Surface code fidelity at finite temperatures

TL;DR

This paper investigates how finite-temperature environments affect the fidelity of surface codes, revealing that quantum error correction remains effective under certain conditions despite environment-induced interactions.

Contribution

It provides a detailed analysis of surface code fidelity at finite temperatures across different environmental spectral densities, highlighting the existence of a temperature-sensitive threshold.

Findings

Quantum error correction remains effective at finite temperatures.

Thresholds depend on environment type and temperature.

Critical coupling varies with environment parameters and cycle duration.

Abstract

We study the dependence of the fidelity of the surface code in the presence of a single finite-temperature massless bosonic environment after a quantum error correction cycle. The three standard types of environment are considered: super-Ohmic, Ohmic, and sub-Ohmic. Our results show that, for regimes relevant to current experiments, quantum error correction works well even in the presence of environment-induced, long-range inter-qubit interactions. A threshold always exists at finite temperatures, although its temperature dependence is very sensitive to the type of environment. For the super-Ohmic case, the critical coupling constant separating high- from low-fidelity decreases with increasing temperature. For both Ohmic and super-Ohmic cases, the dependence of the critical coupling on temperature is weak. In all cases, the critical coupling is determined by microscopic parameters of the environment. For the sub-Ohmic case, it also depends strongly on the duration of the QEC cycle.