Title: Quantum Algorithm to Prepare Quasi-Stationary States Show Chinese title

Title: 量子算法制备准稳态

Abstract: 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. Show Chinese abstract

Abstract: 量子动力学可以通过能量本征态的结构进行分析。 然而，在多体情况下，准备与有限温度相关的本征态需要随系统大小指数级增长的时间。 在本工作中，我们提出了一种高效的量子搜索算法，该算法生成准稳态，其能量集中在密集多体谱的狭窄窗口内。 在系统大小的多项式时间尺度内，该算法生成具有逆多项式能量宽度的状态，这些状态可以用于分析多体动力学直至多项式时间。 该算法基于量子奇异值变换和量子信号处理，并相对于基于测量的方法提供了二次加速。 我们讨论了如何将此算法作为基本工具来研究多体量子系统中热化和流体力学机制的原理。