Scientific Publications

Elijah Pelofske, Frank Barrows, Pratik Sathe, and Cristiano Nisoli

https://www.science.org/doi/10.1126/sciadv.aeb5192

While quantum annealers have emerged as versatile and controllable platforms for experimenting on correlated spin systems, the important phenomenology of magnetic memory and hysteresis remain unexplored on hardware designed to escape metastable states via quantum tunneling. Here, we present the first general protocol to experiment on magnetic hysteresis on programmable quantum annealers and implement it on three D-Wave superconducting qubit quantum annealers, using up to thousands of spins, for both ferromagnetic and disordered Ising models, and across different graph topologies. We observe hysteresis loops whose area depends nonmonotonically on quantum fluctuations, exhibiting both expected and unexpected features, such as disorder-induced steps and nonmonotonicities. Our work establishes quantum annealers as a platform for probing nonequilibrium emergent magnetic phenomena, thereby broadening the role of analog quantum computers into foundational questions in condensed matter physics.

Hayato Kunugi, Mohsen Rahmani, Yosuke Iyama, Yutaro Hirono, Akira Suma, Matthew Woolway, Vladimir Vargas-Calderón, William Kim, Kevin Chern, Mohammad Amin, Masaru Tateno

https://arxiv.org/abs/2602.15451

Deep generative modeling to stochastically design small molecules is an emerging technology for accelerating drug discovery and development. However, one major issue in molecular generative models is their lower frequency of drug-like compounds. To resolve this problem, we developed a novel framework for optimization of deep generative models integrated with a D-Wave quantum annealing computer, where our Neural Hash Function (NHF) presented herein is used both as the regularization and binarization schemes simultaneously, of which the latter is for transformation between continuous and discrete signals of the classical and quantum neural networks, respectively, in the error evaluation (i.e., objective) function. The compounds generated via the quantum-annealing generative models exhibited higher quality in both validity and drug-likeness than those generated via the fully-classical models, and was further indicated to exceed even the training data in terms of drug-likeness features, without any restraints and conditions to deliberately induce such an optimization. These results indicated an advantage of quantum annealing to aim at a stochastic generator integrated with our novel neural network architectures, for the extended performance of feature space sampling and extraction of characteristic features in drug design.

Pratik Sathe, Andrew D. King, Susan M. Mniszewski, Carleton Coffrin, Cristiano Nisoli & Francesco Caravelli

https://www.nature.com/articles/s41467-025-67568-w

Quantum annealing provides a powerful platform for simulating magnetic materials and realizing statistical physics models, presenting a compelling alternative to classical Monte Carlo methods. We demonstrate that quantum annealers can accurately reproduce phase diagrams and simulate critical phenomena without suffering from the critical slowing down that often affects classical algorithms. To illustrate this, we study the piled-up dominoes model, which interpolates between the ferromagnetic 2D Ising model and Villain’s fully frustrated “odd model”. We map out its phase diagram and employ finite-size scaling and Binder cumulants on a quantum annealer to study critical exponents for thermal phase transitions. Our method achieves systematic temperature control by tuning the energy scale of the Hamiltonian, eliminating the need to adjust the physical temperature of the quantum hardware. This work demonstrates how, through fine-tuning and calibration, a quantum annealer can be employed to apply sophisticated finite-size scaling techniques from statistical mechanics. Our results establish quantum annealers as robust statistical physics simulators, offering a novel pathway for studying phase transitions and critical behavior.

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.

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.

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.

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.

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

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.

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.

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.

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.