sampling using an improved version of quantum sampling. To prevent overfitting, they propose some solutions that help acquire less probable samples from the distribution by adjusting D-wave control and embedding parameters.

Alejandro Lopez-Bezanilla, William Bernoudy, Kelly Boothby, Jack Raymond, Alberto Nocera, Andrew D. King

arXiv:2505.08994 

The complex energy landscapes exhibited by frustrated magnetic systems undergoing quantum fluctuations are a challenge to accurately simulate, and thus of great interest for testing diverse qubit platforms in the field of quantum simulation. This study experimentally demonstrates quantum fluctuations lifting the degenerate ground-state manifold of classical magnetic configurations in fullerene Ising models with resonating dimers. The interplay between degeneracy and quantum fluctuations makes these boundary-free models a suitable benchmark for quantum simulators. Indeed, we observe significant performance improvement across generations of superconducting quantum annealers, showing the potential of highly symmetric, frustrated systems for assessing the precision of quantum-simulation technologies.

Toyota CRDL developed a hybrid quantum-classical algorithm for model predictive control (MPC). Unlike the usual application scenario for MPC algorithms the research team used the D-Wave system for dynamic control problems in which solutions must be obtained at high speed, specifically stabilization of a spring-mass-damper system, such as the ones in our cars that absorb shock on uneven roads; and dynamic audio quantization for radios and GPS devices. In both cases, the D-Wave method exhibited better performance than two classical approaches.

This is a heuristic approach on how to optimally schedule jobs using a quantum computer. Given a set of jobs and a finite number of machines, how should we schedule the jobs on those machines such that all the jobs are completed at the earliest possible time?

On the Volkswagen factory floor, the production process creates a series of constantly changing conditions. Delays, shifting wait times, and irregular requests all impact business objectives and outcomes. In order to find optimization solutions, Volkswagen is developing a hybrid algorithm that relies on both classical and quantum approaches to problem solving.

Given a set of jobs and a finite number of machines, this demo show how to schedule jobs on those machines such that all the jobs are completed at the earliest possible time.

In 2019, DENSO and Tohoku University announced the creation of an algorithm designed to improve the ability of a D-Wave system to handle complicated problems. The algorithm partitions an original, large problem into a group of subproblems. The D-Wave system then iteratively optimizes each subproblem to eventually solve the original, larger one. DENSO plans to use the algorithm to address everything from public transportation to the coordination of robotic systems in factories.

In addition to creating smarter, safer, more environmentally friendly automotive components, DENSO envisions incorporating quantum computing into everything from production and robotics to scheduling and logistics for product delivery. Work is already underway to make that vision a reality. DENSO recently completed proof-of-concept work using D-Wave's quantum platform, aimed at optimizing control of Automated Guided Vehicles (AGVs) on their factory floors.

When BMW began looking for ways to optimize their production lines, they turned to D-Wave. Using quantum algorithms, the company streamlined the complexity and requirements for programming robots used in PVC application and joint sealing.

As part of their work supporting Innovate UK, British multinational defense, security, and aerospace company BAE Systems undertook an assessment of how to optimize planning and scheduling of operations, distribution, and telecommunications across dozens of major industries using quantum computing.

Keeping GE’s robust R&D program running presents significant logistical challenges, especially when it comes to asset sustainment. Using D-Wave’s quantum computing system, the company set out to improve resource allocations for machine repairs and minimize resource contention when multiple repairs are requested at once.

In this talk we present a short overview of recent quantum applications in VW. Using the Quantum Shuttle project as motivation, we show how to construct live quantum optimization services for production applications. Specifically, we showcase a new application—the multi-car paint shop problem—and provide a live demo of this optimization system with real-world data.

At this webinar, Hyperion Research SVP Bob Sorensen discussed the results and his analysis of new survey data on the challenges and opportunities experienced by early adopters of commercial quantum computing (QC). The intent of this effort is to explore and more clearly define potential quantum computing growth and expansion paths within organizations that have already taken their first steps in exploring the potential of quantum computing.

Here we use portfolio optimization as a case study by which to benchmark quantum annealing controls and their relative effects on computational accuracy. We compare empirical results from the D-Wave 2000Q quantum annealer to the computational ground truth for a variety of portfolio optimization instances.

In this presentation, we present an application on multimodal container planning. We show how to map this problem to a QUBO problem formulation and how the practical implementation can be done on the quantum annealer produced by D-Wave Systems.

We developed the feature selection module for the internal automated machine learning (AutoML) system by using D-Wave Advantage. The internal AutoML system, called Crafto, allows non-expert users to build a ML pipeline from the data on various environments to the ready-to-use ML models. With the help of more available qubits of D-Wave Advantage, raw data with more features can be handled by QAFS. This is an important property in the view of being used in the production system.

We analyze 3,171 US common stocks to create an efficient portfolio based on the Chicago Quantum Net Score (CQNS) and portfolio optimization. We begin with classical solvers and incorporate quantum annealing. We add a simulated bifurcator as a new classical solver and the new D-Wave Advantage(TM) quantum annealing computer as our new quantum solver.

VW is leading the way in the application of quantum computing in the automotive industry. In addition to using D-Wave's 2000Q to optimize factory production, the company has tested a wide range of applications, including the optimization of traffic flow via GPS, the development of neural networks and machine learning for self-driving cars, discovery of new materials for manufacturing, and catalyzing improvements in automotive design.

Shopping for the right car can be a complicated process, but software engineers at Volkswagen are hoping to make it just a little bit easier. Using a hybrid classical-quantum approach, they’ve built a recommendation system that understands customer biases, preferences, and behaviors, then helps them select and customize their ideal vehicle. The initial results show rapid convergence and look very promising.

Understanding gene regulatory pathways is critical in forming concepts of how organisms grow and develop. The authors sought to use Bayesian network machine learning in tandem with the D-Wave quantum computer on a particular genetic problem.

For almost four years, Susan Mniszewski and colleagues at Los Alamos National Laboratory have been exploring the well-known graph partitioning problem with the D-Wave quantum computer. This recent report, involving a new multilevel algorithm, shows continued good results when compared to the industry-standard classical algorithms.

We continue to investigate the use of quantum computers for building an optimal portfolio out of a universe of 60 U.S. listed, liquid equities. Starting from historical market data, we apply our unique problem formulation on the D-Wave Systems Inc. D-Wave 2000Q (TM) quantum annealing system (hereafter called D-Wave) to find the optimal risk vs return portfolio. We approach this first classically, then using the D-Wave, to select efficient buy and hold portfolios. Our results show that practitioners can use either classical or quantum annealing methods to select attractive portfolios. This builds upon our prior work on optimization of 40 stocks.

A key problem in financial mathematics is the forecasting of financial crashes: If we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem...In this Rapid Communication, we show how this problem can be handled by quantum annealers.

Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, i.e., a problem which cannot be solved efficiently with a classical computer. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer to obtain financial equilibrium more efficiently... Our experiment paves the way to study quantitative macroeconomics, enlarging the number of problems that can be handled by current quantum computers.

Different quantum algorithms have been built to find currency arbitrage opportunities, perform feature selection in credit scoring, and optimize trading trajectories. Hybrid techniques have been explored in order to overcome the limitations in the size of the problem, taking into consideration the number of qubits and connectivity in the Chimera architecture in D-Wave processors.

Recent work that solves the equilibrium of a nonlinear financial network and configuration of an optimal logistic network. (1) Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, i.e., a problem which cannot be solved efficiently with a classical computer. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer to obtain financial equilibrium more efficiently.(2) The logistic network design is an abstract optimization problem which, under the assumption of minimal cost, seeks the optimal configuration of infrastructures and facilities of the supply chain based on customer demand.

Previous work by GE Research has looked at using quantum computing to do resource and path planning to improve the efficiency of our asset sustainment operations around things like jet engines,  wind turbines and medical equipment repairs.  The work was meant to be exploratory and our projections showed it taking a few more years before it would be competitive with other approaches.  With access to the latest generation of hardware and hybrid algorithms we are beginning to believe that our projections are too conservative and that the time for industrial use of quantum computing has already started.

Chicago Quantum (SM) has built an equity portfolio optimization application that helps investors and investment managers to select groups of stocks to buy and hold. This application selects groups of stocks out of a universe of 60 liquid, US stocks that have expected returns that outweigh the expected variance of returns based on one year of historical trading data. Initial results are positive and compelling.

In this paper a quadratic problem in finance is taken, the Portfolio Optimisation problem. Here, a set of assets is chosen for investment, such that the total risk is minimised, a minimum return is realised and a budget constraint is met. This problem is solved for several instances in two main indices, the Nikkei225 and the S&P500 index, using the state-of-the-art implementation of D-Wave’s quantum annealer and its hybrid solvers. The results are benchmarked against conventional, state- of-the-art, commercially available tooling. Results show that for problems of the size of the used instances, the D-Wave solution, in its current, still limited size, comes already close to the performance of commercial solvers.

A novel quantum-classical hybrid scheme is proposed to efficiently solve largescale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers

In this manuscript we explore an experimentally observed statistical phenomenon by which domain walls on an Ising chain programmed onto a flux qubit quantum annealer tend toward a non-uniform distribution.

In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints. This problem, well-known to be NP-Hard, is central to quantitative finance.

This paper provides a quantum annealing algorithm in QUBO form for a dynamic asset allocation problem using expected shortfall constraint.

In this work, the authors propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. They have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor.

The 3-dimensional fold of an RNA molecule is largely determined by patterns of intramolecular hydrogen bonds between bases. Predicting the hydrogen bonding network from the sequence, also referred to as RNA secondary structure prediction or RNA folding, is a nondeterministic polynomial-time (NP)-complete computational problem. An Adiabatic Quantum Computer (AQC) is compared to a Replica Exchange Monte Carlo (REMC) algorithm programmed with the same objective function, with the AQC being shown to be highly competitive at rapidly identifying low energy solutions. The method proposed in this study was compared to three algorithms from literature and was found to have the highest success rate.

Many financial investors today are including cryptocurrency as part of their portfolios. At the University of Tennessee, researchers investigated how quantum computing can be used to optimize these investment selections to minimize risk, maximize returns, and stay on budget.

Topological Data Analysis is an exciting new field of mathematics, in which data scientists look for patterns in data using mathematical concepts of shape. The authors explored using the D-Wave quantum computer on a small problem called Wasserstein distance.

The idea of “forward-reverse error mitigation” (FREM) was formulated during an open forum session at the Qubits North American 2018 meeting. We hence explored FREM sampling as a novel way to try to improve ground-state sampling statistics on quantum annealers with no cost in ancilla qubits.

The study of protein-ligand binding is a critical part of drug development, the development of novel materials for medical applications, and understanding many of the processes that take place in the human body. Booz Allen Hamilton has taken the next step on that road by applying the power of quantum computing to these important chemical processes.

Peptides are mid-size molecules composed of amino acids and constitute some of nature's best drugs. Designing these mid-size molecules computationally remains a challenge due to the astronomical search space and complex energy dynamics. Here, we explore how quantum annealing and hybrid approaches may offer a new alternative toolkit for designing peptide therapeutics that could hold the key to groundbreaking new drugs.

Reverse translation of polypeptide sequences to expressible mRNA constructs is a NP- hard combinatorial optimization problem. This work investigates the potential impact of leveraging quantum computing technology for codon optimization. An adiabatic quantum computer (AQC) is compared to a standard genetic algorithm (GA) programmed with the same objective function. The AQC is found to be competitive in identifying optimal solutions and future generations of AQCs may be able to outperform classical GAs.

Financial stress testing is becoming an increasingly important tool in the arsenal built by regulators to preserve economic stability and prevent a domino effect when financial institutions experience periods of distress. Assad Bouayou applied the power of quantum computing to an XVA model to build a more qualitative, systematic approach to stress testing aimed at preventing future banking crises.

In partnership with Reply Data, FS Italiane has begun to explore quantum solutions to a number of hard optimization problems, including scheduling, assigning platforms to incoming trains, worker deployment, maintenance, and freight load distribution.

"One-hot constraints" are common in QUBO formulations - these are constraints in which exactly one out of many choices must be selected. Using the Volkswagen traffic flow problem as an example, DENSO sought to find an improved QUBO formulation for one-hot problems. Their results are promising for certain types of problems, and their research continues.

In the world of finance, even small improvements in Return on Assets (ROA) can make a massive impact. Powered by D-Wave's infrastructure, CogniFrame's quantum computing software allows financial institutions to make better investment and management decisions. Using a hybrid approach, CogniFrame demonstrated a dramatic decrease in the amount of time needed to find optimal solutions for complex problems involving insurance, pensions, and asset management.

In this work the author shows how to solve non-linear integer programs using a novel hybrid quantum-classical approach, and present exciting numerical results on D-Wave that outclass best-in-class commercial classical software; how to compile using novel methods from algebraic Ggeometry; and analyzes quantum speedups by reframing it in the language of birth and death of anti-crossings and algebraic topology.

D-Wave's annealer has mostly been applied to QUBO problems with integer variables, and CINECA sought to explore problems with real variables, which require a large number of binary variables. CINECA sought to use D-Wave's latest annealing features (anneal pause and reverse anneal) to explore one problem with real variables, low-rank matrix factorization.

The Large Hadron Collider (LHC) circulates counter-rotating beams of protons in closely packed bunches that cross at designated interaction points. Particle physics apparatuses at these interaction points detect particles created at each proton-proton (p-p) collision and are used to reconstruct physics at the TeV energy scale. We use the D-Wave 2000Q to perform this reconstruction on artificial events where the positions of p-p collisions and tracks are drawn from measured LHC distributions.

Groovenauts and Mitsubishi Estate used a D-Wave system to optimize truck routes for waste collection, reducing total distance traveled from 2,300 km to just 1,000 km. As a result, CO2 emissions would be reduced by approximately 57%, and the number of vehicles reduced by approximately 59%.

A typical day at the Frankfurt Airport involves coordinating the real-time movements of hundreds of aircraft carrying more than 170,000 passengers between 278 gates. DLR applied quantum annealing to the problem of optimizing gate assignments, with the goal of reducing total passenger transit time.

Resource allocation and planning problems in telecommunications—such as network layouts, job scheduling, configuring overlapping calls, are often algorithmically hard to address. Using quantum annealing, British Telecom’s Applied Research division uncovered how D-Wave’s 2000Q could dramatically transform the industry.

Several finance-related applications are discussed in this talk including (1) A Multi-Period Optimal Trading Strategy, (2) Quantum-Ready Hierarchical Risk Parity (QHRP), (3) Real-Time Optimization Framework, and (4) Tax Loss Harvesting

In this paper, researchers from Volkswagen present a real-world application that uses quantum technologies. Specifically, they show how to map certain parts of a real-world traffic flow optimization problem to be suitable for quantum annealing. They show that time-critical optimization tasks, such as continuous redistribution of position data for cars in dense road networks, are suitable candidates for quantum computing.

Accenture has explored more than 150 use cases and developed 10 functional cross-industry applications for quantum computers. One of the most promising involves finding optimal donor-patient matches in a kidney exchange network, as Accenture aims to develop a robust algorithm to be used by hospital networks and government agencies nationwide.

Recruit Communications provides a wide variety of online services including online advertising, job search, travel, dining, hotel reservations and more. In this project, Recruit used several new methods to optimize how an advertiser's budget is allocated over time for display advertising. Their results showed that the D-Wave quantum annealer found a better solution than the often-used greedy method.

Western Canadian grocery retailer Save-On-Foods is using hybrid quantum algorithms to bring grocery optimization solutions to their business, with pilot tests underway. The company has been able to reduce the time an important optimization task takes from 25 hours to a mere 2 minutes of calculations each week. Even more important than the reduction in time is the ability to optimize performance configuring all interactions - this is simply not possible using traditional methods.

Employing D-Wave's annealing quantum computing solutions as accelerators in the speed and quality of training our generative AI-driven, drug discovery (DD) analysis systems, we constructed a hybrid quantum and classical computer system, aiming to extend the applicable range of molecular-generation AI systems in the DD field (i.e., AI-driven Drug Design). The goal of our project is to pioneer a new process for discovering 'first-in-class' pharmaceutical small compounds, which is performed with supports by D-Wave's team of professional services experts. In my talk, we report substantial aspects of our projects, based on the above-mentioned strategy and present progress.

King, A. D., Raymond, J., Lanting, T., Harris, R., Zucca, A., Altomare, F., Berkley, A. J., Boothby, K., Ejtemaee, S., Enderud, C., Hoskinson, E., Huang, S., Ladizinsky, E., MacDonald, A. J. R., Marsden, G., & others. (2025). Beyond-classical computation in quantum simulation. Science. https://www.science.org/doi/10.1126/science.ado6285

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

https://www.science.org/doi/10.1126/science.ado6285

Amin, M. H., Raymond, J., Kinn, D., Hamze, F., Hamer, K., Pasvolsky, J., Bernoudy, W., King, A. D., & Kortas, S. (2025). Blockchain with proof of quantum work. arXiv preprint arXiv:2503.14462. https://arxiv.org/abs/2503.14462v1

We propose a blockchain architecture in which mining requires a quantum computer. The consensus mechanism is based on proof of quantum work, a quantum-enhanced alternative to traditional proof of work that leverages quantum supremacy to make mining intractable for classical computers. We have refined the blockchain framework to incorporate the probabilistic nature of quantum mechanics, ensuring stability against sampling errors and hardware inaccuracies. To validate our approach, we implemented a prototype blockchain on four D-WaveTM quantum annealing processors geographically distributed within North America, demonstrating stable operation across hundreds of thousands of quantum hashing operations. Our experimental protocol follows the same approach used in the recent demonstration of quantum supremacy [1], ensuring that classical computers cannot efficiently perform the same computation task. By replacing classical machines with quantum systems for mining, it is possible to significantly reduce the energy consumption and environmental impact traditionally associated with blockchain mining. Beyond serving as a proof of concept for a meaningful application of quantum computing, this work highlights the potential for other near-term quantum computing applications using existing technology.

https://arxiv.org/abs/2503.14462v1

OPTIMIZING MANUFACTURING WITH FLOW-SHOP SCHEDULING

Flow-shop scheduling (FSS) is an optimization challenge that involves organizing a set of jobs that need to be processed through multiple machines in a specific order. This type of scheduling is important in manufacturing and production environments where operators are pressed to efficiently manage the workflow by optimizing the time it takes to complete each job and thus maintain a smooth and linear progression through the production line.

OPTIMIZING THE QUADRATIC ASSIGNMENT PROBLEM

The Quadratic Assignment Problem (QAP) is to select locations that minimize the total flow cost between facilities. The optimization tasks for this problem include minimizing transportation costs, reducing travel distances, and optimizing resource allocation. These tasks are commonly found in industries where efficient layout planning and logistics are essential, such as manufacturing, supply chain management, and facility layout design.

Zhang, H., Boothby, K. & Kamenev, A. Cyclic quantum annealing: searching for deep low-energy states in 5000-qubit spin glass. Sci Rep 14, 30784 (2024). https://doi.org/10.1038/s41598-024-80761-z

Quantum computers promise a qualitative speedup in solving a broad spectrum of practical optimization problems. The latter can be mapped onto the task of finding low-energy states of spin glasses, which is known to be exceedingly difficult. Using D-Wave’s 5000-qubit quantum processor, we demonstrate that a recently proposed iterative cyclic quantum annealing algorithm can find deep low-energy states in record time. We also find intricate structures in a low-energy landscape of spin glasses, such as a power-law distribution of connected clusters with a small surface energy. These observations offer guidance for further improvement of the optimization algorithms.

Maintaining steady connections on a mobile network entails a lot of behind-the-scenes effort. Work done by Japanese telecommunications company NTT DOCOMO demonstrated that quantum computing can help mitigate potential performance issues on mobile networks during periods of heavy use. This is now an in-production application for NTT DOCOMO.

Thomas Lubinski, Carleton Coffrin, Catherine McGeoch, Pratik Sathe, Joshua Apanavicius, David Bernal Neira, Quantum Economic Development Consortium(QED-C) Collaboration

ACM Transactions on Quantum Computing, Volume 5, Issue 3

Catherine McGeoch, D-Wave; David Esteban Bernal Neira, Purdue University; Susan Mniszewski, Los Alamos National Laboratory; Nicholas Chancellor, Durham University 

The past decade has seen four generations of quantum annealing processors, with qubit counts increasing from 512 on the D-Wave Two (released in 2013), to over 5000 on Advantage processors available in 2023. During this time, expanding access for researchers has sparked enormous growth in publications and in the body of knowledge surrounding capabilities, applications, and best practices in use of these novel computing systems.

This Research Topic will invite submissions on all aspects of empirical experience with annealing-based quantum computers. The intention is to present a broad survey of the current state of knowledge about quantum annealing hardware, performance, software infrastructures, and application

Supreeth Mysore Venkatesh, Antonio Macaluso, Marlon Nuske, Matthias Klusch, Andreas Dengel 

Deutsches Forschungszentrum für Künstliche

https://arxiv.org/abs/2408.06007

The increasing number of Low Earth Orbit (LEO) satellites, driven by lower manufacturing and launch costs, is proving invaluable for Earth observation missions and low-latency internet connectivity. However, as the number of satellites increases, the number of communication links to maintain also rises, making the management of this vast network increasingly challenging and highlighting the need for clustering satellites into efficient groups as a promising solution. This paper formulates the clustering of LEO satellites as a coalition structure generation (CSG) problem and leverages quantum annealing to solve it. We represent the satellite network as a graph and obtain the optimal partitions using a hybrid quantum-classical algorithm called GCS-Q. The algorithm follows a top-down approach by iteratively splitting the graph at each step using a quadratic unconstrained binary optimization (QUBO) formulation. To evaluate our approach, we utilize real-world three-line element set (TLE/3LE) data for Starlink satellites from Celestrak. Our experiments, conducted using the D-Wave Advantage annealer and the state-of-the-art solver Gurobi, demonstrate that the quantum annealer significantly outperforms classical methods in terms of runtime while maintaining the solution quality. The performance achieved with quantum annealers surpasses the capabilities of classical computers, highlighting the transformative potential of quantum computing in optimizing the management of large-scale satellite networks.

Abhishek Awasthi∗, Nico Kraus†, Florian Krellner‡, David Zambrano†

*BASF Digital Solutions GmbH, Ludwigshafen am Rhein, Germany

†Aqarios GmbH, Munich, Germany

‡SAP SE, Walldorf, Germany

This work is a benchmark study for quantum- classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We first present the motivation and the problem description, along with different modeling techniques for classical and quantum computing. The modeling for classical solvers has been done as a mixed-integer convex program, while for the quantum-classical solver we model the problem as a binary quadratic program, which is best suited to the D-Wave Leap’s Hybrid Solver. This ensures that all the solvers we use are fetched with dedicated and most suitable model(s). Henceforth, we carry out benchmarking and comparisons between classical and quantum-classical methods, on problem sizes ranging till approximately 150, 000 variables. We utilize an industry grade classical solver and compare its results with D-Wave Leap’s Hybrid Solver. The results we obtain from D-Wave are highly competitive and sometimes offer speedups, compared to the classical solver.

Abhishek Awasthi∗, Nico Kraus†, Florian Krellner‡, David Zambrano† ∗BASF Digital Solutions GmbH, Ludwigshafen am Rhein, Germany †Aqarios GmbH, Munich, Germany
‡SAP SE, Walldorf, Germany

This work is a benchmark study for quantum- classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We first present the motivation and the problem description, along with different modeling techniques for classical and quantum computing. The modeling for classical solvers has been done as a mixed-integer convex program, while for the quantum-classical solver we model the problem as a binary quadratic program, which is best suited to the D-Wave Leap’s Hybrid Solver. This ensures that all the solvers we use are fetched with dedicated and most suitable model(s). Henceforth, we carry out benchmarking and comparisons between classical and quantum-classical methods, on problem sizes ranging till approximately 150, 000 variables. We utilize an industry grade classical solver and compare its results with D-Wave Leap’s Hybrid Solver. The results we obtain from D-Wave are highly competitive and sometimes offer speedups, compared to the classical solver.

Pérez Armas, L.F., Creemers, S. & Deleplanque, S. Solving the resource constrained project scheduling problem with quantum annealing. Scientific Reports14, 16784 (2024). 

Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations researc

N. Nikmehr, P. Zhang, H. Zheng, T. -C. Wei, G. He and Y. A. Shamash, "Quantum Annealing-Infused Microgrids Formation: Distribution System Restoration and Resilience Enhancement," in IEEE Transactions on Power Systems, DOI: 10.1109/TPWRS.2024.3399122

In this paper, the use of quantum computing is explored to solve a crucial optimization problem in the formation of microgrids (MGs), which can enhance the resilience of distribution networks against natural disasters or faults. The study focuses on developing a quantum-inspired optimization model for critical load restoration via MGs formation, leveraging the power of quantum annealing to solve complex combinatorial problems that classical methods struggle with. The Constrained Quadratic Model (CQM) solver from D-Wave is used to merge classical and quantum optimization approaches, delivering improved solutions to complex optimization problems. The solver has been optimized to take advantage of quantum computing's parallelism to provide high-performance solutions. The study compares outcomes from the D-Wave hybrid quantum-classical solver and the classical Gurobi solver, underscoring the effectiveness of quantum computing in addressing resilience-oriented optimization challenges. This assessment is validated through two case studies: the IEEE 37-bus system and the IEEE 240-bus distribution system.

Pelofske, E., Bärtschi, A. & Eidenbenz, S. Short-depth QAOA circuits and quantum annealing on higher-order ising models. npj Quantum Information 10, 30 (2024). 

We present a direct comparison between QAOA (Quantum Alternating Operator Ansatz), and QA (Quantum Annealing) on 127 qubit problem instances. QAOA with p = 1, 2 rounds is executed on the 127 qubit heavy-hex graph gate-model quantum computer ibm_washington, using on-device grid-searches for angle finding, and QA is executed on two Pegasus-chip D-Wave quantum annealers. The problems are random Ising models whose connectivity matches heavy-hex graphs and the Pegasus graph connectivity, and optionally include hardware-compatible cubic terms (ZZZ terms). The QAOA circuits are heavily optimized and of extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of the heavy-hex lattice. QAOA and QA are both compared against simulated annealing and the optimal solutions are computed exactly using CPLEX. The noiseless mean QAOA expectation values for p = 1, 2 are computed using classical light-cone based simulations. We find QA outperforms QAOA on the evaluated devices.

Andrew D. King, et al.

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. One such problem is the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum phase transition. State-of-the-art classical simulations demand resources that grow exponentially with system size. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench in two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for classical approaches. We assess approximate methods based on tensor networks and neural networks and conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that classical computers cannot.

Anders Irbäck, Lucas Knuthson, Sandipan Mohanty, and Carsten Peterson, Using quantum annealing to design lattice proteins, Phys. Rev. Research 6, 013162 

Quantum annealing has shown promise for finding solutions to difficult optimization problems, including protein folding. Recently, we used the D-Wave Advantage quantum annealer to explore the folding problem in a coarse-grained lattice model, the HP model, in which amino acids are classified into two broad groups: hydrophobic (H) and polar (P). Using a set of 22 HP sequences with up to 64 amino acids, we demonstrated the fast and consistent identification of the correct HP model ground states using the D-Wave hybrid quantum-classical solver. An equally relevant biophysical challenge, called the protein design problem, is the inverse of the above, where the task is to predict protein sequences that fold to a given structure. Here, we approach the design problem by a two-step procedure implemented and executed on a D-Wave machine. In the first step, we perform a pure sequence-space search by varying the type of amino acid at each sequence position, and seek sequences which minimize the HP-model energy of the target structure. After mapping this task onto an Ising spin-glass representation, we employ a hybrid quantum-classical solver to deliver energy-optimal sequences for structures with 30–64 amino acids, with a 100% success rate. In the second step, we filter the optimized sequences from the first step according to their ability to fold to the intended structure. In addition, we try solving the sequence optimization problem using only the quantum processing unit (QPU), which confines us to sizes ≤20, due to exponentially decreasing success rates. To shed light on the pure QPU results, we investigate the effects of control errors caused by an imperfect implementation of the intended Hamiltonian on the QPU, by numerically analyzing the Schrödinger equation. We find that the simulated success rates in the presence of control noise semiquantitatively reproduce the modest pure QPU results for larger chains.

Alejandro Lopez-Bezanilla, Andrew D. King, Cristiano Nisoli, and Avadh Saxena 

Nature Communications volume 15, Article number: 589 (2024) 

Fluctuations may induce the degradation of order by overcoming ordering interactions, consequently leading to an increase of entropy. This is particularly evident in magnetic systems characterized by nontrivial, constrained disorder, where thermal or quantum fluctuations can yield counterintuitive forms of ordering. Using the proven efficiency of quantum annealers as programmable spin system simulators, we present a study based on entropy postulates and experiments on a platform of programmable superconducting qubits to show that a low level of uncertainty can promote ordering in a system impacted by both thermal and quantum fluctuations. A set of experiments is proposed on a lattice of interacting qubits arranged in a triangular geometry with precisely controlled disorder, effective temperature, and quantum fluctuations. Our results demonstrate the creation of ordered ferrimagnetic and layered anisotropic disordered phases, displaying characteristics akin to the elegant order-by-disorder phenomenon. Extensive experimental evidence is provided for the role of quantum fluctuations in lowering the total energy of the system by increasing entropy and defect clustering. Our thorough and comprehensive application of an intentionally introduced noise on a quantum platform provides insight into the dynamics of defects and fluctuations in quantum devices, which may help to reduce the cost associated with quantum processing.

Humberto Munoz Bauza, Daniel A. Lidar, Scaling Advantage in Approximate Optimization with Quantum Annealing, arXiv:2401.07184 

Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected discrete optimization and quantum simulation problems. Nevertheless, despite numerous attempts, a computational quantum advantage in exact optimization using quantum annealing hardware has so far remained elusive. Here, we present evidence for a quantum annealing scaling advantage in approximate optimization. The advantage is relative to the top classical heuristic algorithm: parallel tempering with isoenergetic cluster moves (PT-ICM). The setting is a family of 2D spin-glass problems with high-precision spin-spin interactions. To achieve this advantage, we implement quantum annealing correction (QAC): an embedding of a bit-flip error-correcting code with energy penalties that leverages the properties of the D-Wave Advantage quantum annealer to yield over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. We generate random spin-glass instances on this graph and benchmark their time-to-epsilon, a generalization of the time-to-solution metric for low-energy states. We demonstrate that with QAC, quantum annealing exhibits a scaling advantage over PT-ICM at sampling low energy states with an optimality gap of at least 1.0%. This amounts to the first demonstration of an algorithmic quantum speedup in approximate optimization.

Spontaneous structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, physics-based computer simulations like Molecular Dynamics (MD) enable us to investigate these thermally activated processes with an atomic level of resolution. However, rare conformational transitions are intrinsically hard to investigate with MD, because an exponentially large fraction of computational resources must be invested to simulate thermal fluctuations in metastable states. Path sampling methods like Transition Path Sampling hold the great promise of focusing the available computational power on sampling the rare stochastic transition between metastable states. In these approaches, one of the outstanding limitations is to generate paths that visit significantly different regions of the conformational space at a low computational cost. To overcome these problems we introduce a rigorous approach that integrates a machine learning algorithm and MD simulations implemented on a classical computer with adiabatic quantum computing. First, using functional integral methods, we derive a rigorous low-resolution representation of the system's dynamics, based on a small set of molecular configurations generated with machine learning. Then, a quantum annealing machine is employed to explore the transition path ensemble of this low-resolution theory, without introducing un-physical biasing forces to steer the system's dynamics. Using the D-Wave quantum computer, we validate our scheme by simulating a benchmark conformational transition in a state-of-the-art atomistic description. We show that the quantum computing step generates uncorrelated trajectories, thus facilitating the sampling of the transition region in configuration space. Our results provide a new paradigm for MD simulations to integrate machine learning and quantum computing.

Supply Chain/ Logistics SavantX with videoQuantum Computing has shown how it can make a difference in optimizing logistics. SavantX developed the HONE (Hyper Optimized Nodal Efficiency) Engine, which uses proprietary data science and quantum computing to present real-time optimized solutions for use at the second largest container terminal at the Port of Los Angeles, Pier 300. SavantX leverages the D-Wave quantum computer repeatedly in transportation applications in real-time. Hear about lessons learned in applying quantum solutions to a real-world application and how quantum compares to the classical approach.

The future is quantum – this is precisely why NEC and CSIRO provided a breakdown of the importance of quantum. In this talk, NEC reveals its plans to drive higher sustained performance using D-Wave’s quantum technologies and how CSIRO is making leaps for solving material microstructure modeling with D-Wave Leap™.

Noisy intermediate-scale quantum (NISQ) hardware is almost universally incompatible with full-scale optimization problems of practical importance which can have many variables and unwieldy objective functions. As a consequence, there is a growing body of literature that tests quantum algorithms on miniaturized versions of problems that arise in an operations research setting. Rather than taking this approach, we investigate a problem of substantial commercial value, multi-truck vehicle routing for supply chain logistics, at the scale used by a corporation in their operations. Such a problem is too complex to be fully embedded on any near-term quantum hardware or simulator; we avoid confronting this challenge by taking a hybrid workflow approach: we iteratively assign routes for trucks by generating a new binary optimization problem instance one truck at a time. Each instance has ∼2500 quadratic binary variables, putting it in a range that is feasible for NISQ quantum computing, especially quantum annealing hardware. We test our methods using simulated annealing and the D-Wave Hybrid solver as a place-holder in wait of quantum hardware developments. After feeding the vehicle routes suggested by these runs into a highly realistic classical supply chain simulation, we find excellent performance for the full supply chain. Our work gives a set of techniques that can be adopted in contexts beyond vehicle routing to apply NISQ devices in a hybrid fashion to large-scale problems of commercial interest.

Optimizing package loading within trucks for manufacturers and distributors can result in cost and time savings. In this talk, Senior Manager Nitish Umang discusses his joint work with D-Wave and show a demo for the 3D cuboid loading problem. This is a good candidate for quantum optimization due to the combinatorial nature of the problem.

Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and technologies for this task, the minimal lattice-based HP model is well suited, as it represents a considerable challenge despite its simplicity. The HP model has favorable interactions between adjacent, not directly bound hydrophobic residues. Here, we develop a novel spin representation for lattice protein folding tailored for quantum annealing. With a distributed encoding onto the lattice, it differs from earlier attempts to fold lattice proteins on quantum annealers, which were based upon chain growth techniques. With our encoding, the Hamiltonian by design has the quadratic structure required for calculations on an Ising-type annealer, without having to introduce any auxiliary spin variables. This property greatly facilitates the study of long chains. The approach is robust to changes in the parameters required to constrain the spin system to chain-like configurations, and performs very well in terms of solution quality. The results are evaluated against existing exact results for HP chains with up to N=30 beads with 100% hit rate, thereby also outperforming classical simulated annealing. In addition, the method allows us to recover the lowest known energies for N=48 and N=64 HP chains, with similar hit rates. These results are obtained by the commonly used hybrid quantum-classical approach. For pure quantum annealing, our method successfully folds an N=14 HP chain. The calculations were performed on a D-Wave Advantage quantum annealer.

Computed tomography (CT) is an important imaging technique used in medical analysis of the internal structure of the human body. Previously, image segmentation methods were required after acquiring reconstructed CT images to obtain segmented CT images which made it susceptible to errors from both reconstruction and segmentation algorithms. However, this paper introduces a new approach using an advanced quantum optimization algorithm called quadratic unconstrained binary optimization (QUBO). This algorithm enables acquisition of segmented CT images from X-ray projection data with minimized discrepancies between experimentally obtained sinograms and quantized sinograms derived from quantized segmented CT images using the Radon transform. This study utilized D-Wave's hybrid solver system for verification on real-world X-ray data.

In this paper an application of D-Wave Systems quantum annealer for optimizing initial line-up of a soccer team is presented. Players and their playing position are selected to maximize the sum of players ratings for both a 4-3-3 attack formation and a 4-2-3-1 medium defensive formation. The problem is stated as a binary quadratic model (BQM) and it is solved in a D-Wave Leap Hybrid Solver. Results are presented and compared with already published results obtained with a classical solver.

Some business problems are better suited for quantum/hybrid technology than others. Watch this recording to find out how to identify and assess use cases and applications that would benefit from the use of quantum/hybrid resources.

Machine learning experts no longer need to be experts in optimization or hybrid solving in order to get the benefits of both. D-Wave's feature selection / machine learning tools enable access to the power of quantum hybrid to supercharge feature selection/ML workflows, and includes a plugin for scikit-learn.

Demand Side Response (DSR) is a strategy that enables consumers to actively participate in managing electricity demand. It aims to alleviate strain on the grid during high demand and promote a more balanced and efficient use of electricity resources. We implement DSR through discount scheduling, which involves offering discrete price incentives to consumers to adjust their electricity consumption patterns. Since we tailor the discounts to individual customers' consumption, the Discount Scheduling Problem (DSP) becomes a large combinatorial optimization task. Consequently, we adopt a hybrid quantum computing approach, using D-Wave's Leap Hybrid Cloud. We observe an indication that Leap performs better compared to Gurobi, a classical general-purpose optimizer, in our test setup. Furthermore, we propose a specialized decomposition algorithm for the DSP that significantly reduces the problem size, while maintaining an exceptional solution quality. We use a mix of synthetic data, generated based on real-world data, and real data to benchmark the performance of the different approaches.

Drug discovery is a high-risk, high-reward field, where a blockbuster therapy can deliver life-changing clinical benefits to millions of patients and generate billions of dollars in profit—but more than 90% of new drug development efforts ultimately prove fruitless. PolarisQB is using quantum computing with AI and precision medicine to search chemical space and create novel molecular drugs for specific proteins and diseases much more quickly than using traditional methods. In order to find a new preclinical lead candidate, the first step is to build a library of small molecules that may interact with the target protein binding pocket. Traditionally, library design involves wet lab testing that takes years, costs millions, and is limited to a narrow chemical space. With the power of D-Wave’s quantum technology, PolarisQB finds optimized molecules in days from a highly diverse library of 10^30 possibilities. This size of the library is 20 orders of magnitude bigger than the current industry standard.

Having the ability to efficiently detect the location where a leak occurs in a network is high on the bucket-list of any water distribution company worldwide. The determination of “how many” pressure-sensors to put “where” in the network is known to be an NP-hard problem. delaware in Belgium joined forces with De Watergroep (Belgium) and KWR (The Netherlands) and developed a tractable approach to determine “how many” and “where”. The QUBO-formulation of this problem allows for a fast determination of the optimal number and location of pressure-sensors via D-Wave’s quantum solver, which now becomes feasible in days instead of centuries. This webinar explains the steps taken and the outcome reached.

The Port of Los Angeles is known as America's busiest port. In a time where we are facing global supply chain challenges, it's essential that the Port operates to its maximum capacity with the highest level of efficiency possible. In conjunction with Fenix Marine Services, SavantX developed and deployed new technology using AI and D-Wave’s quantum computer to optimize terminal operations. The results of their work doubled cargo handling equipment productivity and produced more predictable cargo flows. Watch this webinar to learn more.

Pattison Food Group has over 100 stores that offer e-commerce delivery. 3-4 people are dedicated to manually creating driver schedules each week. Pattison worked with D-Wave to create these schedules automatically, taking scheduling rules (seniority, preferences/history, and policies) into account. As a result, weekly manual efforts for initial scheduling creation was reduced by ~80%​.

Recently, the demand for the optimization of TV commercials (CMs) has been increasing. Specifically, it is important to determine the assignment of TVCMs so that each viewer watches the TVCMs with specific number of times. This problem is known as frequency control. By controlling the frequency of multiple TVCMs for each viewer, the message of TVCMs can be conveyed to the viewers in the intended way. In our project, we considered the problem to maximize the KPI which is the number of viewers who watch all kinds of TVCMs more than once. We solved the optimization problem and broadcasted the TVCMs based on the result of the optimization. We also compared the increase in the business KPI calculated using the actual viewing data for 3 different methods, CPLEX, D-Wave CQM, and an existing manual method. As a result, D-Wave CQM increased the KPI by 92% compared to an existing manual method, and it also outperformed CPLEX by 4%, which is a significant impact on our business. 

Annealing is a heuristic for solving optimization problems that have seen a recent surge in usage owing to the success of D-Wave Systems. This paper aims to find a good heuristic for solving the Electric Vehicle Charger Placement (EVCP) problem, a problem that stands to be very important given the costs of setting up an electric vehicle (EV) charger and the expected surge in electric vehicles across the world. The same problem statement can also be generalized to the optimal placement of any entity in a grid and can be explored for further uses. Finally, the authors introduce a novel heuristic combining Quantum Annealing and Genetic Algorithms to solve the problem. The proposed hybrid approach entails seeding the genetic algorithms with the results of quantum annealing. Experimental results show that this method decreases the minimum distance from Points of Interest (POI) by 42.89% compared to vanilla quantum annealing over the sample EVCP datasets.

Transportation has lifted to a new meaning via the sky. In this talk, Sumitomo and Seino Holdings demonstrate how they partnered with Aeronext to create SkyHub, a transportation service using quantum annealing to optimize drone and truck delivery to depopulated areas.

Towards the realization of efficient transport systems, DENSO develops a method of route optimization by using D-Wave hybrid solvers. The first system is optimizing on-demand taxies and efficiency of sharing taxi with customers will be presented. The second system is collaborated with Toyota Tsusho Corperation for delivery logistics and practical advantage compared with conventional system will be presented.

A strategy for the analysis of active debris removal missions targeting multiple objects from a set of objects in near-circular orbit with similar inclination is presented. Algebraic techniques successfully reduce the orbital mechanics regarding specific inter-debris transfer and disposal methods to simple computations, which can be used as the coefficients of a quadratic unconstrained binary optimisation (QUBO) problem formulation which minimises the total propellant used in the mission whilst allowing for servicing time and meeting the mission deadline. The QUBO is validated by solving artificial small problems (from 2 to 11 debris) using classical computational methods and the weaknesses in using these methods are examined prior to solution using quantum annealing hardware. The quantum processing unit (QPU) and quantum-classical hybrid solvers provided by D-Wave are then used to solve the same small problems, with attention paid to evident strengths and weaknesses of each approach. Hybrid solvers are found to be significantly more effective at solving larger problems. Finally, the hybrid method is used to solve a large problem using a real dataset. From a set of 79 debris objects resulting from the destruction of the Kosmos-1408 satellite, an active debris removal mission starting on 30 September 2023 targeting 5 debris objects for disposal within a year with 20 days servicing time per object is successfully planned. This plan calculates the total propellant cost of transfer and disposal to be 0.87km/s and would be complete well within the deadline at 241 days from the start date. This problem uses 6,478 binary variables in total and is solved using around 25s of QPU access time.

This paper proposes a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem. Yet, this field's current state of affairs is that deep neural networks (DNNs) have demonstrated far superior results than traditional approaches. Nevertheless, quantum computing is expected to become increasingly prominent for machine learning problems soon. As a result, in this work, we take the privilege to perform an early exploration of applying a quantum computing algorithm to this important image enhancement problem, i.e., SISR. Among the two paradigms of quantum computing, namely universal gate quantum computing and adiabatic quantum computing (AQC), the latter has been successfully applied to practical computer vision problems, in which quantum parallelism has been exploited to solve combinatorial optimization efficiently. This work demonstrates formulating quantum SISR as a sparse coding optimization problem, which is solved using quantum annealers accessed via the D-Wave Leap platform. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.

Lopez-Bezanilla, A., Raymond, J., Boothby, K. et al. Kagome qubit ice. Nat Commun 14, 1105 (2023). https://doi.org/10.1038/s41467-023-36760-1

Topological phases of spin liquids with constrained disorder can host a kinetics of fractionalized excitations. However, spin-liquid phases with distinct kinetic regimes have proven difficult to observe experimentally. Here we present a realization of kagome spin ice in the superconducting qubits of a quantum annealer, and use it to demonstrate a field-induced kinetic crossover between spin-liquid phases. Employing fine control over local magnetic fields, we show evidence of both the Ice-I phase and an unconventional field-induced Ice-II phase. In the latter, a charge-ordered yet spin-disordered topological phase, the kinetics proceeds via pair creation and annihilation of strongly correlated, charge conserving, fractionalized excitations. As these kinetic regimes have resisted characterization in other artificial spin ice realizations, our results demonstrate the utility of quantum-driven kinetics in advancing the study of topological phases of spin liquids.

Mohammad H. Amin, et al.

Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation (ZNE). We implement ZNE through zero-temperature extrapolation as well as energy-time rescaling. We conduct experimental investigations into the quantum critical dynamics of a transverse-field Ising spin chain, demonstrating the successful mitigation of thermal noise through both of these techniques. Moreover, we show that energy-time rescaling effectively mitigates control errors in the coherent regime where the effect of thermal noise is minimal. Our ZNE results agree with exact calculations of the coherent evolution over a range of annealing times that exceeds the coherent annealing range by almost an order of magnitude.

Pokharel, B., Izquierdo, Z.G., Lott, P.A. et al. Inter-generational comparison of quantum annealers in solving hard scheduling problems. Quantum Inf Process 22, 364 (2023). 

We compare the performance of four quantum annealers, the D-Wave Two, 2X, 2000Q, and Advantage in solving an identical ensemble of a parametrized family of scheduling problems. These problems are NP-complete and, in fact, equivalent to vertex coloring problems. They are also practically motivated and closely connected to planning problems from artificial intelligence. We examine factors contributing to the performance differences while separating the contributions from hardware upgrades, support for shorter anneal times, and possible optimization of ferromagnetic couplings. While shorter anneal times can improve the time to solution (TTS) at any given problem size, the scaling of TTS with respect to the problem size worsens for shorter anneal times. In contrast, optimizing the ferromagnetic coupling improves both the absolute TTS and the scaling. There is a statistically significant improvement in performance between D-Wave Two and 2X and from all older generation annealers to Advantage, even when operated under identical anneal time and ferromagnetic couplings. However, the performance improvement from 2X to 2000Q requires the anneal time and ferromagnetic couplings to be optimized. Overall, owing to these inter-generational hardware improvements and optimizations, the scaling exponent reduces from 1.01 ± 0.01 on Two to 0.259 ± 0.008 on Advantage.

S. Arai et al., Effectiveness of quantum annealing for continuous-variable optimization, Physical Review A, 108, 042403 (2023)

The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the time-evolving block decimation (TEBD) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations

Kevin Chern, Kelly Boothby, Jack Raymond, Pau Farré, Andrew D. King

Front. Comput. Sci., 15 September 2023
Sec. Theoretical Computer Science
Volume 5 - 2023 | https://doi.org/10.3389/fcomp.2023.1238988

Quantum annealing has emerged as a powerful platform for simulating and optimizing classical and quantum Ising models. Quantum annealers, like other quantum and/or analog computing devices, are susceptible to non-idealities including crosstalk, device variation, and environmental noise. Compensating for these effects through calibration refinement or “shimming” can significantly improve performance but often relies on ad-hoc methods that exploit symmetries in both the problem being solved and the quantum annealer itself. In this tutorial, we attempt to demystify these methods. We introduce methods for finding exploitable symmetries in Ising models and discuss how to use these symmetries to suppress unwanted bias. We work through several examples of increasing complexity and provide complete Python code. We include automated methods for two important tasks: finding copies of small subgraphs in the qubit connectivity graph and automatically finding symmetries of an Ising model via generalized graph automorphism. We conclude the tutorial by surveying additional methods, providing practical implementation tips, and discussing limitations and remedies of the calibration procedure. Code is available at: https://github.com/dwavesystems/shimming-tutorial.

Dixit, V.V., Niu, C. Quantum computing for transport network design problems. Sci Rep13, 12267 (2023).

Transport network design problem (TNDP) is a well-studied problem for planning and operations of transportation systems. They are widely used to determine links for capacity enhancement, link closures to schedule maintenance, identify new road or transit links and more generally network enhancements under resource constraints. As changes in network capacities result in a redistribution of demand on the network, resulting in changes in the congestion patterns, TNDP is generally modelled as a bi-level problem, which is known to be NP-hard. Meta-heuristic methods, such as Tabu Search Method are relied upon to solve these problems, which have been demonstrated to achieve near optimality in reasonable time. The advent of quantum computing has afforded an opportunity to solve these problems faster. We formulate the TNDP problem as a bi-level problem, with the upper level formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem that is solved using quantum annealing on a D-Wave quantum computer. We compare the results with Tabu Search. We find that quantum annealing provides significant computational benefit. The proposed solution has implications for networks across different contexts including communications, traffic, industrial operations, electricity, water, broader supply chains and epidemiology.

Satellite image acquisition scheduling is a problem that is omnipresent in the earth observation field; its goal is to find the optimal subset of images to be taken during a given orbit pass under a set of constraints. This problem, which can be modeled via combinatorial optimization, has been dealt with many times by the artificial intelligence and operations research communities. However, despite its inherent interest, it has been scarcely studied through the quantum computing paradigm. Taking this situation as motivation, we present in this paper two QUBO formulations for the problem, using different approaches to handle the non-trivial constraints. We compare the formulations experimentally over 20 problem instances using three quantum annealers currently available from D-Wave, as well as one of its hybrid solvers. Fourteen of the tested instances have been obtained from the well-known SPOT5 benchmark, while the remaining six have been generated ad-hoc for this study. Our results show that the formulation and the ancilla handling technique is crucial to solve the problem successfully. Finally, we also provide practical guidelines on the size limits of problem instances that can be realistically solved on current quantum computers.

Traffic jams create significant negative effects on daily life in terms of time, money, and the environment. DENSO and Toyota set out to change that by optimizing multimodal transportation systems, coordinating passenger and traffic flow between rideshare services and public buses.

A few minutes spent browsing the web is enough to expose most internet users to lots of advertisements, most of which have been targeted to some extent based on the viewer’s preferences and interests. But even if this has become one of the predominant form of marketing in the 21st century, the global market value for TV advertising exceeded $225B in 2022.

Catherine C. McGeoch, Pau Farre.

We introduce quantum utility, a new approach to evaluating quantum performance that aims to capture the user experience by including overhead costs associated with the quantum computation. A demonstration of quantum utility by a quantum processing unit (QPU) shows that the QPU can outperform classical solvers at some tasks of interest to practitioners, when considering computational overheads. We consider overhead costs that arise in standalone use of the QPU (as opposed to a hybrid computation context). We define three early milestones on the path to broad-scale quantum utility that focus on restricted subsets of overheads: Milestone 0 considers pure anneal time (no overheads) and has been demonstrated in previous work; Milestone 1 includes overhead times to access the QPU (that is, programming and readout); and Milestone 2 incorporates an indirect cost associated with minor embedding.

We evaluate the performance of a D-Wave Advantage QPU with respect to Milestones 1 and 2, using a testbed of 13 input classes and seven classical solvers implemented on CPUs and GPUs. For Milestone 1, the QPU outperformed all classical solvers in 99% of our tests. For Milestone 2, the QPU outperformed all classical solvers in 19% of our tests, and the scenarios in which the QPU found success correspond to cases where classical solvers most frequently failed.
Analysis of test results on specific inputs reveals fundamentally distinct underlying mechanisms that explain the observed differences in quantum and classical performance profiles. We present evidence-based arguments that these distinctions bode well for future annealing quantum processors to support demonstrations of quantum utility on ever-expanding classes of inputs and for more challenging milestones.

Earth observation satellites (EOS) collect vital data for various applications such as weather forecasting, disaster management, environmental monitoring, etc. Maximizing the value of this data requires designing optimal EOS missions to capture targets with high business value or priority while satisfying complex constraints such as storage capacity, energy limits, weather, etc. However, traditional computing methods often struggle with the complexity of optimizing EOS mission schedules, leading to suboptimal target selection and reduced data collection efficiency.

In this paper, we demonstrate the potential of our quantum algorithm to optimize EOS mission schedules and improve the efficiency of multiple EOS in real-time. The aim is to maximize the acquisition of high-priority targets with significant business value within the constraints of limited resources. We evaluated the performance of our quantum algorithm by comparing it with two classical optimization algorithms: simulated annealing and Gurobi optimizer. Our quantum algorithm outperformed the Gurobi optimizer by 23.46%.

R. Sandt and R. Spatschek, Efficient low temperature Monte Carlo sampling using quantum annealing, Nature Scientific Reports, 13, Article number 6754 (2023)

Quantum annealing is an efficient technology to determine ground state configurations of discrete binary optimization problems, described through Ising Hamiltonians. Here we show that—at very low computational cost—finite temperature properties can be calculated. The approach is most efficient at low temperatures, where conventional approaches like Metropolis Monte Carlo sampling suffer from high rejection rates and therefore large statistical noise. To demonstrate the general approach, we apply it to spin glasses and Ising chains.

E.  Pelofske, Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems, arXiv:2301.03009 

Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. Quantum annealing in the Transverse Ising model, implemented on D-Wave QPUs, are available as cloud computing resources. In this article we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-Hard combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently QUBO, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly complex, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples and chain break proportions. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is also quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

King, A.D., Raymond, J., Lanting, T. et al. Quantum critical dynamics in a 5,000-qubit programmable spin glass. Nature 617, 61–66 (2023). https://doi.org/10.1038/s41586-023-05867-2

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Owing to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization4–13. Here we achieve this goal by realizing quantum-critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and timeevolution of the Schrödinger equation in small spin glasses. We then measure dynamics in three-dimensional spin glasses on thousands of qubits, for which classical simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for large-scale quantum simulation and a scaling advantage in energy optimization.

The first commercial quantum applications in production are using D-Wave’s quantum technology. An “in-production” quantum application means that the business has gone through the quantum journey from use case exploration and identification, to validation, POC and pilot, all the way to deploying a real-world application that is delivering ROI-driving business outcomes. Read the case story to get a deep dive into one commercial quantum application in production using D-Wave.

Jack Raymond et al. (2023). Hybrid Quantum Annealing for Larger-than-QPU Lattice-structured Problems. ACM Transactions on Quantum Computing 4, 3, Article 17

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to larger applications. We present a simple greedy method for solving larger-than-QPU lattice-structured Ising optimization problems. The method, implemented in the open source D-Wave Hybrid framework, uses a QPU coprocessor operating with generic parameters. Performance is evaluated for standard spin-glass problems on two lattice types with up to 11,616 spin variables, double the size that is directly programmable on any available QPU. The proposed method is shown to converge to low-energy solutions faster than an open source simulated annealing method that is either directly employed or substituted as a coprocessor in the hybrid method. Using newer Advantage QPUs in place of D-Wave 2000Q QPUs is shown to enhance convergence of the hybrid method to low energies and to achieve a lower final energy.

Alexander M. Whiticar, et al.

We report on measurements of flux and charge noise in an rf-SQUID (superconducting quantum interference device) flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical model that allows us to extract information about flux and charge noise within one experimental setup. The model agrees very well with experimental data over a wide dynamic range and provides parameters that characterize charge and flux noise.

Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. 

We show how to leverage quantum annealers to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use quantum annealers that sample from the ground state(s) of a problem-dependent Ising Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables.

We explore a combined approach of associated memory and quantum annealing (QA) for pattern matching. In particular, we consider on high energy applications of this approach to binary classification, where the objective is to distinguish signal and background detection events.

The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience.

This demo group satellites into constellations such that their average observation coverage is maximized. It is an example of a constraint satisfaction project.

In this talk, I will present 4 new hybrid quantum annealing algorithms for solving the Vehicle Routing Problem and its variant: the Capacitated Vehicle Routing Problem. Both are NP-hard combinatorial optimization problems with important applications in logistics.

Quantum computing is currently entering an era of real-world application development. Here we present our work on developing one of the first such applications by simulating an experiment, which exhibits quantum tunnelling between different electronic configurations. The material system we deal with is 1T-TaS2 in a metastable state, where electrons crystalize into a mosaic of lattices separated by domain walls. We developed a strongly correlated model which is able to describe the configurational ordering of electrons.

Mathematics play a key role in how data is expressed and analyzed in the sciences and engineering--for example, in describing the relationships between subatomic particles in nuclear physics. In the case of high-dimensional functional spaces (a way of modelling datasets with staggeringly high numbers of attributes), the calculations required to solve systems of equations are extremely complex, and are often beyond the capabilities of classical algorithms to solve. Riken turned to quantum computing for new ways to process these problems.

Machine learning--giving computers the ability to learn new things without being pre-programmed with specific knowledge--plays an important role in a growing number of applications, including spam detection, natural language processing, and recommendation systems. USC and their research partners used the D-Wave 2000Q to apply quantum annealing to machine learning approaches to several problems in the life and physical sciences, including TF-DNA binding, cancer classification, and solving a Higgs boson optimization problem.

Quantum computers present a unique opportunity to simulate quantum phenomena efficiently and its implied that quantum computers will be able to simulate quantum chemistry problems more efficiently than classical computers. This global search is very difficult, but by using Ising machines (quantum annealers) the ground state energy can be reliably found. We show that a quantum annealer accelerates the calculation by reducing the number of optimization steps and thus enabling a faster convergence to the ground state. This has important implications for finding the true optimized molecular states of excited states or complex ground states.

The mathematical procedure of minor embedding is used to "reshape" a user's QUBO or Ising problem onto the Chimera graph of the D-Wave QPU. D-Wave's embedding algorithm, published in 2013 by Cai & Macready & Roy, is effective, but reseachers have questioned its efficiency. Prasanna Date, of RPI, developed an embedding algorithm which ran faster, and also used fewer qubits.

Kernel-based support vector machines (SVMs) are supervised machine learning algorithms for classification and regression problems. We introduce a method to train SVMs on a D-Wave 2000Q quantum annealer and study its performance in comparison to SVMs trained on conventional computers.

The author present a compilation framework called “C to D-Wave” that enables programmers to write programs in a stylized subset of the C programming language and compile these to a minimization problem in the form of a D-Wave quantum machine instruction. The solution to the minimization problem corresponds to the output of the C program.

Since the difficulty of automated materials design grows exponentially in the number of variables, designing complex materials is often beyond the ability of classical algorithms. We show how quantum annealing can be incorporated into automated materials discovery and conduct a proof-of-principle study on designing complex thermofunctional metamaterials.

We will share our preliminary results of the D-Wave Advantage beta testing on the Hamiltonian path problem for genome variant analysis and the time-scheduled vehicle routing problem with multiple time-window. Besides, our hybrid quantum annealing (HQA) solver is presented. This talk includes the results of the D-Wave Advantage Beta Test.

Addressing the world’s climate emergency is an uphill battle, requiring a multifaceted approach including optimal deployment of green-energy alternatives. Such undertakings often involve computationally-expensive optimisation of black-box models in a continuous parameter space. We observe good performance on the DW-2000Q QPU - even using default settings - and higher sensitivity of performance to number of samples and annealing time for the Advantage QPU. These results are promising and potentially justify further investment in hardware, software, and optimisation research, in particular, in the area of solvers for dense QUBOs

The use of quantum computing in graph community detection and regularity checking related to Szemeredi’s Regularity Lemma (SRL) are demonstrated with D-Wave Systems’ quantum annealer and simulations. We demonstrate the capability of quantum computing in solving hard problems relevant to big data

To date, classical heuristics have consistently outperformed quantum-annealing based approaches. Here we introduce a class of problems based on frustrated cluster loops — deceptive cluster loops — for which all currently known state-of-the-art classical heuristics are outperformed by the DW2000Q quantum annealing machine.

This work describes quantum programming, compilation, and execution with XACC, a compiler framework and software tools developed at ORNL. XACC is available as an open source project on Github.

We experimentally quantify the impact that the quality of graph embeddings, used in programming a QAP, has on the sample distribution collected from the device. Quantum annealers have been shown, and we have experimentally corroborated, to sample from a distribution close to Boltzmann.

Social networks map relationships between people or organizations onto graphs, with the people/organizations as nodes and relationships as edges. Signed social networks map both friendly and hostile relationships by setting the values of the edges between nodes with either plus ("+") or minus ("-") signs. This demo calculates and shows structural imbalance for social networks of militant organization based on data from the Stanford Militants Mapping Project.

In this talk, we will introduce new use cases of Advantage in real problems from global brand clients. See how the use of D-wave quantum computing in our product, MAGELLAN BLOCKS, solves combinational optimization problems to radically improve business outcomes for our clients.

Jij Inc. is a venture company developing software for annealing-based optimization. They have developed an open-source project named “OpenJij” to provide an environment for developing annealing applications, evaluating performance, and benchmarking.

The authors investigate whether quantum annealers with select chip layouts can outperform classical computers in reinforcement learning tasks.

This paper describes the logic and creativity needed in order to have high probability of solving discrete optimization problems on a quantum annealing computer

XACC is an extensible compilation framework for hybrid quantum-classical computing architectures. It provides extensible language frontend and hardware backend compilation components glued together via a novel quantum intermediate representation.

Fault diagnosis is the combinational problem of quickly localizing failures as soon as they are detected in systems. Circuit fault diagnosis is the problem of identifying a minimum-sized set of components that, if faulty, explains an observation of incorrect outputs given a set of inputs.

We demonstrate experimentally the ability of a quantum annealer to distinguish between sets of non-isomorphic graphs that share the same classical Ising spectrum.

As the results of the 2016 US Presidential Election were finalized, it was clear that the majority of professional polling groups had significantly overestimated their predictions. This work investigated the use case of quantum computation to train Boltzmann machines for predicting the 2016 Presidential election.

We will present several case studies of QC Ware professional services helping out large enterprise customers with their quantum computing initiatives. Examples include Airbus in aerospace,  Equinor in Oil and Gas,  and BMW and Aisin in automotive. We will also demonstrate our QC Ware Forge platform, a cloud service, that bundles performance boosting algorithms with hardware access. 

Here we studied the ability of a quantum machine learning approach to classify and rank binding affinities. Using simplified data sets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding.

This problem is an example of an optimization problem known as the maximum independent set problem. The objective is to maximize the number of nodes in a set, with the constraint that no edges be contained in the set. There are a wide variety of applications for this problem, such as scheduling and error correcting codes.

We introduce the reinforcement quantum annealing (RQA) scheme in which an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and tries to iteratively find better Ising Hamiltonians for the given problem of interest

We present a comparison study of state-of-the-art classical optimisation methods to a D-Wave 2000Q quantum annealer for the planning of Earth observation missions. The problem is to acquire high value images while obeying the attitude manoeuvring constraint of the satellite.

Pipeline networks can be viewed as a graph built up of edges (pipeline segments) and nodes (junctions of pipeline segments). This demo is designed to determine a set of junctions within the pipeline network from which every pipeline segment can be monitored. This problem can be modeled as a vertex cover problem in which the goal is to find a subset of nodes in a graph such that every edge has at least one end point in the subset.

Many problems across several disciplines, ranging from production planning over DNA sequencing, can be represented as constrained integer optimization problems. Utilizing classical algorithms, generally exact solutions to integer linear programming (ILP) problems are exponentially hard to obtain, and heuristic algorithms are employed to find approximate solutions. This talk demonstrates a new algorithm that solves such constrained ILP problems on a quantum annealer.

This talk will give updates on achievements and extensions of project PlanQK (Platform and Ecosystem for Quantum-assisted Artificial Intelligence), funded by Federal Ministry for Economic Affairs and Energy. Furthermore, we will present novel research results, including - Insights on Training Neural Networks for QUBO Tasks - Approximating Archetypal Analysis Using Quantum Annealing - A Quantum Annealing Algorithm for Finding Pure Nash Equilibria in Graphical Games - Approximate Approximation on a Quantum Annealer

The demo illustrates the MIQUBO method by finding an optimal feature set for predicting survival of Titanic passengers. Its output is a ranking of subsets of features that have high MI with the variable of interest (survival) and low redundancy.

This is a demo on how to solve a Sudoku puzzle with D-Wave Ocean. It describes the Sudoku puzzle as a constraint satisfaction problem. By laying down these constraints, we can get the solver to optimize over them with the goal of returning a solution that satisfies all the constraints.

This paper describes a quantum isomer search procedure for determining all the structural isomers of alkanes.

Simulating electronic structure properties is important for different areas of research and industry but numerical approximations rapidly become unfeasible on classical systems. In this project, VW investigated the use of a D-Wave system to find advanced materials. 

In 2018, D-Wave scientists announced the first large-scale quantum simulation of topological state of matter, simulating the phenomenon behind the 2016 Nobel Prize

The spread of intelligent transportation systems in urban cities has caused heavy computational loads, requiring a novel architecture for managing large-scale traffic..the solutions to the global control method obtained with the quantum annealing machine are better than those obtained with conventional simulated annealing.

In the spring of 2019, Groovenauts announced the beta launch of the world’s first business optimization system using D-Wave’s 2000Q quantum platform. By combining the power of quantum computing with Magellan Blocks, Groovenaut’s web-based suite of machine learning services and tools, the new system will help customers optimize shipping routes and staff schedules more quickly and accurately than ever before.

A quantum annealer exploits quantum effects to solve a particular type of optimization problem. The advantage of this specialized hardware is that it effectively considers all possible solutions in parallel, thereby potentially outperforming classical computing systems. In this article, we show how to compile a subset of Prolog enhanced with support for constraint logic programming into a two-local Ising-model Hamiltonian suitable for execution on a quantum annealer.

In this paper, we apply a recursive quantum algorithm to a D-Wave quantum annealer housed at the University of Southern California to recover a sound wave speed profile, typical in seismic inversion experiments.

Identifying new methods for integer factorization plays an important role in modern information security. Shor’s algorithm is perhaps the most well-known method for integer factorization. An equally powerful model of quantum computing is the adiabatic quantum computing (AQC) model, which can also solve the integer factorization problem. In this work, the authors developed a framework to convert an arbitrary integer factorization problem to an executable Ising model and tested it on the D-Wave 2000Q.

With quantum computers still under heavy development, already numerous quantum machine learning algorithms have been proposed for both gate-based quantum computers and quantum annealers. Recently, a quantum annealing version of a reinforcement learning algorithm for grid-traversal using one agent was published. We extend this work based on quantum Boltzmann machines, by allowing for any number of agents. We show that the use of quantum annealing can improve the learning compared to classical methods. We do this both by means of actual quantum hardware and by simulated quantum annealing.

This code demonstrates the use of the D-Wave system to solve a factoring problem. This is done by turning the problem into a three-bit multiplier circuit.

Researchers from 1QBit developed a method to perform reinforcement learning using the D-Wave 2000Q system. The experimental results showed that their technique is a promising method for harnessing the power of quantum sampling in reinforcement learning tasks.

New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of problems like the Shortest Vector Problem to a quantum adversary. In this paper we describe two variants of a quantum Ising algorithm to solve this problem.

We show our collaborations with various companies in T-QARD research network. We generate several seeds of the application of quantum annealing in the industry. In addition, we demonstrate several techniques for solving wider optimization problems by using quantum annealer.

Mathematical optimization problems with real business data raise various implementation issues that are not described in a paper, such as communication delay. In the case of slow communication over the network, it is often the case that delays accumulate due to iterations of Request and Response, which prevent smooth computation. In this presentation, we introduce a technical trick for communication delay reduction that can be used in combination with various algorithms. These activities are just one of the examples of D-Wave/mathematical optimization at NTT DATA.

Understanding how the D-Wave quantum computer could be used for machine learning problems is of growing interest. Our work, in particular, evaluates the feasibility of using the D-Wave as a sampler for machine learning. We describe a hybrid system that combines a classical deep neural network autoencoder with a quantum annealing Restricted Boltzmann Machine (RBM) using the D-Wave.

What if computers could do more for materials science research than just run and evaluate pre-programmed simulations? The University of Tokyo set out to answer that question with the goal of accelerating and eventually automating the design of metamaterials. These artificial substances have properties that do not exist in nature, which are derived from the structure of the material rather than its composition. Using D-Wave's 2000Q quantum annealer, researchers sought optimal solutions for designing a thermal radiator.

The fundamental goal of homomorphic encryption is to enable (untrusted) Oscar to perform a computation for Alice without Oscar knowing the input to the computation or the output from the computation. We describe an approach to homomorphic encryption for quantum annealing based on spin reversal transformations and show that it comes with little or no performance penalty. This is in contrast to approaches to homomorphic encryption for classical computing, which incur a significant additional computational cost. If sensitive information, such as health-related data subject to the Health Insurance Portability and Accountability Act, is to be processed with annealers, such a technique could be useful.

We present an algorithm for quantum-assisted cluster analysis that makes use of the topological properties of a D-Wave 2000Q quantum processing unit. 

In this talk, we present a QUBO formatting of the problem of optimal control of time-dependent traffic signals on an artificial grid-structured road network so as to ease the flow of traffic, and the use of D-Wave Systems' quantum annealer to solve it.

In this talk, I would like to talk about the recent advance of quantum hybrid systems, especially the scaling and performance of quadratic unconstrained binary optimization (QUBO) formulation of Time-scheduled Vehicle Routing Problem with multiple time-window. This talk includes the results of D-Wave Advantage Beta Test.

It has been recently been shown that the new lower noise model of D-Wave QPU can perform better than previous versions at a solving spin glass problems. In the work I present here we investigate why and explore the effect of reduced noise on reverse annealing protocols by performing the same experiment on both lower noise and higher noise QPUs.

The ability to accurately classify disease subtypes is of vital importance, especially in oncology where this capability could have a life saving impact. Here we report a classification between two subtypes of non-small cell lung cancer, namely Adenocarcinoma versus Squamous cell carcinoma.

In 2018, D-Wave scientists announced a breakthrough in materials simulation, demonstrating a large-scale programmable quantum simulation on the D-Wave system. 

QMASM fills a gap in the software ecosystem for D-Wave's adiabatic quantum computers by shielding the programmer from having to know system-specific hardware details while still enabling programs to be expressed at a fairly low level of abstraction. It is therefore analogous to a conventional macro assembler and can be used in much the same way: as a target either for programmers who want a great deal of control over the hardware or for compilers that implement higher-level languages.

We present results of solving various types of optimization problems on the Advantage QPU and on the HSS version 2. The first set of optimization problems consists of garden optimization problems, sizeable optimization problems with constraints. The task is to fill and place pots taking into account the characteristics of neighboring plants. The number of variables is given by the number of pots multiplied by the number of plant species and the number plants is equal to the number of pots (one plant per pot). The second set of optimization problems comprises exact cover problems and the third set 2-SAT problems.

As consequences of disruptions in railway traffic affect passenger experience/satisfaction, appropriate dispatching decisions are necessary. The problem of optimal scheduling the order of trains is known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve optimization problems...We demonstrate the implementation on the D-Wave Quantum Processing Unit and its hybrid solver.

The Ising Hamiltonian offers a versatile model for studying the microscopic behavior of several material systems. Here we study an Ising Hamiltonian on a geometrically-frustrated Shastry-Sutherland lattice which has been used to explain the magnetic properties in the rare-earth tetraborides. Using quantum Monte-Carlo calculations to validate our results, this work indicates that quantum annealing provides a versatile method of material simulation that can accelerate scientific discovery.

What is the form and the nature of the distribution produced by quantum annealers? It turns out that much can be said by analysing the statistics of a single-qubit problem. We estimate the effective local field that describes the output distribution of a single-qubit problem for different input problem instances.

A very important problem in combinatorial optimization is partitioning a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences...This paper addresses a systematic study of detecting two or more communities in a network using a quantum annealer.

By combining multiple A.I. strategies with the power of quantum computing, WuXi NextCODE Genomics can identify previously unseen patterns and causal dependencies in biological data that allow for faster, more cost-effective, and more efficient drug development. These medications have the potential to make a profound impact on the treatment of cancer, heart disease, Alzheimer’s, and liver disease.

OTI specializes in developing advanced materials to solve large s cale industrial problems for displays and lighting in smart devices, televisions, VR headsets, and more. By using D-Wave's quantum platform to better understand and predict the structure-property relationship of new materials, OTI is breaking new ground in the world of quantum chemistry and materials development.

In this work, we consider a practical railway dispatching problem: delay and conflict management on a single- track railway line. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the segment being considered. This problem is computationally hard and often needs to be solved timely. Here, we introduce a quadratic unconstrained binary optimization (QUBO) model of the problem in question, compatible with the emerging quantum annealing technology. The model’s instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers.

Here, we study the ability of the quantum hardware to solve the number partitioning problem, a well-known NP-hard optimization model that poses some challenges typical of those encountered in real-world applications. 

We study the interplay between quantum annealing parameters in embedded problems, providing both deeper insights into the physics of these devices and pragmatic recommendations to improve performance on optimization problems. We choose as our test case the class of degree-bounded minimum spanning tree problems

In this work the researchers use quantum and classical annealing to solve a Higgs-signal-versus-background machine learning optimization problem, mapped to a problem of finding the ground state of a corresponding Ising spin model.The results show that the resulting quantum and classical annealing-based classifier systems perform comparably to the state-of-the-art machine learning methods that are currently used in particle physics.

D-Wave 2000Q offers annealing options that allow a better control on the annealing parameters, which options can be used to mitigate the effects of hardware biases or to get additional insight into the dynamics of the process. We discuss our experience with three such features--spin reversal, quenching, and h-gain--for three different purposes.

We show that the symmetry-breaking gap of the quantum Ising model in the transverse field can be extracted from free evolution of the longitudinal magnetization taking place after a gradual quench of the magnetic field. Our results should be relevant for ongoing cold atom and ion experiments targeting either equilibrium or dynamical aspects of quantum phase transitions.

A demo on using the D-Wave Ocean SDK to solve the map coloring problem. Namely, given a map, color the regions of the map such that no two regions sharing a border would share the same color.

Optimization methods are critical to delivering enough radiation to kill cancerous cells while avoiding non-cancerous nearby cells. Reseachers at Roswell Park used a D-Wave system for the first application of quantum annealing for beamlet intensity optimization for IMRT

We discuss here three use studies of domain wall encoding. One is the flight gate scheduling problem, another is the network routing problem and the third is the 3-color problem. The data for the flight gate problem is retrieved from database of a medium size

Data Reply studied the ability of the D-Wave system to solve the number partitioning problem, a well-known NP-hard optimization model that poses some challenges typical of those encountered in real-world applications. The results showed remarkable results in most instances of the model; for the most complex ones, they investigated further the D-Wave Hybrid suite.

We evaluated these implementations of ML decoding for lowdensity parity-check (LDPC) codes, analyzing the number of spins and connections and comparing the decoding performance with belief propagation (BP) decoding and brute-force ML decoding with classical computers.

We design and implement a quantum laboratory to experimentally observe and study dynamical processes in quantum mechanics and quantum field theories. Our approach encodes the wave-function in an Ising model, which is then solved by a quantum annealer. As a proof-of-concept, we measure the probability for tunnelling from the false to true minimum for various tunnelling times, vacuum displacements and potential profiles.

Molecular Docking is an important step of the drug discovery process which aims at calculating the preferred position and shape of one molecule to a second when they are bound to each other. It is possible to identify three phases of Molecular Docking: 1) Ligand Expansion, i.e. unfolding of the ligand molecule; 2) Initial Placement, i.e. placement of the ligand into the protein pocket with rigid roto-translations; 3) Shape Refinement, i.e. rotation of the ligand bonds in order to match the protein pocket. In. our work, we focused on the Ligand Expansion phase and considered a quantum annealing approach to the Molecular Unfolding (MU) problem.

Recent advances in high-throughput genomic technologies coupled with exponential increases in computer processing and memory have allowed us to interrogate the complex aberrant molecular underpinnings of human disease from a genome-wide perspective. Inspired in part by recent advances in physical quantum processors, we evaluated several unconventional machine learning (ML) strategies on actual human tumor data. Here we show for the first time the efficacy of multiple annealing-based ML algorithms for classification of high-dimensional, multi-omics human cancer data from the Cancer Genome Atlas.

In the applied physics lab at Johns Hopkins, researchers are leveraging quantum annealing for pattern recognition in high energy physics particle detection. Quantum annealing enables more accurate pattern matching and access to a family of low-energy solutions that improve track reconstruction.

In this work we propose a novel Ising model for benchmarking optimization algorithms called the Corrupted Biased Ferromagnets (CBFM). A detailed evaluation of the CBFM instance class across six classical algorithms suggest that it is a challenging problem for both heuristics and global optimization algorithms.

Quantum computers have long been on the horizon as conventional computing technologies approach their physical limits. While general-purpose quantum computers remain on the horizon for the time being, a special kind of quantum computer already exists and could be a game changer for simulation and computing tools in support of Los Alamos National Laboratory’s mission of stockpile stewardship without nuclear testing. It may also enable a slew of broader national security and computer science applications. But first, it will undoubtedly draw a vibrant community of top creative thinkers in many scientific fields to Los Alamos.

Using optimal phasor measurement unit placement as a prototypical problem, we assess the computational viability of the current generation D-Wave Systems 2000Q quantum annealer for power systems design problems.

We format three problems essential to mitigating the effects of the COVID-19 pandemic to fit the quantum annealing regime, namely, the Nurse Scheduling Problem (NSP), the Physician Scheduling Problem (PSP), and the Nurse-Physician Scheduling Problem (NPSP).

Machine learning relies heavily on sampling from complex probability distributions. NASA scientists successfully trained the D-Wave 2X system on image data sets in a generative unsupervised learning setting, one of the most difficult paradigms in machine learning.

We report on a method for globally controlling traffic signals arranged on a square lattice by means of the D-Wave quantum annealer. We consider a situation in which many cars moving on a lattice network are controlled via traffic signals installed at each intersection. This study makes three contributions to signal optimization.

Tohoku University isn’t just blazing their own path in the field of quantum computing, they’re recruiting others to work with them. As part of a public-private consortium across Japan and parts of western Europe, Tohoku University Quantum Annealing Research & Development (T-QARD) is tackling research in diverse areas such as stock market forecasting, public transit scheduling, black-box optimization, and calibrating transmission systems in cars.

The Griffiths-McCoy singularity is a phenomenon characteristic of low-dimensional disordered quantum spin systems, in which the magnetic susceptibility shows singular behavior as a function of the external field even within the paramagnetic phase. We study whether this phenomenon is observed in the transverse-field Ising model with disordered ferromagnetic interactions on the quasi-two-dimensional diluted Chimera graph both by quantum Monte Carlo simulations and by extensive experiments on the D-Wave quantum annealer used as a quantum simulator.

Quantum annealing has emerged in the last few years as a promising quantum computing approach to solving large-scale combinatorial optimization problems. In this paper, we formulate the problem of correctly placing pressure sensors on a Water Distribution Network (WDN) as a combinatorial optimization problem in the form of a Quadratic Unconstrained Binary Optimization (QUBO) or Ising model. Optimal sensor placement is indeed key to detect and isolate fault events. We outline the QUBO and Ising formulations for the sensor placement problem starting from the network topology and few other features. We present a detailed procedure to solve the problem by minimizing its Hamiltonian using PyQUBO, an open-source Python Library. We then apply our methods to the case of a real Water Distribution Network. Both simulated annealing and a hybrid quantum-classical approach on a D-Wave machine are employed.

New users of the D-Wave QPU are often surprised to learn that the QPU doesn't find the global minimum in all of its returned samples. The QPU is a probabilistic device; and there are many algorithmic and numeric approaches to increasing the number of "correct" solutions. John Dorband of UMBC has been studying the D-Wave QPU for a few years, and has presented a numeric algorithm for optimizing the returned solutions.

OTI has made their name creating advanced materials intended to solve large scale industrial problems for lighting and visual displays, such as mobile phone and television screens. Quantum simulations and machine learning play an increasingly important role in discovering and producing better materials for this purpose. OTI broke new ground by developing a quantum solver which makes an annealing approach to quantum chemistry problems viable for the first time.

This article assesses the performance of the D-Wave 2X quantum annealer on two NP hard graph problems, in particular clique finding and graph partitioning.

The authors develop a method to optimize control schedules for general adiabatic quantum computation (AQC) algorithms that is scalable/efficient, practical, and robust.

Global mobile data traffic is increasing expotentially every year, and with it, user demand for fast data rates and increased wireless capacity. Researchers at Princeton University wanted to discover if quantum computing could reduce the amount of time it takes to process data in real time and cut through the noise created by countless interfering data streams.

We demonstrate our research activities with several companies spreading the capability of quantum annealing. In addition, we show our products deepening the potential of quantum annealing. One of the products is "New Normal Scheduler", creating the most appropriate schedule while reducing the ratio of the office workers and maintaining the occasion of communication among all the employees.

The solution technique is to construct a set of constraints that enforces the rules of moving through a maze. These constraints are then converted by Ocean software tools to a binary quadratic model (BQM) that can then be solved with a D-Wave quantum computer. The solution that gets returned by the quantum computer is the path needed to get through the maze.

The US has more than 100,000 contaminated groundwater sites and the total cost to remediate them will exceed $100,000,000,000. In order to design cost-effective remedial measures, the properties of the subsurface must be understood and hydrologic inverse analysis helps us understand the properties of the subsurface. While there is a way to go before practical applications to hydrology can be made, this project demonstrated that the D-Wave system can be used solve hydrologic inverse problems.

A graph partitioning problem is an interesting problem from graph theory with a wide variety of applications. In this demo our goal is to split a group of people into two equal-sized teams with a constraint of having as few friends on opposite teams as possible.

Unfolding is the procedure of correcting for distortions due to limited resolution of a measuring device or transmission medium. High-energy physics is replete with hard computational problems and unfolding is one of the areas where quantum computing could be used to speed up calculations. In this talk, we present an implementation of likelihood-based unfolding on a DWave quantum computer.

Motivated by graph-based methods for quantum molecular dynamics (QMD) simulations, researchers explored graph partitioning/clustering methods and implementations that run on the D-Wave. The demonstrated “proof of principle” results on benchmark graphs, example graphs and electronic structure graphs and showed results that equal or out-perform current “state of the art” methods.

On the Emerging Potential of Quantum Annealing Hardware for Combinatorial Optimization

Byron Tasseff (Los Alamos), Tameem Albash (New Mexico U.), Zachary Morrell (Los Alamos), Marc Vuffray (Los Alamos), Andrey Y. Lokhov (Los Alamos) et al.

e-Print: 2210.04291 [math.OC]

Anatoly Y. Smirnov, et al.

Macroscopic resonant tunneling (MRT) in flux qubits is an important experimental tool for extracting information about noise produced by a qubit's surroundings. Here we present a detailed derivation of the MRT signal in the RF-SQUID flux qubit allowing for effects of flux and charge fluctuations on the interwell and intrawell transitions in the system. Taking into consideration transitions between the ground state in the initial well and excited states in the target well enable us to characterize both flux and charge noise source affecting the operation of the flux qubit. The MRT peak is formed by the dominant noise source affecting specific transition, with flux noise determining the lineshape of the ground to ground tunneling, whereas charge noise reveals itself as additional broadening of the ground to excited peak.

King, A.D., Suzuki, S., Raymond, J. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nat. Phys. (2022)

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been successfully used in simulating a range of open quantum systems, both at equilibrium and out of equilibrium. However, in all previous experiments, annealing has been too slow to coherently simulate a closed quantum system, due to the onset of thermal effects from the environment. Here we demonstrate coherent evolution through a quantum phase transition in the paradigmatic setting of a one-dimensional transverse-field Ising chain, using up to 2,000 superconducting flux qubits in a programmable quantum annealer. In large systems, we observe the quantum Kibble–Zurek mechanism with theoretically predicted kink statistics, as well as characteristic positive kink–kink correlations, independent of temperature. In small chains, excitation statistics validate the picture of a Landau–Zener transition at a minimum gap. In both cases, the results are in quantitative agreement with analytical solutions to the closed-system quantum model. For slower anneals, we observe anti-Kibble–Zurek scaling in a crossover to the open quantum regime. The coherent dynamics of large-scale quantum annealers demonstrated here can be exploited to perform approximate quantum optimization, machine learning and simulation tasks.

A. Braida et al., On constant-time quantum annealing and guaranteed approximations for graph optimization problems, Quantum Science and Technology, 7, 4, 045030  (2022)

Quantum annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for optimization problems, including NP-hard ones if we allow an exponentially large running time. While QA is widely studied from a heuristic point of view, little is known about theoretical guarantees on the quality of the solutions obtained in polynomial time. In this paper, we use a technique borrowed from theoretical physics, the Lieb–Robinson (LR) bound, and develop new tools proving that short, constant-time QA guarantees constant factor approximations ratios for some optimization problems when restricted to bounded degree graphs. Informally, on bounded degree graphs the LR bound allows us to retrieve a (relaxed) locality argument, through which the approximation ratio can be deduced by studying subgraphs of bounded radius. We illustrate our tools on problems MaxCut and maximum independent set for cubic graphs, providing explicit approximation ratios and the runtimes needed to obtain them. Our results are of similar flavor to the well-known ones obtained in the different but related QAOA (quantum optimization algorithms) framework.

T. Morstyn, "Annealing-based Quantum Computing for Combinatorial Optimal Power Flow," in IEEE Transactions on Smart Grid, 2022,

This paper proposes the use of annealing-based quantum computing for solving combinatorial optimal power flow problems. Quantum annealers provide a physical computing platform which utilises quantum phase transitions to solve specific classes of combinatorial problems. These devices have seen rapid increases in scale and performance, and are now approaching the point where they could be valuable for industrial applications. This paper shows how an optimal power flow problem incorporating linear multiphase network modelling, discrete sources of energy flexibility, renewable generation placement/sizing and network upgrade decisions can be formulated as a quadratic unconstrained binary optimisation problem, which can be solved by quantum annealing. Case studies with these components integrated with the IEEE European Low Voltage Test Feeder are implemented using D-Wave Systems’ 5,760 qubit Advantage quantum processing unit and hybrid quantum-classical solver.

D. Von Dollen et al., Quantum-enhanced selection operators for evolutionary algorithms,  Proceedings of GECCO’22,  pp. 463-466 arXiv:2206.10743 

Genetic algorithms have unique properties which are useful when applied to black box optimization. Using selection, crossover, and mutation operators, candidate solutions may be obtained without the need to calculate a gradient. In this work, we study results obtained from using quantum-enhanced operators within the selection mechanism of a genetic algorithm. Our approach frames the selection process as a minimization of a binary quadratic model with which we encode fitness and distance between members of a population, and we leverage a quantum annealing system to sample low energy solutions for the selection mechanism. We benchmark these quantum-enhanced algorithms against classical algorithms over various black-box objective functions, including the OneMax function, and functions from the IOHProfiler library for black-box optimization. We observe a performance gain in average number of generations to convergence for the quantum-enhanced elitist selection operator in comparison to classical on the OneMax function. We also find that the quantum-enhanced selection operator with non-elitist selection outperform benchmarks on functions with fitness perturbation from the IOHProfiler library. Additionally, we find that in the case of elitist selection, the quantum-enhanced operators outperform classical benchmarks on functions with varying degrees of dummy variables and neutrality.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. 

Pelofske et al., Quantum annealing algorithms for Boolean tensor networks, Nature Scientific Reports, 12, 8539 (2022).

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., {0,1}" role="presentation" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

Nelson et al., High quality thermal Gibbs sampling with quantum annealing hardware, Physical Review Applied, 17, 044046 (2022) 

Quantum annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA-hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a procedure for executing these models on QA hardware to maximize Gibbs-sampling performance. The experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature. Furthermore, we show that this effective temperature can be adjusted by modulating the annealing time and energy scale. The procedure proposed in this work provides an approach to using QA hardware for Ising-model sampling presenting potential opportunities for applications in machine learning and physics simulation.

Inadequately planned factory layouts can lead to higher operational costs. The planning process is time-consuming and multiple planning parameters must be considered simultaneously, leading to large solution spaces. Automated planning approaches can support the planning team in the early phases of layout planning by generating layout variants that can afterwards be further specified. Recent studies from other disciplines have shown the potential of Quantum Annealing (QA) to solve complex assignment problems within seconds. Consequently, this paper presents a first implementation of a QA-based layout planning approach and demonstrates its advantages regarding scalability, solution quality, and computing time.

With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable flexibility. Dividing the grid into logical clusters entails several organization and technical benefits, helping overcome these challenges. However, finding the optimal grid partitioning remains a challenging task due to its complexity. Learn how E.ON, a leading German utility company, approached this hard problem with D-Wave technology.

Willsch et al., Benchmarking Advantage and D-Wave 2000Q quantum annealers with exact cover problems, Quantum Information Processing, Vol 21, No 141 (2022)

We benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance.

Pelofske, E., Hahn, G. & Djidjev, H.N. Parallel quantum annealing. Scientific Reports 12, 4499 (2022).

The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the time-evolving block decimation (TEBD) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations. 

Andrew D. King, et al.

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been used successfully in stimulating a range of open quantum systems, both at equilibrium and out of equilibrium. However, in all previous experiments, annealing has been too slow to simulate a closed quantum system coherently, due to the onset of thermal effects from the environment. Here we demonstrate coherent evolution through a quantum phase transition in the paradigmatic setting of the 1D transverse-field Ising chain, using up to 2000 superconducting flux qubits in a programmable quantum annealer. In large systems we observe the quantum Kibble-Zurek mechanism with theoretically predicted kink statistics, as well as characteristic positive kink-kink correlations, independent of system temperature. In small chains, excitation statistics validate the picture of a Landau-Zener transition at a minimum gap. In both cases, results are in quantitative agreement with analytical solutions to the closed-system quantum model. For slower anneals we observe anti-Kibble-Zurek scaling in a crossover to the open quantum regime. These experiments demonstrate that large-scale quantum annealers can be operated coherently, paving the way to exploiting coherent dynamics in quantum optimization, machine learning, and simulation tasks.

Jack Raymond, et al.

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to additional applications of larger scale. We present a straightforward and effective method for solving larger-than-QPU lattice-structured Ising optimization problems. Performance is compared against simulated annealing with promising results, and improvement is shown as a function of the generation of D-Wave QPU used.

Download white paper.

R. Zielewski and H. Takizawa, A method for reducing time-to-solution in quantum annealing through pausing,  Proc. Int. Conf. HPC in Asia-Pacific Region pp. 137-145 (2023)

Recent research has shown that alternative annealing schedules provide the means for improving performance in modern quantum annealing devices. One such type of schedule is forward annealing with a pause, in which there is a period of time when system evolution is paused. While the results from using this type of schedule have been promising, effectively using a pause is not a trivial task. One challenge associated with introducing a pause into the schedule is determining the point in the anneal at which the pause will start. Additionally, tuning the schedule in real-time requires a significant amount of time. A second challenge is that while a pause may increase the number of correct solutions returned from the annealer, the time-to-solution, a standard metric for measuring performance in quantum annealing, will not necessarily be improved. We propose a method for constructing annealing schedules containing a pause that avoids the costly process of determining the optimal pause location in an online manner. We also evaluate our method on the subset sum problem, a problem of practical significance, and show that our method is able to achieve a 70% reduction in time-to-solution from a standard schedule containing no pause.

With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable flexibility. Dividing the grid into logical clusters entails several organization and technical benefits, helping overcome these challenges.However, finding the optimal grid partitioning remains a challenging task due to its complexity. At the same time, a new technology has gained traction in the last decades for its promising speed-up potential in solving non-trivial combinatorial optimization problems: quantum computing. This work explores its application in Graph Partitioning using electrical modularity. We benchmarked several quantum annealing and hybrid methods on IEEE well-known test cases. The results obtained for the IEEE 14-bus test case show that quantum annealing DWaveSampler brings equal solutions or, for the optimal number partitions, a 1% improvement. For the more significant test cases, hybrid quantum annealing shows a relative error of less than 0.02% compared to the classical benchmark and for IEEE 118-bus test case shows time performance speed-up. The increment in performance would enable real time planning and operations of electrical grids in real time. This work intends to be the first step to showcase the potentials of quantum computing towards the modernization and adaption of electrical grids to the decentralized future of energy systems.

Marina Fernández-Campoamor, et al.

With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable flexibility. Dividing the grid into logical clusters entails several organizational and technical benefits, helping overcome these challenges. However, finding the optimal grid partitioning remains a challenging task due to its complexity. At the same time, new technology has gained traction in the last decades for its promising speed-up potential in solving non-trivial combinatorial optimization problems: quantum computing. This work explores its application in Graph Partitioning using electrical modularity. We benchmarked several quantum annealing and hybrid methods on IEEE well-known test cases. The results obtained for the IEEE 14-bus test case show that quantum annealing DWaveSampler brings equal solutions or, for the optimal number partitions, a 1% improvement. For the more significant test cases, hybrid quantum annealing shows a relative error of less than 0.02% compared to the classical benchmark and for IEEE 118-bus test case shows time performance speed-up. The increment in performance would enable real-time planning and operations of electrical grids in real-time. This work intends to be the first step to showcase the potentials of quantum computing towards the modernization and adaption of electrical grids to the decentralized future of energy systems.

With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable flexibility. Dividing the grid into logical clusters entails several organization and technical benefits, helping overcome these challenges.However, finding the optimal grid partitioning remains a challenging task due to its complexity. At the same time, a new technology has gained traction in the last decades for its promising speed-up potential in solving non-trivial combinatorial optimization problems: quantum computing. This work explores its application in Graph Partitioning using electrical modularity. We benchmarked several quantum annealing and hybrid methods on IEEE well-known test cases. The results obtained for the IEEE 14-bus test case show that quantum annealing DWaveSampler brings equal solutions or, for the optimal number partitions, a 1% improvement. For the more significant test cases, hybrid quantum annealing shows a relative error of less than 0.02% compared to the classical benchmark and for IEEE 118-bus test case shows time performance speed-up. The increment in performance would enable real time planning and operations of electrical grids in real time. This work intends to be the first step to showcase the potentials of quantum computing towards the modernization and adaption of electrical grids to the decentralized future of energy systems.

In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory in a dataset of 50 assets spanning a one year trading period using the D-Wave 2000Q processor. Our method is remarkably efficient, and produces results much closer to the efficient frontier than typical portfolios. Moreover, we also show how our approach can easily produce trajectories adapted to different risk profiles, as typically offered in financial products. Our results are a clear example of how the combination of quantum and classical techniques can offer novel valuable tools to deal with real-life problems, beyond simple toy models, in current NISQ quantum processors.

Digital transformation is altering our lives in many positive ways. This acceleration of digital transformation, however, has also led to an increased potential risk in identity fraud, as well as social engineering and data theft to businesses, consumers and the broader ecosystem. In this talk, learn how PayPal is tapping advances in quantum computing to innovate on feature selection, a critical step in building powerful models to fight sophisticated fraud.

In this session, the an Mphasis expert will discuss how quantum computing can reduce the execution time for algorithms, achieve better accuracy, identify complex patterns in data to improve accuracy, and help solve complex problems. It will also showcase live quantum computing demos running on quantum hardware to solve targeted industry challenges.

NEC Australia and D-Wave were selected by the Australian Department of Defence to demonstrate the use of hybrid quantum computing technology to solve a “last mile resupply” problem. The technology optimised how autonomous vehicles were used to resupply army forces from a central base. A live demonstration is included in this talk.

Urban Air Mobility (UAM) has been envisioned as a technology that utilizes automated air transportation services to carry people or cargo at lower altitudes in and around urban areas. In this talk, experts from Sumitomo, OneSky Systems, and Tohoku University formulate the problem of discovering the safe and short routes for multiple aircraft to fly as quadratic forms and present a dynamic route planning algorithm for time-dependent simultaneous flight requests.

In this talk, hear a summary of current practices in asset liability modelling (ALM) within the insurance sector and an insight into what ALM may be like in the immediate future by demonstration of how quantum annealing can be used for ALM.

Modelling behaviors in networks is highly complicated but essential for understanding dynamics of the current world, especially the adoption of new technologies. In this talk, experts from Bank of Canada and Multiverse Computing extend Jackson and Watts (2002) to study how firms located in a trade network adopt cryptocurrency as a method of payment

Molecular Docking is an important step of the drug discovery process which aims at calculating the preferred position and shape of one molecule to a second when they are bound to each other. Using D-Wave's quantum system, results and performances are compared with state of art classical solvers.

Recommender systems help users navigate the vast number of options at their disposal in this era of information. A challenging step is to understand how to select item attributes that best represent the user perception, which is often time consuming and requires domain knowledge and understanding of user behavior. They represent the feature selection as an optimization problem and solve it on a D-Wave system.

DirectFood.store (DFS) is a truly farm to table solution that pickups food from local farms and vendors across a region and delivers customer the same day it was picked up. This is done without the use of warehouses and all of the food a customer ordered arrives at the same time. Scaling this delivery model, which they call many-to-many delivery, is made more complex when various business rules (constraints) are added to the equation. During this talk, they discuss how DFS successfully worked with D-Wave to scale this delivery model.

Residual Statics Estimation (RSE) is a computationally challenging example of a geophysical optimization problem. In this work, researchers from researchers from TNO, Aramco, and TU Delft show how to map the RSE problem to a quadratic unconstrained binary optimization (QUBO) formulation, how to implement it on the quantum annealer, and present their early computational results.

In this work, Durham University seeks efficient optimal or near-optimal solutions for energy efficient routing of wireless sensor network. Their preliminary results show that this approach using quantum computing has great promise and may open the door for other significant improvements in the efficacy of network algorithms.

Groovenauts has successfully released the world’s first business service powered with quantum annealing technology in their service, MAGELLAN BLOCKS. Since then, they have been advancing the application of quantum annealing to companies in various industries, such as manufacturing, logistics, transportation, and service. As a pioneer of solving the actual corporate issues, they will share how they handle projects and what kind of achievement we make.

In this talk, Steven Abel, Professor at Durham University, discusses recent developments in the implementation of complex physical systems on quantum annealers. These include systems that allow quantum tunnelling and barrier penetration across specified potentials. The results we find are in accord with those predicted theoretically showing that a quantum annealer is a genuine quantum system that can be used as a quantum laboratory. More generally he shows how his techniques can generally be used to optimise arbitrary potentials in several dimensions. He compares classical with quantum optimisation methods and finds a qualitative improvement over classical techniques.

An artificial spin ice is a manufactured physical system defined by interacting binary variables. Interesting physical properties arise when all constraints defining the interactions cannot be satisfied, namely the system is frustrated. Researchers from Los Alamos National Laboratory (LANL) presents the first realization of artificial spin ice in a lattice of coupled qubits to recreate physical phenomena found in actual magnetic materials.

Lattice gauge theory is an essential tool for strongly interacting non-Abelian elds, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. In this work, researchers from York University implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition.

Researchers from University of California, Berkeley, present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variable. Calculations from quantum annealing show promising results and hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system.

Accenture is working with telecom companies on the application of quantum computers to complex business problems. Watch this talk and find out more.

Ramin Ayanzadeh, et al.

We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels—i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value—and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.

Quantum Annealing is a heuristic for solving optimization problems that have seen a recent surge in usage owing to the success of D-Wave Systems. This paper aims to find a good heuristic for solving the Electric Vehicle Charger Placement (EVCP) problem, a problem that stands to be very important given the costs of setting up an electric vehicle (EV) charger and the expected surge in electric vehicles across the world. The same problem statement can also be generalised to the optimal placement of any entity in a grid and can be explored for further uses. Finally, the authors introduce a novel heuristic combining Quantum Annealing and Genetic Algorithms to solve the problem. The proposed hybrid approach entails seeding the genetic algorithm with the results of a quantum annealer. Our experiments show this method decreases the minimum distance from POIs by 42.89% compared to vanilla quantum annealing over our sample EVCP datasets.

Matthew R.C. Fitzpatrick, et al.

We present an essentially exact numerical method for modeling flux qubit chains subject to charge and flux noise. We define an essentially exact method as one that introduces errors that are completely controlled such that they can be made arbitrarily small by tuning the simulation parameters. The method adopts the quasi-adiabatic path integral formalism to express the system's reduced density matrix as a time-discretized path integral, comprising a series of influence functionals that encode the non-Markovian dynamics of the system. We present a detailed derivation of the path integral expression for the system's reduced density matrix and describe in detail the tensor network algorithm used to evaluate the path integral expression. We have implemented our method in an open-sourced Python library called "spinbosonchain". When appropriate, we draw connections between concepts covered in this manuscript and the library's code.

We developed and compared Constraint Programming (CP) and Quantum Annealing (QA) approaches for rolling stock optimisation considering necessary maintenance tasks. To deal with such problems in CP we investigated specialised pruning rules and implemented them in a global constraint. For the QA approach, we developed quadratic unconstrained binary optimisation (QUBO) models. For testing, we use data sets based on real data from Deutsche Bahn and run the QA approach on real quantum computers from D-Wave.

Sarmed A Rahman, Randy Lewis, Emanuele Mendicelli, and Sarah Powell, SU(2) lattice gauge theory on a quantum annealer, Physical Review D 104, 034501

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.

Kelly Boothby, et al.

Early generations of superconducting quantum annealing processors have provided a valuable platform for studying the performance of a scalable quantum computing technology. These studies have directly informed our approach to the design of the next-generation processor. Our design priorities for this generation include an increase in per-qubit connectivity, a problem Hamiltonian energy scale similar to previous generations, reduced Hamiltonian specification errors, and an increase in the processor scale that also leaves programming and readout times fixed or reduced. Here we discuss the specific innovations that resulted in a processor architecture that satisfies these design priorities.

Andrew D. King, et al.

Artificial spin ices are frustrated spin systems that can be engineered, in which fine-tuning of geometry and topology has allowed the design and characterization of exotic emergent phenomena at the constituent level. Here, we report a realization of spin ice in a lattice of superconducting qubits. Unlike conventional artificial spin ice, our system is disordered by both quantum and thermal fluctuations. The ground state is classically described by the ice rule, and we achieved control over a fragile degeneracy point, leading to a Coulomb phase. The ability to pin individual spins allows us to demonstrate Gauss’s law for emergent effective monopoles in two dimensions. The demonstrated qubit control lays the groundwork for potential future study of topologically protected artificial quantum spin liquids.

Eleni Marina Lykiardopoulou, et al.

Nonstoquastic Hamiltonians are hard to simulate due to the sign problem in quantum Monte Carlo simulation. It is, however, unclear whether nonstoquasticity can lead to an advantage in quantum annealing. Here we show that YY interactions between the qubits make the adiabatic path during quantum annealing, and therefore the performance, dependent on spin-reversal transformations. With the right choice of spin-reversal transformation, a nonstoquastic Hamiltonian with YY interaction can outperform stoquastic Hamiltonians with similar parameters. We introduce an optimization protocol to determine the optimal transformation and discuss the effect of suboptimality.

Groovenauts' MAGELLAN BLOCKS is the world's first service to market that combines optimizations run on a quantum computer with AI-based predictions. We began by successfully applying our service to various corporate issues like logistics and delivery optimization, as well as factory optimization and construction site optimization. We then expanded this practice of corporate optimization at scale to transform entire municipal service chains. Join us to learn more about our "City as a Service" solution through city-wide use cases that implement big data, AI, and quantum computing to optimize city activities.

D-Wave quantum computer is used to optimize the lockdown schedule as disease evolution is modeled using a SEIRD model. The already known QUBO formulation for the knapsack problem is used along with a transfer function to link the evolving diseases betweeen cities. An alternating schedule of disease evolution along with city lockdown optimization is then compared between classical probabilistic and quantum annealing methods. Results show that the knapsack formulation is able to substantially reduce morbidity while reducing the economic disruption

Alexander Teplukhin, et al.

The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree-Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm-Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example H2 molecule and is also applied to several other molecular species.

In this paper, the authors show how to implement in a simple way some complex real-life constraints on the portfolio optimization problem, so that it becomes amenable to quantum optimization algorithms. Specifically, first we explain how to obtain the best investment portfolio with a given target risk. This is important in order to produce portfolios with different risk profiles, as typically offered by financial institutions. Second, we show how to implement individual investment bands, i.e., minimum and maximum possible investments for each asset. This is also important in order to impose diversification and avoid corner solutions. Quite remarkably, we show how to build the constrained cost function as a quadratic binary optimization (QUBO) problem, this being the natural input of quantum annealers. The validity of our implementation is proven by finding the optimal portfolios, using D-Wave Hybrid and its Advantage quantum processor, on portfolios built with all the assets from S&P100 and S&P500.

Addressing the world’s climate emergency is an uphill battle, requiring a multifaceted approach including optimal deployment of green-energy alternatives. Such undertakings often involve computationally-expensive optimization of black-box models in continuous parameter space. We observe good performance on the DW-2000Q QPU - even using default settings - and higher sensitivity of performance to a number of samples and annealing time for the Advantage QPU. These results are promising and potentially justify further investment in hardware, software, and optimization research, in particular, in the area of solvers for dense QUBOs.

Andrew D. King, et al.

The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of equilibration in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) equilibration timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation compared with spatially local update dynamics of path-integral Monte Carlo (PIMC). The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over an efficient CPU implementation. PIMC is a leading classical method for such simulations, and a scaling advantage of this type was recently shown to be impossible in certain restricted settings. This is therefore an important piece of experimental evidence that PIMC does not simulate QA dynamics even for sign-problem-free Hamiltonians, and that near-term quantum devices can be used to accelerate computational tasks of practical relevance.

Andrew D. King, et al.

Geometrically frustrated spin-chain compounds such as Ca3Co2O6 exhibit extremely slow relaxation under a changing magnetic field. Consequently, both low-temperature laboratory experiments and Monte Carlo simulations have shown peculiar out-of-equilibrium magnetization curves, which arise from trapping in metastable configurations. In this work we simulate this phenomenon in a superconducting quantum annealing processor, allowing us to probe the impact of quantum fluctuations on both equilibrium and dynamics of the system. Increasing the quantum fluctuations with a transverse field reduces the impact of metastable traps in out-of-equilibrium samples, and aids the development of three-sublattice ferrimagnetic (up-up-down) long-range order. At equilibrium we identify a finite-temperature shoulder in the 1/3-to-saturated phase transition, promoted by quantum fluctuations but with entropic origin. This work demonstrates the viability of dynamical as well as equilibrium studies of frustrated magnetism using large-scale programmable quantum systems, and is therefore an important step toward programmable simulation of dynamics in materials using quantum hardware.

Paul Kairys, et al.

A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials. These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher. In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits. This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short- and long-range orders and fractional order parameters. We show that a large-scale finite-field quantum annealing experiment is possible on 468 logical spins of this model embedded into the quantum hardware. We determine microscopic spin configurations using an iterative quantum annealing protocol and develop mean-field boundary conditions to attenuate finite-size effects and defects. We not only recover all phases of the Shastry-Sutherland Ising model—including the well-known fractional magnetization plateau in a longitudinal field—but also predict the spin behavior at the critical points with significant ground-state degeneracy and in the presence of defects. The results lead us to establish the connection to the diffuse neutron scattering experiments by calculation of the static structure factors.

Jack Raymond, et al.

Optimization or sampling of arbitrary pairwise Ising models, in a quantum annealing protocol of constrained interaction topology, can be enabled by a minor-embedding procedure. The logical problem of interest is transformed to a physical (device programmable) problem, where one binary variable is represented by a logical qubit consisting of multiple physical qubits. In this paper we discuss tuning of this transformation for the cases of clique, biclique, and cubic lattice problems on the D-Wave 2000Q quantum computer. We demonstrate parameter tuning protocols in spin glasses and channel communication problems, focusing on anneal duration, chain strength, and mapping from the result on physical qubits back to the logical space. Inhomogeneities in effective coupling strength arising from minor-embedding are shown to be mitigated by an efficient reweighting of programmed couplings, accounting for logical qubit topology.

The D-Wave hybrid solver service (HSS), available from the Leap quantum cloud service, was launched in February 2020. This document presents an overview and performance evaluation of an upgraded version of HSS launched in September 2020. The new version incorporates the Advantage quantum computer and contains software enhancements that expand the size and scope of problems that can be solved efficiently. This report shows how a hybrid approach incorporating both quantum and classical components can outperform either method used alone. A small performance study demonstrates that the upgraded version outperforms its predecessor as well as state-of-the art classical alternatives. Download white paper.

Elizabeth Crosson¹, Tameem Albash^1,2, Itay Hen^3,4, and A. P. Young⁵

Quantum 4, 334 (2020) https://doi.org/10.22331/q-2020-09-24-334

Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that maps every non-stoquastic adiabatic path ending in a classical Hamiltonian to a corresponding stoquastic adiabatic path by appropriately adjusting the phase of each matrix entry in the computational basis. We compare the spectral gaps of these adiabatic paths and find both theoretically and numerically that the paths based on non-stoquastic Hamiltonians have generically smaller spectral gaps between the ground and first excited states, suggesting they are less useful than stoquastic Hamiltonians for quantum adiabatic optimization. These results apply to any adiabatic algorithm which interpolates to a final Hamiltonian that is diagonal in the computational basis.

¹Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy , University of New Mexico, Albuquerque, NM 87131, USA
²Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131, USA
³Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA
⁴Department of Physics and Astronomy and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
⁵Department of Physics, University of California, Santa Cruz, California 95064, USA

This guide provides a gentle introduction to Ocean programs for beginners new to D-Wave’s Ocean SDK. Here you will find the building blocks and basic components required in an Ocean program in order to successfully run problems using D-Wave’s hardware and software tools. Download white paper.

Many complex optimization problems arise in research and industry. Solving these problems helps researchers make new scientific discoveries, build better materials, and synthesize new medicine; and helps businesses make better decisions, reduce costs, increase production, and design better products. Quantum annealing is a heuristic method for solving many of the optimization problems that appear in a range of disciplines. This document provides the background to help you choose the right problems for quantum annealing. Download white paper.

Nicholas Chancellor, et al.

A finite length ferromagnetic chain with opposite spin polarisation imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit, the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterizing the annealer. The noise measured in this fashion is smaller than what is seen during the single-qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.

This document presents an overview and preliminary performance analysis of the D-Wave hybrid solver service (HSS), available from the Leap quantum cloud service. We survey the benefits of taking a hybrid quantum-classical approach to computation and introduce the concept of quantum acceleration to describe the type of computational speedups that may be observed. A comparison of one hybrid solver from the HSS portfolio to a collection of state-of-the art classical alternatives show that the solver performs well on a variety of input structures.

Download white paper.

We explore the importance of the chain strength in programming the D-Wave quantum processing unit (QPU). The need to adjust the chain strength may arise when minor embedding problems onto the D-Wave QPU hardware. Download the white paper.

T. Lanting, et al.

We present measurements of the dynamics of a polarized magnetic environment coupled to the flux degree of freedom of rf-SQUID flux qubits. The qubits are used as both sources of polarizing field and detectors of the environmental polarization. We probe dynamics at timescales from 5 μs to 5 ms and at temperatures between 12.5 and 22 mK. The measured polarization versus temperature provides strong evidence for a phase transition at a temperature of 5.7±0.3 mK. Furthermore, the environmental polarization grows initially as t√, consistent with spin diffusion dynamics. However, spin diffusion model deviates from data at long timescales, suggesting that a different phenomenon is responsible for the low-frequency behavior. A simple 1/f model can fit the data at all time scales but it requires empirical low- and high-frequency cutoffs. We argue that these results are consistent with an environment comprised of random clusters of spins, with fast spin diffusion dynamics within the clusters and slow fluctuations of the total moments of the clusters.

Walter Vinci, et al.

The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists of a classical auto-encoding structure realized by traditional deep neural networks to perform inference to, and generation from, a discrete latent space. The latent generative process is formalized as thermal sampling from either a quantum or classical Boltzmann machine (QBM or BM). This setup allows quantum-assisted training of deep generative models by physically simulating the generative process with quantum annealers. In this paper, we have successfully employed D-Wave quantum annealers as Boltzmann samplers to perform quantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAE allows us to deploy current-generation quantum annealers in QCH generative models to achieve competitive performance on datasets such as MNIST. The results presented in this paper suggest that commercially available quantum annealers can be deployed, in conjunction with well-crafted classical deep neutral networks, to achieve competitive results in unsupervised and semisupervised tasks on large-scale datasets. We also provide evidence that our setup is able to exploit large latent-space (Q)BMs, which develop slowly mixing modes. This expressive latent space results in slow and inefficient classical sampling, and paves the way to achieve quantum advantage with quantum annealing in realistic sampling applications.

D-Wave has been continually developing its fabrication stack in order to reduce sources of noise. Here, we present the noise assessment results for two prototype lower-noise D-Wave 2000Q fabrication stacks, recently developed as part of the low-noise quantum annealing processor development project. Using single-qubit and multi-qubit tunneling rates measurements, we compare the flux noise in lower-noise D-Wave 2000Q fabrication stacks to the baseline D-Wave 2000Q fabrication stack and show 4.3× reduction in mid-band noise and 3× reduction in broad-band noise levels. The reduced-noise levels in the newly-developed processor result in 7.4× enhancement in tunneling rates.

Download white paper. 

I. Ozfidan, et al.

Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo (QMC) simulations. In this paper, we report implementation and measurements of two superconducting flux qubits coupled via two canonically conjugate degrees of freedom (charge and flux) to achieve a nonstoquastic Hamiltonian. Such coupling can enhance performance of QA processors, extend the range of quantum simulations. We perform microwave spectroscopy to extract circuit parameters and show that the charge coupling manifests itself as a YY interaction in the computational basis. We observe destructive interference in quantum coherent oscillations between the computational basis states of the two-qubit system. Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide range of parameters.

D-Wave has fabricated a series of quantum processing units (QPUs) possessing the same design but different materials within the QPU. In order to demonstrate the sensitivity of QPU performance to materials-related noise, a common set of identical spin glass problems, similar to those studied in a July 2018 Science article, has been posed to two such QPUs. The experimental results confirm a positive correlation between reduced noise and improved performance with at least a 25x speed up in solving spin glass problems having been observed.

Download white paper.  Download a presentation.

"Gate-model quantum computers are theoretically capable of exceptional performance in certain applications, al-though it is unclear how useful they will be in general. The Quantum Approximate Optimization Algorithm (QAOA) of Farhi et al. has been proposed as a possible path towards making gate-model quantum computers effective at solving problems in combinatorial optimization.

Recently, Rigetti Computing published results of QAOA run on their 19-qubit gate-model quantum computer. The inputs they considered can also be solved on D-Wave quantum annealing systems, providing an opportunity to compare the two quantum processing units (QPUs) directly. Re-producing their tests, we found the probabilities of returning an optimal solution to be 99.6% for the D-Wave 2000Q and 0.001% for the Rigetti 19Q. In addition, the D-Wave 2000Q was able to solve 102 copies of the problem in parallel. The advantages in quality and size of the D-Wave 2000Q, taken together, provide an improvement of 10 million times in terms of ground-state throughput per sample."

Download white paper.

Zhengbing Bian, et al.

Quantum annealers (QAs) are specialized quantum computers that minimize objective functions over discrete variables by physically exploiting quantum effects. Current QA platforms allow for the optimization of quadratic objectives defined over binary variables (qubits), also known as Ising problems. In the last decade, QA systems as implemented by D-Wave have scaled with Moore-like growth. Current architectures provide 2048 sparsely-connected qubits, and continued exponential growth is anticipated, together with increased connectivity.We explore the feasibility of such architectures for solving SAT and MaxSAT problems as QA systems scale. We develop techniques for effectively encoding SAT –and, with some limitations, MaxSAT– into Ising problems compatible with sparse QA architectures. We provide the theoretical foundations for this mapping, and present encoding techniques that combine offline Satisfiability and Optimization Modulo Theories with on-the-fly placement and routing. Preliminary empirical tests on a current generation 2048-qubit D-Wave system support the feasibility of the approach for certain SAT and MaxSAT problems.

Jesse J. Berwald, et al.

Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a metric, the Wasserstein distance (closely related to but not the same as the homonymous metric from probability theory). Further, this metric provides a notion of stability; that is, small noise in the input causes at worst small differences in the output. In this paper, we show that the Wasserstein distance for persistence diagrams can be computed through quantum annealing. We provide a formulation of the problem as a Quadratic Unconstrained Binary Optimization problem, or QUBO, and prove correctness. Finally, we test our algorithm, exploring parameter choices and problem size capabilities, using a D-Wave 2000Q quantum annealing computer.

Anatoly Yu Smirnov, et al. 

We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system–bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch–Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat. Commun. 4 1903) and show qualitative agreement with experimental results.

Investigations of quantum computing were originally motivated by the possibility of efficiently simulating quantum systems. Here we approach this challenge using a D-Wave 2000Q system to estimate quantum Boltzmann statistics. We compare performance with state-of-the-art classical Monte Carlo simulations of the quantum systems, and find that, over the problems studied, the D-Wave processor realizes a performance advantage over classical methods that increases with simulated system size. 

DOWNLOAD

Andrew King, et al.

The work of Berezinskii, Kosterlitz and Thouless in the 1970s revealed exotic phases of matter governed by the topological properties of low-dimensional materials such as thin films of superfluids and superconductors. A hallmark of this phenomenon is the appearance and interaction of vortices and antivortices in an angular degree of freedom—typified by the classical XY model—owing to thermal fluctuations. In the two-dimensional Ising model this angular degree of freedom is absent in the classical case, but with the addition of a transverse field it can emerge from the interplay between frustration and quantum fluctuations. Consequently, a Kosterlitz–Thouless phase transition has been predicted in the quantum system—the two-dimensional transverse-field Ising model—by theory and simulation. Here we demonstrate a large-scale quantum simulation of this phenomenon in a network of 1,800 in situ programmable superconducting niobium flux qubits whose pairwise couplings are arranged in a fully frustrated square-octagonal lattice. Essential to the critical behaviour, we observe the emergence of a complex order parameter with continuous rotational symmetry, and the onset of quasi-long-range order as the system approaches a critical temperature. We describe and use a simple approach to statistical estimation with an annealing-based quantum processor that performs Monte Carlo sampling in a chain of reverse quantum annealing protocols. Observations are consistent with classical simulations across a range of Hamiltonian parameters. We anticipate that our approach of using a quantum processor as a programmable magnetic lattice will find widespread use in the simulation and development of exotic materials.

Summary

In Science, July 13, 2018, researchers from D-Wave Systems Inc. report upon using a 2048-qubit quantum processing unit to experimentally study a computationally difficult problem known within the eld of quantum magnetism as the transverse eld Ising model. The researchers programmed 3-dimensional cubic lattices containing up to 512 quantum spins into their processor and studied the magnetic properties as a function of energy scales and intentionally induced disorder. The predicted phase tran- sitions between paramagnetic and ordered antiferromagnetic phases for low concentrations of disorder, and between paramagnetic and spin-glass phases for high con- centrations of disorder, were demonstrated as a function of the quantum mechanical energy scale.

Read the Synopsis

R. Harris, et. al

Understanding magnetic phases in quantum mechanical systems is one of the essential goals in condensed matter physics, and the advent of prototype quantum simulation hardware has provided new tools for experimentally probing such systems. We report on the experimental realization of a quantum simulation of interacting Ising spins on three-dimensional cubic lattices up to dimensions 8 × 8 × 8 on a D-Wave processor (D-Wave Systems, Burnaby, Canada). The ability to control and read out the state of individual spins provides direct access to several order parameters, which we used to determine the lattice’s magnetic phases as well as critical disorder and one of its universal exponents. By tuning the degree of disorder and effective transverse magnetic field, we observed phase transitions between a paramagnetic, an antiferromagnetic, and a spin-glass phase.

Richard H. Warren, et al.

This paper describes the logic and creativity needed in order to have a high probability of solving discrete optimization problems on a quantum annealing computer. Current features of quantum computing via annealing are discussed. We illustrate the logic at the forefront of this new era of computing, describe some of the work done in this field, and indicate the distinct mindset that is used when programming this type of machine. The traveling salesman problem is formulated for solving on a quantum annealing computer, which illustrates the methods for this computer.

Florian Neukart, et al.

We present an algorithm for quantum-assisted cluster analysis that makes use of the topological properties of a D-Wave 2000Q quantum processing unit. Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a priori, but generated by the algorithm. We explain how the problem can be expressed as a quadratic unconstrained binary optimization problem and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms.

Amir H. Khoshaman, et al.

Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, indifferentiability of the discrete units prohibits using the reparameterization trick, essential for low-noise back propagation. The Gumbel trick resolves this problem in a consistent way by relaxing the variables and distributions, but it is incompatible with BM priors. Here, we propose the GumBolt, a model that extends the Gumbel trick to BM priors in VAEs. GumBolt is significantly simpler than the recently proposed methods with BM prior and outperforms them by a considerable margin. It achieves state-of-the-art performance on permutation invariant MNIST and OMNIGLOT datasets in the scope of models with only discrete latent variables. Moreover, the performance can be further improved by allowing multi-sampled (importance-weighted) estimation of log-likelihood in training, which was not possible with previous models.