Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation

TL;DR

This paper introduces a method to reduce the sampling overhead in probabilistic error cancellation for quantum circuits by using Pauli error propagation and classical preprocessing, especially effective for Clifford circuits.

Contribution

The authors propose a novel technique combining Pauli error propagation with classical preprocessing to lower sampling costs in PEC, particularly for Clifford circuits.

Findings

Significant reduction in sampling overhead for Clifford circuits.

Applicability to non-Clifford circuits with limited effectiveness.

Useful for resource state generation in measurement-based quantum computing.

Abstract

Quantum error mitigation is regarded as a possible path to near-term quantum utility. The methods under the quantum error mitigation umbrella term, such as probabilistic error cancellation (PEC), zero-noise extrapolation (ZNE) or Clifford data regression (CDR) are able to significantly reduce the error for the estimation of expectation values, although at an exponentially scaling cost, i.e., in the sampling overhead. In this work, we present a method to reduce the sampling overhead of PEC through Pauli error propagation combined with classical preprocessing. Our findings indicate that this method significantly reduces sampling overheads for Clifford circuits, leveraging the well-defined interaction between the Clifford group and Pauli noise. Additionally, we show that the method is applicable to non-Clifford circuits, though with more limited effectiveness, primarily constrained by the number of non-Clifford gates present in the circuit. We further provide examples of Clifford sub-circuits commonly encountered in relevant calculations, such as resource state generation in measurement-based quantum computing.