https://doi.org/10.1007/s10955-020-02682-1

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Document Type

Article

Abstract

In this article, we introduce a new approach towards the statistical learning problem argmin pΘis an element of P Θ WQ2(P *,p(Θ)) to approximate a target quantum state p* by a set of parametrized quantum states p(Θ) in a quantum L2-Wasserstein metric. We solve this estimation problem by considering Wasserstein natural gradient flows for density operators on finite-dimensional C* algebras. For continuous parametric models of density operators, we pull back the quantum Wasserstein metric such that the parameter space becomes a Riemannian manifold with quantum Wasserstein information matrix. Using a quantum analogue of the Benamou-Brenier formula, we derive a natural gradient flow on the parameter space. We also discuss certain continuous-variable quantum states by studying the transport of the associated Wigner probability distributions.

Digital Object Identifier (DOI)

https://doi.org/10.1007/s10955-020-02682-1

APA Citation

Becker, S., & Li, W. (2021). Quantum Statistical Learning via Quantum Wasserstein Natural Gradient. Journal of Statistical Physics, 182(1). https://doi.org/10.1007/s10955-020-02682-1

Rights

© The Author(s) 2020 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Mathematics Commons

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