Document Type
Article
Abstract
In this article, we introduce a new approach towards the statistical learning problem argminρ(θ )∈Pθ W2 Q(ρ*, ρ(θ )) to approximate a target quantum state ρ* by a set of parametrized quantum states ρ(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)
Publication Info
Published in Journal of Statistical Physics, Volume 182, 2021.
APA Citation
Becker, S., & Li, W. (2021). Quantum Statistical Learning via Quantum Wasserstein Natural Gradient. Journal of Statistical Physics, 182. https://doi.org/10.1007/s10955-020-02682-1
Rights
© The Author(s) 2020
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