AI 中文总结
本文提出连续过程随机编译（CPRC），将随机编译从离散电路扩展到连续时间记忆性量子过程，统一了随机控制轨迹与环境动力学，并提供了误差界、收敛性证明及数值验证。
AI 中文摘要
传统的离散随机编译（RC）通过在逻辑门边界处施加随机控制框架来定制误差，但无法捕捉仪器内部的控制演化或持久的系统-环境耦合。在具有记忆的环境中，误差在时间上相关，而不仅仅是单个门。我们在连续过程张量（cPT）框架中构建了连续过程随机编译（CPRC），将随机幺正控制轨迹、逐点协变的有限时长仪器以及环境动力学统一在一条时间轴上。我们研究了四种协议：固定泡利刷新、有界Cayley路径、幺正布朗运动、Ornstein-Uhlenbeck驱动。我们获得了三个关键结果：（1）逐点协变性确保每条轨迹在无系统-环境耦合的情况下精确复现目标逻辑；一个闭环反例证明仅端点补偿会导致一阶仪器误差。（2）在全区间上独立的泡利共轭在边界处对角化误差历史，但经典标签保留环境诱导的相关性，这一点通过精确的静态浴解得到证实。（3）我们推导了在有界中心耦合和混合条件下完整自适应输出记录的总变差误差界。我们证明了在固定粒子扇区内，对于有限非高斯环境和具有时间可积协方差的高斯浴（包括未截断的Drude谱），轨迹平均的cPT系数收敛。我们通过输出概率、算子条件互信息以及量子比特和热Drude浴的所有双粒子系数，在量子比特模型中数值验证了该理论。这项工作将RC从离散电路扩展到连续时间的记忆性量子过程，为非马尔可夫误差定制提供了统一框架、定量工具、可实现的方案和基准。
英文摘要
Traditional discrete randomized compiling (RC) tailors errors with random control frames at logical-gate boundaries, but fails to capture intra-instrument control evolution or persistent system-environment coupling. In memory-bearing environments, errors correlate across times, not just single gates. We build continuous-process randomized compilation (CPRC) in the continuous process tensor (cPT) framework, unifying random unitary control trajectories, pointwise-covariant finite-duration instruments, and environmental dynamics on one time axis. We study four protocols: fixed Pauli refresh, bounded Cayley paths, unitary Brownian motion, Ornstein-Uhlenbeck driving. We obtain three key results: (1) Pointwise covariance ensures each trajectory exactly reproduces the target logic without system-environment coupling; a closed-frame counterexample proves endpoint-only compensation causes first-order instrument errors. (2) Independent Pauli conjugations over full intervals diagonalize error histories at boundaries, but classical labels retain environment-induced correlations, confirmed by an exact static-bath solution. (3) We derive a total-variation error bound for full adaptive output records under bounded centered coupling and mixing conditions. We prove the Fock norm convergence of the entire trajectory-averaged cPT for finite non-Gaussian environments and Gaussian baths with time-integrable covariance, including the uncut Drude spectrum. We numerically validate the theory in a qubit model via output probabilities, operator conditional mutual information, and all two-particle coefficients for both qubit and thermal Drude baths. This work extends RC from discrete circuits to continuous-time memory-bearing quantum processes, offering a unified framework, quantitative tools, implementable schemes, and benchmarks for non-Markovian error tailoring.
