Repetition Versus Noiseless Quantum Codes For Correlated Errors

TL;DR

This paper compares the effectiveness of repetition and noiseless quantum codes in correcting correlated errors in quantum memory channels, identifying a threshold of correlation strength where one outperforms the other.

Contribution

It introduces a comparative analysis of simple quantum error correcting codes under correlated noise, highlighting a threshold for optimal code selection based on correlation strength.

Findings

Repetition codes outperform noiseless codes below a certain correlation threshold.

Noiseless codes are more effective when correlation strength exceeds the threshold.

A quantitative threshold for correlation strength determines the optimal code choice.

Abstract

We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity as function of the error probability and degree of memory. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold for the correlation strength that allows to select the code with better performance.