Gaussian Process States: A data-driven representation of quantum many-body physics

• URL: http://arxiv.org/abs/2002.12208v4
• Date: Thu, 17 Sep 2020 12:07:25 GMT
• Title: Gaussian Process States: A data-driven representation of quantum many-body physics
• Authors: Aldo Glielmo, Yannic Rath, Gabor Csanyi, Alessandro De Vita and George H. Booth
• Abstract summary: We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
• Score: 59.7232780552418
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a novel, non-parametric form for compactly representing entangled many-body quantum states, which we call a `Gaussian Process State'. In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way the non-local physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a `universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size. We develop two numerical approaches which can learn this form directly: a fragmentation approach, and direct variational optimization, and apply these schemes to the Fermionic Hubbard model. We find competitive or superior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.

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