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Learning hard quantum distributions with variational autoencoders

Rocchetto, A; Grant, E; Strelchuk, S; Carleo, G; Severini, S; (2018) Learning hard quantum distributions with variational autoencoders. npj Quantum Information , 4 , Article 28. 10.1038/s41534-018-0077-z. Green open access

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The exact description of many-body quantum systems represents one of the major challenges in modern physics, because it requires an amount of computational resources that scales exponentially with the size of the system. Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a practically usable deep architecture for representing and sampling from probability distributions of quantum states. Our representation is based on variational auto-encoders, a type of generative model in the form of a neural network. We show that this model is able to learn efficient representations of states that are easy to simulate classically and can compress states that are not classically tractable. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterizing states of the size expected in first generation quantum hardware.

Type: Article
Title: Learning hard quantum distributions with variational autoencoders
Open access status: An open access version is available from UCL Discovery
DOI: 10.1038/s41534-018-0077-z
Publisher version: https://doi.org/10.1038/s41534-018-0077-z
Language: English
Additional information: 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/
Keywords: Science & Technology, Physical Sciences, Physics, Applied, Physics, Atomic, Molecular & Chemical, Physics, Condensed Matter, Physics, ENTANGLED PAIR STATES, MATRIX PRODUCT STATES, NETWORKS, SYSTEMS, BOUNDS
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10057278
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