Abstract Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based homologous, QAOA with proven performance, has attracted a lot of attention to the NISQ era. Several numerical benchmarks try to compare these two metaheuristics, however, classical computational power highly limits the performance insights. In this work, we introduce a parametrized version of QA enabling a precise 1-local analysis of the algorithm. We develop a tight Lieb–Robinson bound for regular graphs, achieving the best-known numerical value to analyze QA locally. Studying MaxCut over cubic graph as a benchmark optimization problem, we show that a linear-schedule QA with a 1-local analysis achieves an approximation ratio over 0.7020, outperforming any known 1-local algorithms.
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.
We investigate whether the Quantum Approximate Optimization Algorithm (QAOA) can compete with classical metaheuristics for multi-product, multi-location retail inventory optimization under demand uncertainty. We formulate the binary inventory decision problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and benchmark QAOA (simulated via classical statevector simulation,
p=2 layers) against Mixed-Integer Linear Programming (MILP), Simulated Annealing (SA), Genetic Algorithms (GA), and Tabu Search across problem sizes from
n=5 to
n=200 binary variables, using Walmart sales and Kaggle retail demand datasets. Our key finding is a \textbf{negative result}: while QAOA achieves a 2.3\% optimality gap and 97\% constraint satisfaction at small scales (
n≤20), it is not competitive with classical metaheuristics at practical problem sizes. Classical heuristics---particularly SA and Tabu Search---consistently outperform QAOA on all instances tested and scale efficiently to
n=200, whereas QAOA simulation becomes intractable beyond
n=30 due to exponential memory requirements. We do not claim any quantum speedup. This comparative study provides important insights into the limitations of current QAOA implementations for supply chain problems, including the effects of penalty parameter scaling, barren plateaus in the optimization landscape, and circuit depth constraints. We additionally present an economic sensitivity analysis linking macroeconomic indicators to optimal inventory decisions and a rolling-horizon proof-of-concept for multi-period planning.