Surface Code Threshold in the Presence of Correlated Errors

TL;DR

This paper investigates how correlated errors from a bosonic environment affect the surface code's fidelity, linking error thresholds to phase transitions in a statistical model.

Contribution

It introduces a novel approach by mapping the surface code's error dynamics with correlated errors onto a statistical spin model to analyze error thresholds.

Findings

Error threshold is connected to an order-disorder phase transition.

Threshold depends on bath parameters and error correlation range.

Phase transition analysis provides insights into code robustness.

Abstract

We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a statistical spin model, we show that the existence of an error threshold is related to the appearance of an order-disorder phase transition in the statistical model in the thermodynamic limit. This allows us to relate the error threshold to bath parameters and to the spatial range of the correlated errors.