Light-Cone Scaling of In-Circuit Noise in Randomized Measurements

• URL: http://arxiv.org/abs/2607.17740v1
• Date: Mon, 20 Jul 2026 09:34:06 GMT
• Title: Light-Cone Scaling of In-Circuit Noise in Randomized Measurements
• Abstract summary: Gate and readout errors bias the reconstructed observables.<n>Independent local twirling reduces local noise to Pauli damping.<n>Noise event contributes only when it overlaps the Heisenberg evolution of the measured Pauli operator.
• Score: 5.0619425714233985
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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