TY  - JOUR
EP  - 7
AV  - public
N2  - 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.
JF  - npj Quantum Information
UR  - https://doi.org/10.1038/s41534-018-0077-z
VL  - 4
A1  - Rocchetto, A
A1  - Grant, E
A1  - Strelchuk, S
A1  - Carleo, G
A1  - Severini, S
KW  - Science & Technology
KW  -  Physical Sciences
KW  -  Physics
KW  -  Applied
KW  -  Physics
KW  -  Atomic
KW  -  Molecular & Chemical
KW  -  Physics
KW  -  Condensed Matter
KW  -  Physics
KW  -  ENTANGLED PAIR STATES
KW  -  MATRIX PRODUCT STATES
KW  -  NETWORKS
KW  -  SYSTEMS
KW  -  BOUNDS
ID  - discovery10057278
N1  - 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/
PB  - SPRINGERNATURE
Y1  - 2018/06/28/
SN  - 2056-6387
TI  - Learning hard quantum distributions with variational autoencoders
ER  -