Approximate quantum error correction for correlated noise

TL;DR

This paper investigates quantum error correction under correlated noise models, demonstrating limitations and possibilities for approximate correction of specific error types, contrasting with traditional independent noise assumptions.

Contribution

It introduces analysis of correlated noise models in quantum error correction, showing that controlled-X errors can be approximately corrected, while controlled phase errors cannot, highlighting new limitations and potentials.

Findings

Controlled-X errors can be approximately corrected with sub-constant error

Controlled phase errors cannot be approximately corrected with sub-constant error

Highlights limitations of quantum error correction under correlated noise

Abstract

Most of the research done on quantum error correction studies an error model in which each qubit is affected by noise, independently of the other qubits. In this paper we study a different noise model -- one in which the noise may be correlated with the qubits it acts upon. We show both positive and negative results. On the one hand, we show controlled-X errors cannot be perfectly corrected, yet can be approximately corrected with sub-constant approximation error. On the other hand, we show that no non-trivial quantum error correcting code can approximately correct controlled phase error with sub-constant approximation error.