The Implications of Ignorance for Quantum Error Correction Thresholds

TL;DR

This paper explores how assumptions about noise models influence quantum error correction thresholds, demonstrating that thresholds can still exist for the 2D Toric code despite discrepancies in noise assumptions.

Contribution

It introduces a framework linking noise model assumptions to error correction thresholds, and proves threshold existence for the 2D Toric code via a mapping to the 2D random bond Ising model.

Findings

Thresholds depend on noise model assumptions

Thresholds can still exist beyond the distance limit

Mapping to Ising model aids threshold analysis

Abstract

Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for the likes of the Toric code require them to work well beyond this limit. We argue that without the assumption of being below the distance limit, the success of error correction is not only contingent on the noise model, but what the noise model is believed to be. Any discrepancy must adversely affect the threshold rate, and risks invalidating existing threshold theorems. We prove that for the 2D Toric code, suitable thresholds still exist by utilising a mapping to the 2D random bond Ising model.