Error threshold estimates for surface code with loss of qubits

TL;DR

This paper develops an analytical method from statistical physics to estimate optimal error thresholds for surface codes under qubit loss, revealing their robustness and relating thresholds to critical points in spin glass models.

Contribution

It introduces a novel analytical approach to estimate surface code thresholds with qubit loss, connecting quantum error correction to spin glass physics.

Findings

Optimal thresholds are closely related to critical points in spin glass models.

The method shows surface codes are robust even with qubit loss.

Estimates compare favorably with previous numerical results.

Abstract

We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a finite-dimensional spin glass, which is disordered magnetic material. We compare our estimations to the heuristic numerical results reported in earlier studies. Further application of our method to the depolarizing channel, a natural generalization of the noise model, unveils its wider robustness even with loss of qubits.