Vector Annealing, a Quantum-Inspired Technique: Benchmarking Performance Against Quantum and Simulated Annealing within the BACQ Framework

In this paper, we aim to compare Vector Annealing (VA), a quantum-inspired metaheuristic introduced by NEC, with other metaheuristics. For this comparison, we utilize Quantum Annealing (QA), as implemented by D-Wave, and the conventional Simulated Annealing (SA) as a reference point for the capabilities of classical hardware with classical algorithms. The applications used for performance evaluation are two important benchmark programs designed to assess quantum hardware. This comparison is relevant because, for benchmarking purposes, it is valuable to have reference points between classical and quantum computing. It is widely thought that quantum computers will take some time to reach the level of relevance currently held by classical computing. This research, focusing on the Q-Score benchmark and Maximum Cardinality Matching (MCM) problems -both part of the MetriQs/BACQ benchmarking initiative- demonstrates this point. Through this work, we also trace the evolution from VA 2.0 to VA 3.0. While VA 2.0 already showed a significant advantage over both QA and SA in constrained problems, VA 3.0 introduces substantial optimizations and overcomes previous limitations in unconstrained problems. This advancement highlights the potential of VA 3.0. Furthermore, this work paves the way for the comprehensive testing of VA within the context of the MetriQs/BACQ quantum benchmark, an application-oriented French benchmarking initiative for quantum computers.