Noise Correlations as a Resource in Pauli-Twirled Circuits

TL;DR

This paper demonstrates that randomized compiling can reduce noise correlations and surprisingly increase fidelity in quantum circuits, even with correlated Gaussian noise, making correlations a potential resource.

Contribution

It provides analytical and numerical evidence that randomized compiling mitigates correlations and enhances fidelity, revealing correlations as a resource in quantum noise management.

Findings

RC reduces both the strength and temporal range of noise correlations.

Fidelity of Clifford circuits is increased by correlations under RC.

RC suppresses quantum bath correlations, treating weak noise as classical.

Abstract

Randomized compiling (RC) is an established tool to tailor arbitrary quantum noise channels into Pauli errors. The effect of both spatial and temporal noise correlations in randomly compiled circuits, however, is not fully understood. Here, we show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the circuit fidelity of randomly compiled circuits. Surprisingly, we show that this fidelity is always increased by the presence of correlations, suggesting that correlations are a resource in randomly compiled circuits. To leading order in system-bath coupling, we also show that RC suppresses the quantum component of bath correlations, implying that one can safely treat weak noise as being classical. Finally, through extensive numerical simulations, we show that our results remain valid for many relevant non-Clifford circuits. These results clarify how RC mitigates memory effects and enhances circuit robustness.