AI 中文总结
研究随机测量中电路内噪声的光锥缩放，通过独立局部旋转降低噪声，给出激活路径平均公式，验证其在一维浅电路中的缩放，支持小字符串校准协议，将噪声偏差与算符演化动力学联系起来。
AI 中文摘要
随机测量提供了一种从有限数据中提取未知量子态物理性质的有效方法。在近期硬件上，门和读出误差会使重建的可观测量产生偏差。本文针对局部加扰的浅电路，对这种偏差进行了微观描述。独立局部旋转将局部实现噪声降低为随机泡利阻尼，且只有当噪声事件与测量泡利算符的海森堡演化重叠时才会有贡献。这给出了有噪声泡利系数的激活路径平均公式。在一维浅电路中，激活噪声体积随连续可观测量的大小线性增长，导致指数阻尼率。我们用两比特泡利噪声验证了两比特随机克利福德和局部加扰iSWAP电路的这种缩放，包括空间波动和时间漂移。这种缩放支持一种小字符串校准协议，该协议无需学习完整的噪声测量通道就能预测更大的字符串可观测量。我们的结果将浅阴影协议的噪声偏差直接与算符演化动力学联系起来。
英文摘要
Randomized measurements provide an efficient way to extract physical properties of an unknown quantum state from limited data. On near-term hardware, gate and readout errors bias the reconstructed observables. Here we develop a microscopic description of this bias for locally scrambled shallow circuits. Independent local twirling reduces local implementation noise to stochastic Pauli damping, and a noise event contributes only when it overlaps the Heisenberg evolution of the measured Pauli operator. This gives an activated path-average formula for the noisy Pauli coefficient. In one-dimensional shallow circuits, the activated noise volume grows linearly with the size of a contiguous observable, leading to an exponential damping ratio. We verify this scaling for two-qubit random Clifford and locally scrambled iSWAP circuits with two-qubit Pauli noise, including spatial fluctuations and temporal drift. The scaling supports a small-string calibration protocol that predicts larger string observables without learning the full noisy measurement channel. Our result relates the noise bias of shallow-shadow protocols directly to operator-evolving dynamics.
