Fault Tolerant Quantum Error Mitigation

TL;DR

This paper introduces fault-tolerant quantum error mitigation (FTQEM), showing how it can exponentially reduce errors using code concatenation and fault-tolerant operations, with analytical thresholds and practical demonstrations.

Contribution

It demonstrates that fault-tolerant operations significantly enhance symmetry-based error mitigation and provides analytical error thresholds for FTQEM with concatenated codes.

Findings

FTQEM can exponentially suppress errors with code concatenation.

Fault-tolerant operations improve the performance of symmetry-based error mitigation.

Numerical simulations and hardware experiments validate FTQEM benefits.

Abstract

Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based error mitigation techniques. We also demonstrate that similar to results in fault tolerant quantum computing, code concatenation in fault-tolerant quantum error mitigation (FTQEM) can exponentially suppress the errors to arbitrary levels. For a family of circuits, we provide analytical error thresholds for FTQEM with the repetition code. These circuits include a set of quantum circuits that can generate all of reversible classical computing. The post-selection rate in FTQEM can also be increased by correcting some of the outcomes. Our threshold results can also be viewed from the perspective of quantifying the number of gate operations we can delay checking the stabilizers in a concatenated code before errors overwhelm the encoding. The benefits of FTQEM are demonstrated with numerical simulations and hardware demonstrations.