制备准稳态的量子算法
Quantum Algorithm to Prepare Quasi-Stationary States
AI总结：
针对多体场景下有限温度本征态制备时间随系统规模指数增长的问题，提出基于量子奇异值变换和量子信号处理的高效量子搜索算法，可多项式时间制备准稳态，实现相对测量方法的二次加速，可用于探究多体量子系统热化等机制。
摘要：
量子动力学可通过能量本征态的结构进行分析。但在多体场景中，制备与有限温度相关的本征态所需的时间会随系统规模呈指数级增长。本研究提出了一种高效的量子搜索算法，可生成能量集中在稠密多体能谱窄窗口内的准稳态。该算法的运行时间随系统规模呈多项式级增长，生成的态具有逆多项式级的能量宽度，可用于分析多项式时间尺度内的多体动力学。该算法基于量子奇异值变换与量子信号处理，相比基于测量的方法实现了二次加速。我们还讨论了该算法如何作为基础模块，用于探究多体量子系统中热化与流体动力学的内在机制。
英文摘要：
Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we present an efficient quantum search algorithm which produces quasi-stationary states, having energies supported within narrow windows of a dense many-body spectrum. In time scaling polynomially with system size, the algorithm produces states with inverse polynomial energy width, which can in turn be used to analyze many-body dynamics out to polynomial times. The algorithm is based on quantum singular value transformations and quantum signal processing, and provides a quadratic speedup over measurement-based approaches. We discuss how this algorithm can be used as a primitive to investigate the mechanisms underlying thermalization and hydrodynamics in many-body quantum systems.
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