Simulating the Effects of Quantum Error-correction Schemes

TL;DR

This paper uses simulation to analyze the effectiveness of various quantum error-correcting codes and fault-tolerant operations, highlighting their performance when the correction process introduces errors.

Contribution

It provides a comparative simulation study of key QEC codes and fault-tolerant procedures, emphasizing their robustness against errors during correction.

Findings

Five, seven, and nine qubit codes tested

Fault-tolerant operations improve error resilience

Simulation results guide optimal code selection

Abstract

It is important to protect quantum information against decoherence and operational errors, and quantum error-correcting (QEC) codes are the keys to solving this problem. Of course, just the existence of codes is not efficient. It is necessary to perform operations fault-tolerantly on encoded states because error-correction process (i.e., encoding, decoding, syndrome measurement and recovery) itself induces an error. By using simulation, this paper investigates the effects of some important QEC codes (the five qubit code, the seven qubit code and the nine qubit code) and their fault-tolerant operations when the error-correction process itself induces an error. The corresponding results, statistics and analyses are presented in this paper.