Randomized compiling in fault-tolerant quantum computation

TL;DR

This paper introduces a randomized compiling algorithm that decoheres noise at the logical level in fault-tolerant quantum computation, improving error thresholds by mitigating coherent errors without significantly increasing circuit depth.

Contribution

The paper presents a general randomized compiling method that decoheres logical noise, enhancing fault-tolerance by reducing the impact of coherent errors in quantum error correction.

Findings

Decoheres logical noise, making errors more stochastic.

Does not significantly increase circuit depth.

Applicable to most fault-tolerant gadgets.

Abstract

Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which generic errors can be corrected. However, rigorous estimates of the threshold for generic errors are typically orders of magnitude worse than the threshold for stochastic Pauli errors. Specifically, coherent errors have a particularly harmful impact on the encoded space because they can map encoded states to superpositions of logical and error states. Further, coherent errors can add up and interfere over multiple rounds of error correction or between syndrome measurements, which may result in significantly worse errors than expected under a stochastic Pauli error model. In this paper, we present an algorithm which decoheres noise at the logical level, projecting the state of the system onto a logical state with a well-defined error. The algorithm does not significantly increase the depth of the logical circuit (and usually does not lead to any increase in depth), and applies generally to most fault-tolerant gadgets and error correction steps.