Abstract Two classes of quantum-annealing-inspired-algorithms (QAIA), namely different variants of simulated coherent Ising machine and simulated bifurcation, have been proposed for efficiently solving combinatorial optimization problems recently. In order to certify the superiority of these algorithms, standardized comparisons among them and against other physics-based algorithms are necessary. In this work, for Max-Cut problems up to 20,000 nodes, we benchmark QAIA against quantum annealing and other physics-based algorithms. We found that ballistic simulated bifurcation excelled for chimera and small-scale graphs, achieving nearly a 50-fold reduction in time-to-solution compared to quantum annealing. For large-scale graphs, discrete simulated bifurcation achieves the lowest time-to-target and outperforms D-Wave Advantage system when tasked with finding the maximum cut value in pegasus graphs. Our results suggest that QAIA represents a promising means for solving combinatorial optimization problems in practice, and can act as a natural baseline for competing quantum algorithms.
Abstract Two classes of quantum-annealing-inspired-algorithms (QAIA), namely different variants of simulated coherent Ising machine and simulated bifurcation, have been proposed for efficiently solving combinatorial optimization problems recently. In order to certify the superiority of these algorithms, standardized comparisons among them and against other physics-based algorithms are necessary. In this work, for Max-Cut problems up to 20,000 nodes, we benchmark QAIA against quantum annealing and other physics-based algorithms. We found that ballistic simulated bifurcation excelled for chimera and small-scale graphs, achieving nearly a 50-fold reduction in time-to-solution compared to quantum annealing. For large-scale graphs, discrete simulated bifurcation achieves the lowest time-to-target and outperforms D-Wave Advantage system when tasked with finding the maximum cut value in pegasus graphs. Our results suggest that QAIA represents a promising means for solving combinatorial optimization problems in practice, and can act as a natural baseline for competing quantum algorithms.
Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of the practical quantum advantage remains elusive. Recent studies have reported that both gate-based quantum circuits and quantum annealers can outperform state-of-the-art classical heuristics on multi-objective optimization (MO-MaxCut) problems. However, these studies did not fully account for the substantial pre- and post-processing overheads intrinsic to quantum solvers, leading to incomplete comparisons between quantum and classical approaches. In this work, we re-examine the same benchmark suite using GPU-based quantum-annealing-inspired algorithms (QAIAs), which, analogously to quantum processors, generate probabilistic samples and thus serve as formidable classical contenders. Our results show that QAIAs can sample candidate solutions approximately two orders of magnitude faster than previously studied quantum processors. In terms of end-to-end runtime, QAIAs also surpass industry-leading classical solvers, thereby establishing themselves as the superior performers among the quantum and classical solvers evaluated thus far for the MO-MaxCut instances.
Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs. We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these approaches for comparing our solution values to those obtained on the current quantum annealing machine, D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware. In addition, we also evaluate the performance of a heuristic by Selby. It has been a matter of discussion in the literature how well the D-Wave hardware performs at its native task, and our experiments shed some more light on this issue. In particular, we examine how reliably the D-Wave computer can deliver true optimum solutions and present some surprising results.
Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of the Ising model, tremendous effort has been devoted to developing solvers for Ising-type problems over the past decades. Recent advances in controlling and manipulating both quantum and classical systems have enabled novel computing paradigms such as quantum simulators and coherent Ising machines to tackle hard optimization problems. Here, we examine and benchmark several physics-inspired optimization algorithms, including coherent Ising machines, gain-dissipative algorithms, simulated bifurcation machines, and Hopfield neural networks, which we collectively refer to as stochastic driven nonlinear dynamical systems. Most importantly, we benchmark these algorithms against random Ising problems with planted solutions and compare them to simulated annealing as a baseline leveraging the same software stack for all solvers. We further study how different numerical integration techniques and graph connectivity affect performance. This work provides an overview of a diverse set of new optimization paradigms.
Optimization algorithms for combinatorial problems play a critical role in a wide range of applications, from logistics and scheduling to cryptography and artificial intelligence. Traditional classical methods, such as simulated annealing, genetic algorithms, and branch-and-bound techniques, have been widely employed to solve these problems, but they often face limitations in terms of computational efficiency and scalability as problem complexity grows. In recent years, quantum computing has emerged as a promising alternative, with quantum annealing offering a novel approach to solving combinatorial optimization problems. This study provides a comparative analysis of quantum annealing and classical optimization methods, highlighting their respective strengths and limitations. We explore how quantum annealing, through leveraging quantum tunnelling and superposition, has the potential to outperform classical algorithms in specific problem domains and Noisy Mean Field Annealing (NMFA) is used to comparisons of all algorithms. Benchmarking various combinatorial problems, such as the Traveling Salesman Problem (TSP), Max-Cut, Knapsack, and Quadratic Assignment Problem (QAP), this paper discusses performance metrics, computational time, and scalability. The findings suggest that while classical methods remain robust and practical for many real-world problems, quantum annealing holds significant promise, especially as quantum hardware continues to mature. However, there remain challenges in terms of noise, coherence, and problem mapping, which currently limit the full realization of quantum annealing's potential. This study offers insights into the future directions of optimization techniques and the evolving role of quantum computing in solving complex combinatorial problems.
We introduce Simulated Bifurcation Quantum Annealing (SBQA), a quantum-inspired optimization algorithm that extends simulated bifurcation by incorporating inter-replica interactions to mimic quantum tunneling. SBQA retains the efficiency and parallelism of simulated bifurcation while improving performance on sparse and rugged energy landscapes. We derive its equations of motion, analyze parameter dependence, and propose a lightweight auto-tuning strategy. A comprehensive benchmarking study on both large-scale problems and smaller instances relevant for current quantum hardware shows that SBQA systematically improves on SBM in the sparse and rugged regimes where SBM is known to struggle, while remaining competitive and versatile across a diverse set of tested problem families. These results position SBQA as a practical quantum-inspired optimization heuristic and a stronger classical baseline for the sparse and rugged regimes studied here.