发表机构
College of Natural Sciences, Korea Advanced Institute of Science and Technology; Research Laboratory of Electronics, Massachusetts Institute of Technology; MIT Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（韩国科学技术院自然科学学院; 麻省理工学院电子研究实验室; 麻省理工学院理论物理中心（莱因韦伯研究所））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明一般局域不含时哈密顿量下，典型高温乘积态的量子电路复杂度在长时间内持续增长至指数级，并推论出鲁棒体积律纠缠和无快速转发结果。
AI 中文摘要
演化中的多体量子系统的量子电路复杂度被认为表现出持续增长，其维持的时间尺度远长于热化开始的时间。以往的大多数工作集中于违反能量守恒的模型，例如随机幺正电路。这里我们研究一般的、局域的、不含时的哈密顿动力学。我们无条件地证明，对于一般局域哈密顿量和有效高温下的典型初始乘积态，鲁棒量子电路复杂度必须在很长一段时间内增长，并在晚期达到指数级大的值。我们的方法依赖于我们严格证明的两个结构性质：(i) 一般局域哈密顿量满足任意阶的广义谱无共振条件，(ii) 典型高温乘积态有效地支持在指数多个能量本征态上。这些性质在以往的工作中被广泛假设而未经证明。作为这一结果的推论，我们表明晚期状态展现出鲁棒的体积律纠缠，这种纠缠无法被多项式大小的电路移除，并且我们确立了一般局域哈密顿量的无快速转发结果。我们还对用局域量子通道制备足够大的子系统给出了复杂度下界，与足够小的热化区域形成对比，我们证明后者在晚期保持低复杂度。
英文摘要
The quantum circuit complexity of an evolving many-body quantum system is believed to exhibit a sustained growth, maintained for timescales much longer than the onset of thermalization. Most previous works have focused on models which violate energy conservation, such as random unitary circuits. Here we study generic, local time-independent Hamiltonian dynamics. We unconditionally prove that for generic local Hamiltonians and typical initial product states at high effective temperature, the robust quantum circuit complexity must grow over a very long period of time, attaining an exponentially large value at late times. Our approach relies on two structural properties that we prove rigorously: (i) generic local Hamiltonians satisfy generalized spectral no-resonance conditions of arbitrary order, and (ii) typical high-temperature product states are effectively supported in exponentially many energy eigenstates. These properties have been widely assumed without proof in prior works. As corollaries of this result, we show the late-time state displays robust volume-law entanglement that is irremovable by polynomial-size circuits, and we establish a no fast-forwarding result for generic local Hamiltonians. We also lower bound the complexity of preparing sufficiently large subsystems with local quantum channels, in contrast with sufficiently small thermalizing regions which we show retain low complexity at late times.
Comments9 pages, 3 figures; 36 pages (supplemental material). v2: corrected figures and typos
