Correcting quantum errors one gradient step at a time
Quantum Physics
2025-12-23 v1 Numerical Analysis
Numerical Analysis
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 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.
Cite
@article{arxiv.2512.18061,
title = {Correcting quantum errors one gradient step at a time},
author = {Manav Seksaria and Anil Prabhakar},
journal= {arXiv preprint arXiv:2512.18061},
year = {2025}
}