Syndrome aware mitigation of logical errors

TL;DR

This paper introduces syndrome-aware logical error mitigation (SALEM), a method that leverages syndrome data during error correction to exponentially reduce runtime overhead and significantly increase the size of reliably executable quantum circuits.

Contribution

SALEM is a novel approach that combines error correction and error mitigation using syndrome data, outperforming previous schemes and even physical error mitigation above the fault-tolerance threshold.

Findings

SALEM reduces runtime overhead exponentially compared to previous LEM schemes.

SALEM increases the size of reliably executable quantum computations by orders of magnitude.

SALEM can outperform physical error mitigation even above the fault-tolerance threshold.

Abstract

Broad applications of quantum computers will require error correction (EC). However, quantum hardware roadmaps indicate that physical qubit numbers will remain limited in the foreseeable future, leading to residual logical errors that limit the size and accuracy of achievable computations. Recent work suggested logical error mitigation (LEM), which applies known error mitigation (EM) methods to logical errors, eliminating their effect at the cost of a runtime overhead. Improving the efficiency of LEM is crucial for increasing the logical circuit volumes it enables to execute. We introduce syndrome-aware logical error mitigation (SALEM), which makes use of the syndrome data measured during error correction, when mitigating the logical errors. The runtime overhead of SALEM is exponentially lower than that of previously proposed LEM schemes, resulting in significantly increased circuit volumes that can be executed accurately. Notably, relative to the routinely used combination of error correction and syndrome rejection (post-selection), SALEM increases the size of reliably executable computations by orders of magnitude. In this practical setting in which space and time are both resources that need to be optimized, our work reveals a surprising phenomenon: SALEM, which tightly combines EC with EM, can outperform physical EM even above the standard fault-tolerance threshold. Thus, SALEM can make use of EC in regimes of physical error rates at which EC is commonly deemed useless.