量子回波马尔可夫过程用于组合优化
Quantum-echo Markov process for combinatorial optimization
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中文总结 AI 辅助
本文提出量子回波马尔可夫过程用于组合优化，利用QA或QAOA设计转移核，结合贪婪下降，实现探索与利用的互补，提升优化性能。
中文摘要 AI 辅助
我们引入了一种用于组合优化的量子回波马尔可夫过程。基于量子退火（QA）或量子近似优化算法（QAOA）的量子动力学被用来设计转移核。增加QA中的退火时间或QAOA中的层数，使得转移能够探索远距离构型，同时抑制大的能量变化。哈密顿空间中的离域源于算符扩展，而能量空间中的局域化则源于动态生成的相关性。对于优化，我们提出了带或不带贪婪下降的量子回波局部优化。我们发现其性能由哈密顿空间非局域性与能量空间局域性之间的相互作用决定，并且过度的能量空间局域化会降低优化性能。加入贪婪下降显著提高了性能，凸显了量子动力学用于探索与贪婪下降用于利用的互补作用。这些结果确立了量子回波动力学作为设计结构化转移核的框架，并为将有限资源的量子多体动力学用作迭代优化的计算原语提供了途径。
英文摘要
We introduce a quantum-echo Markov process for combinatorial optimization. Quantum dynamics based on quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA) is used to engineer the transition kernel. Increasing the annealing time in QA or the number of layers in QAOA enables transitions to explore distant configurations while suppressing large energy changes. The Hamming-space delocalization originates from operator spreading, whereas the energy-space localization arises from a dynamically generated correlation. For optimization, we propose quantum-echo local optimization with and without greedy descent. We find that its performance is governed by the interplay between Hamming-space nonlocality and energy-space locality, and that excessive energy-space localization can degrade optimization performance. Incorporating greedy descent substantially improves the performance, highlighting the complementary roles of quantum dynamics for exploration and greedy descent for exploitation. These results establish quantum-echo dynamics as a framework for engineering structured transition kernels and provide a route to using finite-resource quantum many-body dynamics as a computational primitive for iterative optimization.
发表机构
- Waseda Institute for Advanced Study, Waseda University（早稻田大学高等研究院）
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