dc.contributor.author Becker, S dc.contributor.author Li, W dc.date.accessioned 2021-01-24T16:16:26Z dc.date.available 2021-01-24T16:16:26Z dc.date.issued 2021 dc.date.submitted 2020-09-15 dc.identifier.issn 0022-4715 dc.identifier.other s10955-020-02682-1 dc.identifier.other 2682 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/316643 dc.description.abstract AbstractIn this article, we introduce a new approach towards the statistical learning problem $$\mathrm{argmin}_{\rho (\theta ) \in {\mathcal {P}}_{\theta }} W_{Q}^2 (\rho _{\star },\rho (\theta ))$$ argmin ρ ( θ ) P θ W Q 2 ( ρ , ρ ( θ ) ) to approximate a target quantum state $$\rho _{\star }$$ ρ by a set of parametrized quantum states $$\rho (\theta )$$ ρ ( θ ) in a quantum $$L^2$$ L 2 -Wasserstein metric. We solve this estimation problem by considering Wasserstein natural gradient flows for density operators on finite-dimensional $$C^*$$ 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. dc.language en dc.publisher Springer Science and Business Media LLC dc.rights Attribution 4.0 International (CC BY 4.0) dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.subject Article dc.subject Quantum transport information geometry dc.subject Quantum state estimation dc.subject Quantum Wasserstein information matrix dc.subject Quantum Wasserstein natural gradient dc.subject Quantum Schrödinger bridge problem dc.title Quantum Statistical Learning via Quantum Wasserstein Natural Gradient dc.type Article dc.date.updated 2021-01-24T16:16:26Z prism.issueIdentifier 1 prism.publicationName Journal of Statistical Physics prism.volume 182 dc.identifier.doi 10.17863/CAM.63755 dcterms.dateAccepted 2020-12-07 rioxxterms.versionofrecord 10.1007/s10955-020-02682-1 rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.identifier.eissn 1572-9613 pubs.funder-project-id Engineering and Physical Sciences Research Council (EP/L016516/1) cam.issuedOnline 2021-01-07
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's licence is described as Attribution 4.0 International (CC BY 4.0)