Engineering Quantum Error Correction Codes Using Evolutionary Algorithms

TL;DR

This paper introduces an evolutionary algorithm to optimize quantum error correction codes tailored for specific error models, demonstrating improved code distances and error rates for various qubit configurations.

Contribution

It presents a novel evolutionary algorithm that efficiently searches for optimal stabiliser codes for given error models and code parameters, including a new method for representing and evolving stabiliser codes.

Findings

The algorithm finds stabiliser codes with distances close to the best-known codes for up to 20 qubits.

It optimizes CSS codes, achieving higher distances than existing codes.

It significantly reduces undetectable error rates for biased error models, exemplified by the [[12, 1]] code.

Abstract

Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored for a particular error model may have much better performance. In this work, we present a novel evolutionary algorithm which searches for an optimal stabiliser code for a given error model, number of physical qubits and number of encoded qubits. We demonstrate an efficient representation of stabiliser codes as binary strings -- this allows for random generation of valid stabiliser codes, as well as mutation and crossing of codes. Our algorithm finds stabiliser codes whose distance closely matches the best-known-distance codes of codetables.de for n <= 20 physical qubits. We perform a search for optimal distance CSS codes, and compare their distance to the best-known-codes. Finally, we show that the algorithm can be used to optimise stabiliser codes for biased error models, demonstrating a significant improvement in the undetectable error rate for [[12, 1]] codes versus the best-known-distance code with the same parameters. As part of this work, we also introduce an evolutionary algorithm QDistEvol for finding the distance of quantum error correction codes.