Error Correction and Degeneracy in Surface Codes Suffering Loss

TL;DR

This paper explores how topological quantum memories can tolerate both loss and computational errors, analyzing the effects of degeneracy on error correction thresholds and phase transition estimates.

Contribution

It provides a detailed analysis of degeneracy effects in surface code error correction under loss, and discusses implications for phase transition temperature estimation.

Findings

Degeneracy impacts error correction thresholds in surface codes.

Tradeoff between loss and computational error thresholds is characterized.

Degeneracy influences phase transition temperature estimates in related models.

Abstract

Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss errors and computational errors, with a graceful tradeoff between the threshold for each. We further discuss a number of subtleties that arise when implementing error correction on topological memories. We particularly focus on the role played by degeneracy in the matching algorithms, and present a systematic study its effects on thresholds. We also discuss some of the implications of degeneracy for estimating phase transition temperatures in the random bond Ising model.