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 brought lots of attention to the NISQ era. Several numerical benchmarks try to classify these two metaheuristics however, classical computational power highly limits the performance insights. In this work, we introduce a new 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.

翻译：量子退火（QA）有望解决量子计算中的优化问题，尤其是组合优化问题。这种模拟框架因其处理复杂问题的潜力而备受关注。其基于门电路的同类算法——QAOA（具有可验证性能）——在NISQ时代引起了广泛关注。多项数值基准尝试对这两种元启发式算法进行分类，但经典计算能力严重限制了性能洞察。本文提出一种新型参数化QA版本，可实现对算法的精确1-局域分析。我们针对正则图推导出紧致Lieb-Robinson界，获得了局域分析QA的最佳已知数值结果。以三次图上的MaxCut作为基准优化问题，我们证明采用线性调度QA及1-局域分析可获得超过0.7020的近似比，优于所有已知的1-局域算法。