Closed form logical error rate approximations for surface codes

TL;DR

This paper introduces a new analytical method to accurately estimate logical error rates in surface codes, reducing reliance on costly simulations and enabling better quantum computer design choices.

Contribution

The authors develop a symmetry-based, closed-form approximation method for logical error rates in surface codes, improving accuracy and efficiency over existing simulation-based approaches.

Findings

The method accurately predicts logical error rates across various configurations.

It accounts for measurement errors for comprehensive analysis.

Reduces computational cost compared to traditional simulation methods.

Abstract

We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error, to provably good accuracy. We include an analysis of measurement errors to allow a more complete comparison of different surface code implementations.