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Abstract
Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose (unnormalised) amplitudes in a fixed basis 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 (2017 Science 355 602) 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 making them uniquely unbiased geometrically. The appearance of GHZ correlators also relates NQS to canonical polyadic decompositions of tensors. Another immediate implication of the NQS equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superpositions 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 language | English |
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Article number | 135301 |
Number of pages | 40 |
Journal | Journal of Physics A: Mathematical and General |
Volume | 51 |
Issue number | 13 |
Early online date | 23 Feb 2018 |
DOIs | |
Publication status | Published - 23 Feb 2018 |
Bibliographical note
40 pages, 27 figures. Comments most welcomeKeywords
- correlator product states
- neural-network quantum states
- restricted Boltzmann machines
- tensor network theory
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy
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Dive into the research topics of 'Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks'. Together they form a unique fingerprint.Projects
- 1 Finished
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Emerging Correlations from Strong Driving: A Tensor Network Projection Variational Monte Carlo Approach to 2D Quantum Lattice Systems
Clark, S. (PI)
Engineering and Physical Sciences Research Council
1/08/17 → 31/07/19
Project: Research council