固定深度 Trotter 模拟中的噪声结构：平稳信道与可观测量级别的退极化
Noise structuring in fixed-depth Trotter simulation: stationary channels and observable-level depolarization
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中文总结 AI 辅助
研究固定深度 Trotter 模拟构建硬件噪声的方法，通过选择层数使噪声剂量与端点时间无关，分析局部随机故障下噪声电路特性，揭示可观测量级退极化及相关结果，还指出朴素零噪声外推策略的局限性。
中文摘要 AI 辅助
我们将固定深度 Trotter 模拟分析为一种在数字多体动力学中构建硬件噪声的方法。利用最大端点时间选择层数并在整个时间扫描中保持固定，使总噪声剂量大致与端点时间无关。对于局部随机故障，我们表明，一旦传播的故障失去其插入层的记忆，有噪声的电路就会分解为理想演化，随后是一个平稳的有限深度二项式信道。在稀层极限下，该信道简化为泊松指数。单个故障的记忆时间与洛施密特回波有关。一个重要结果是可观测量级别的退极化：对于低至中等噪声水平下选定的宏观可观测量，即使整个信道不一定是退极化的，平稳信道也可以充当几乎与时间无关的仿射对比度校正，这对于误差缓解至关重要。在短时间内，相同的协议会产生类似数字芝诺的瞬态，其中固定数量的噪声机会与每层消失的相干角竞争。我们的结果还揭示了基于过度简化函数的朴素零噪声外推策略的局限性。
英文摘要
We analyze fixed-depth Trotter simulation as a method for structuring hardware noise in digital many-body dynamics. The number of layers is chosen using the largest endpoint time and is then kept fixed throughout the time scan, making the total noise dose approximately independent of the endpoint time. For local stochastic faults, we show that, once propagated faults lose memory of their insertion layer, the noisy circuit factorizes into ideal evolution followed by a stationary finite-depth binomial channel. In the dilute-layer limit, this channel reduces to a Poissonian exponential. The memory time of a single fault is related to a Loschmidt echo. An important consequence is observable-level depolarization: for selected macroscopic observables at low to moderate noise levels, the stationary channel can act as an almost time-independent affine contrast correction, even though the full channel need not be depolarizing, which is crusial for error mitigation purposes. At short times, the same protocol produces a digital Zeno-like transient, in which a fixed number of noise opportunities competes with a vanishing coherent angle per layer. Our results also reveal limitations of naive zero-noise extrapolatin strategies based on oversimplified functions.
