发表机构
Nagoya University（名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出序贯响应容量量化有限记忆量子过程的复杂性，证明在固定分辨率下容量按$K\log K$增长，并分析泡利噪声对对数增强的影响，揭示相干时间尺度限制。
AI 中文摘要
一个量子设备在固定内部记忆下运行时间越长，其响应能变得多复杂？我们通过序贯响应容量来量化这种复杂性：即有多少个自适应测试阶段（每个阶段使用一次新的运行）能够继续以响应概率的指定差距来区分可能的过程。对于固定的系统和记忆大小，我们建立了一个严格的定律，将该容量与运行长度和概率分辨率联系起来。在固定分辨率下，容量按 $K\log K$ 的数量级增长，其中 $K$ 是每次运行中的时间步数。我们的构造通过单个可见量子比特上的时变相位旋转实现了这种增长，且无需额外的内部记忆；其测试给出的响应概率恰好为零或一。在相同的测试下，每一步在固定基下测量的经典随机过程在固定大小和分辨率下仅具有线性容量。对于由存储的经典标签选择的相位序列，我们随后量化了已知的独立泡利噪声如何改变这种对数增强。在理想控制和校正后弱的残余相位噪声下，我们证明了在固定的小概率间隙下匹配的容量界限。这些界限将残余相位翻转概率的倒数确定为限制额外对数增长的相干时间尺度。
英文摘要
How complex can the responses of a quantum device become as it runs longer with a fixed internal memory? We quantify this complexity through sequential response capacity: how many adaptive testing stages, each using a fresh run, can continue to separate possible processes by a prescribed gap in response probabilities. For fixed system and memory sizes, we establish a tight law relating this capacity to run length and probability resolution. At fixed resolution, the capacity grows on the order of $K\log K$, where $K$ is the number of time steps in each run. Our construction attains this growth using time-dependent phase rotations on a single visible qubit with no additional internal memory; its tests give response probabilities exactly zero or one. Under the same tests, classical stochastic processes that measure in a fixed basis at every step have only linear capacity at fixed sizes and resolution. For phase sequences selected by a stored classical label, we then quantify how known independent Pauli noise changes this logarithmic enhancement. With ideal controls and weak residual phase noise after correction, we prove matching capacity bounds at a fixed small probability gap. These bounds identify the inverse residual phase-flip probability as the coherence timescale that limits the extra logarithmic growth.
