Regularization of Riemannian optimization: Application to process tomography and quantum machine learning

Abstract:Gradient descent algorithms on Riemannian manifolds have recently been proposed as a practical tool for optimizing quantum channels. We add rank-penalizing regularization terms to the cost functions of these methods (in the spirit of Lasso), driving the optimization towards channels with as few Kraus operators as possible. For quantum process tomography of rank-deficient channels, regularization both accelerates convergence and improves the fidelity of the solution compared to the unregularized case. For quantum classification tasks, it reduces the channel rank while maintaining classification accuracy, thereby revealing the minimum rank required by the given input data.

arXiv:2404.19659 [quant-ph]

(or arXiv:2404.19659v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2404.19659 Focus to learn more arXiv-issued DOI via DataCite

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