Correcting quantum errors one gradient step at a time

TL;DR

This paper presents a gradient-based optimization method for quantum error correction codewords, improving fidelity under noise by differentiating and descending on complex coefficients, validated on multiple codes.

Contribution

Introduces a scalable, deterministic gradient-based approach for optimizing quantum error correction codewords tailored to specific noise channels.

Findings

Fidelity improved from 0.783 to 0.915 under isotropic Pauli noise.

Method validated on repetition and [[5, 1, 3]] codes.

Approach is highly parallelisable and scalable.

Abstract

In this work, we introduce a general, gradient-based method that optimises codewords for a given noise channel and fixed recovery. We do so by differentiating fidelity and descending on the complex coefficients using finite-difference Wirtinger gradients with soft penalties to promote orthonormalisation. We validate the gradients on symmetry checks (XXX/ZZZ repetition codes) and the $[[5, 1, 3]]$ code, then demonstrate substantial gains under isotropic Pauli noise with Petz recovery: fidelity improves from 0.783 to 0.915 in 100 steps for an isotropic Pauli noise of strength 0.05. The procedure is deterministic, highly parallelisable, and highly scalable.