Generality of the concatenated five-qubit code

TL;DR

This paper demonstrates that the concatenated five-qubit quantum error correction code can transform arbitrary noise channels into near-perfect qubit channels with extremely low error rates, using a simple characterization protocol.

Contribution

It introduces an explicit protocol to evaluate the performance of the concatenated five-qubit code and shows its general applicability depending only on initial entanglement fidelity.

Findings

The concatenated five-qubit code can achieve error rates below 10^{-5}.

Performance depends solely on initial entanglement fidelity.

The protocol for performance characterization is simple and explicit.

Abstract

In this work, a quantum error correction (QEC) procedure with the concatenated five-qubit code is used to construct a near-perfect effective qubit channel (with a error below $10^{-5}$) from arbitrary noise channels. The exact performance of the QEC is characterized by a Choi matrix, which can be obtained via a simple and explicit protocol. In a noise model with five free parameters, our numerical results indicate that the concatenated five-qubit code is general: To construct a near-perfect effective channel from the noise channels, the necessary size of the concatenated five-qubit code depends only on the entanglement fidelity of the initial noise channels.