Towards practical classical processing for the surface code: timing analysis

TL;DR

This paper analyzes the timing performance of a classical processing algorithm for surface codes in quantum error correction, demonstrating it operates efficiently with quadratic time complexity across various code sizes and error rates.

Contribution

It provides an empirical timing analysis of a minimum weight perfect matching implementation for surface codes, showing it scales as O(n^2) for large code distances.

Findings

Requires only O(n^2) average time per error correction round

Efficiently handles code distances from 4 to 512

Always finds a true minimum weight perfect matching

Abstract

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum weight perfect matching algorithm. Our implementation performs the classical processing associated with an nxn lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n^2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum weight perfect matching.