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arXiv · 2512.18061

Correcting quantum errors one gradient step at a time

Manav Seksaria·Anil Prabhakar
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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.

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Manav Seksaria, Anil Prabhakar. 2025-12-19. Correcting quantum errors one gradient step at a time. https://arxiv.org/abs/2512.18061

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