Error Mitigation Thresholds in Noisy Random Quantum Circuits

TL;DR

This paper investigates the robustness of error mitigation techniques in noisy quantum circuits, revealing a threshold in noise characterization accuracy for effective mitigation in higher dimensions, but not in one dimension.

Contribution

It introduces a theoretical threshold for error mitigation robustness in spatially local quantum circuits with imperfect noise characterization.

Findings

Error mitigation is effective below a certain noise characterization disorder threshold in D≥2.

In one-dimensional circuits, mitigation fails at constant times regardless of noise characterization accuracy.

Implications for quantum advantage tests and near-term quantum algorithms are discussed.

Abstract

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of probabilistic error cancellation and tensor network error mitigation when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of a threshold in the robustness of these error mitigation methods for random spatially local circuits in spatial dimensions $D \geq 2$: noise characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an $\mathcal{O}(1)$ time for any imperfection in the characterization of disorder. As a result, error mitigation is only a practical method for sufficiently well-characterized noise. We discuss further implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.