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Tight Lieb–Robinson Bound for approximation ratio in quantum annealing
npj Quantum Information ( IF 6.6 ) Pub Date : 2024-04-17 , DOI: 10.1038/s41534-024-00832-x
Arthur Braida , Simon Martiel , Ioan Todinca

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.



中文翻译:

量子退火中近似比的紧利布-罗宾逊束缚

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。

更新日期:2024-04-17
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