Optimal correction of concatenated fault-tolerant quantum codes

TL;DR

This paper introduces an improved classical processing method for concatenated quantum error correction, enhancing error correction reliability by utilizing error likelihoods across multiple levels, achieving optimal correction performance.

Contribution

It proposes a novel error correction approach that leverages error likelihoods across concatenation levels, improving fault-tolerance in quantum codes.

Findings

Can correct errors up to half the code distance

Simulation results show improved error correction performance

Method is optimal for the tested code

Abstract

We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a concatenated code independently, our method uses information about the likelihood of errors having occurred at lower levels to maximize the probability of correctly interpreting error syndromes. Results of simulations of our method applied to the [[4,1,2]] subsystem code indicate that it can correct a number of discrete errors up to half of the distance of the concatenated code, which is optimal.