Quantum Error Mitigation Relying on Permutation Filtering

TL;DR

This paper introduces a general framework called permutation filters for quantum error mitigation, which improves error reduction in noisy quantum computations by optimizing permutation-based methods, especially under narrowband noise conditions.

Contribution

It proposes a unified permutation filter framework that guarantees convergence to the global optimum and enhances error mitigation over existing methods.

Findings

Optimal filters significantly reduce errors in high-noise quantum circuits.

The framework converges to the global optimum, ensuring the best possible mitigation.

Performance improvements are notable under narrowband quantum noise conditions.

Abstract

Quantum error mitigation (QEM) is a class of promising techniques capable of reducing the computational error of variational quantum algorithms tailored for current noisy intermediate-scale quantum computers. The recently proposed permutation-based methods are practically attractive, since they do not rely on any a priori information concerning the quantum channels. In this treatise, we propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. In particular, we show that the proposed filter design algorithm always converge to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods in the presence of narrowband quantum noise, corresponding to large-depth, high-error-rate quantum circuits.