AI 中文总结
本文通过几何分析研究纠缠辅助量子比特复位，揭示纠缠操作可使量子比特约化态沿测地线向基态演化，为姆佩姆巴效应启发的复位加速提供几何视角，明确两量子比特方案扩展至大寄存器的优势条件。
AI 中文摘要
快速可靠的量子比特复位是量子处理器高效运行的关键。在已提出的策略中，基于姆佩姆巴效应（Mpemba effect）的方案为加速弛豫提供了简单途径，但对完整复位动力学的最优性缺乏足够的认识；相比之下，几何方法可量化最优性，但通常无法提出实用的加速方案。本文通过对纠缠辅助量子比特复位的几何分析，弥合了这两种视角的差异。研究表明，纠缠操作可在多量子比特寄存器中重新分布局域相干性，使每个量子比特的约化态遵循通往基态的测地线路径。值得注意的是，即使集体演化在全态空间中变为次优，这种局域最优行为仍可出现。本文针对不同类别的初始多量子比特态阐释了这种相互作用，其结果为受姆佩姆巴效应启发的复位加速提供了几何视角，并明确了将两量子比特方案扩展至更大寄存器时在复位过程中何时能提供进一步优势。
英文摘要
Fast and reliable qubit reset is essential for the efficient operation of quantum processors. Among the proposed strategies, Mpemba-effect-based protocols offer a simple route to accelerated relaxation, but provide limited insight into the optimality of the full reset dynamics. Geometric approaches, by contrast, quantify optimality but do not generally suggest practical acceleration protocols. Here, we bridge these perspectives through a geometric analysis of entanglement-assisted qubit reset. We show that entangling operations can redistribute local coherences across a multi-qubit register, allowing the reduced state of each qubit to follow a geodesic path towards the ground state. Remarkably, this locally optimal behaviour can emerge even when the collective evolution becomes suboptimal in the full state space. We illustrate this interplay for different families of initial multi-qubit states. Our results provide a geometric perspective on Mpemba-inspired reset acceleration and clarify when extending two-qubit protocols to larger registers provides a further advantage in the reset process.
Comments17 pages, 5 figures (main text and bibliography: 11 pages, 4 figures; appendices: 6 pages, 1 figure). Comments are welcome!
