Engineering Quantum Error Correction Codes Using Evolutionary Algorithms

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.