Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks

Stephen R. Clark

Research output: Contribution to journalArticle

11 Citations (Scopus)
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Abstract

Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer Science 355, 602 (2017) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators, which are related to a canonical polyadic decomposition of a tensor, making them uniquely unbiased geometrically. Another immediate implication of the equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superposition of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.
Original languageEnglish
Article number135301
Number of pages40
JournalJournal of Physics A: Mathematical and General
Volume51
Issue number13
Early online date23 Feb 2018
DOIs
Publication statusPublished - 3 Apr 2018

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Correlator
Quantum State
correlators
Tensor
tensors
Neural Networks
products
Canonical Decomposition
machine learning
Gluing
Lattice System
Ludwig Boltzmann
Quantum Systems
Superposition
Fermions
Overlapping
equivalence
Machine Learning
High-dimensional
fermions

Keywords

  • quant-ph
  • cond-mat.str-el

Cite this

Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks. / Clark, Stephen R.

In: Journal of Physics A: Mathematical and General, Vol. 51, No. 13, 135301, 03.04.2018.

Research output: Contribution to journalArticle

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