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.

量子退火 (QA) 有望解决量子计算中的优化问题，尤其是组合优化。这种模拟框架因其解决复杂问题的潜力而引起人们的关注。其基于门的同源QAOA，性能经过验证，在NISQ时代引起了广泛关注。几个数值基准试图比较这两种元启发法，然而，经典的计算能力极大地限制了性能洞察力。在这项工作中，我们引入了 QA 的参数化版本，可以对算法进行精确的 1-局部分析。我们为正则图开发了一个严格的 Lieb-Robinson 界限，实现了本地分析 QA 的最著名的数值。研究立方图上的 MaxCut 作为基准优化问题，我们表明，使用 1-局部分析的线性调度 QA 实现了超过 0.7020 的近似比，优于任何已知的 1-局部算法。