Correct answer rate of Max-cut problems solved by quantum-annealing-inspired swarm intelligence

Akio Yoshizawa

Akio Yoshizawa

Qingguo Zeng, Xiaopeng Cui, Bowen Liu +3 more

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.

Huy Phuc Nguyen Ha, Viết Hùng Nguyễn, Anh Son Ta

Akio Yoshizawa

The path-integral quantum Monte Carlo (PIQMC) method is widely used as a classical simulation algorithm for quantum annealing. Replicas represent different points in imaginary time. We propose and demonstrate a swarm-like ground-state searching algorithm based on the PIQMC method for automatically fluctuation-controlled simulated annealing. Replicas help one another to search for the ground state of an Ising system as if forming a swarm and working cooperatively. Their interactions are local, simple and fluctuate to a certain degree. Such fluctuations are necessary to escape local minima, but the fluctuations do not need to be explicitly controlled. The size of fluctuations is automatically adjusted as annealing proceeds. We solve max-cut problems for algorithm evaluation, each of which corresponds to a graph of 100 vertices. We also solve the same problems using a conventional method based on the Metropolis algorithm for comparison.

Y. S. Yang, P. Tyson, A. B Murphy

The weighted Max-Cut problem is an NP-hard problem with application implications. It is investigated on a cubic lattice with 113 nodes and mixed-signed random edge weights. For a fixed upper bound on edge weights, it has been demonstrated that the computational difficulty increases as the lower bound on edge weights becomes more negative. The solution time for the problem using a novel error-mitigated quantum annealing approach is compared with standard D-Wave quantum annealing (QA) and BQM hybrid solvers, as well as various classical solvers. For the QPU-embeddable weighted Max-Cut instances with mixed-signed edge weights, it has been quantitatively demonstrated that the SEMO (spin-error mitigation for optimisation) error-mitigated quantum annealing achieved substantially shorter time-to solution than standard D-Wave QA, D-Wave BQM, simulated annealing and Tabu search baselines. The error-mitigated quantum annealing approach presented in this article potentially elevates the efficiency and application scope of quantum annealing and would be applicable in solving other discrete optimisation problems that can be formulated as QUBO or Ising instances. The promising solution time advantage would be particularly impactful for time-critical optimisation applications.