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Expressive power of complex-valued restricted Boltzmann machines for solving nonstoquastic Hamiltonians

Park, Chae-Yeun and Kastoryano, Michael J. (2022) Expressive power of complex-valued restricted Boltzmann machines for solving nonstoquastic Hamiltonians. Physical Review B, 106 (13). Art. No. 134437. ISSN 2469-9950. doi:10.1103/physrevb.106.134437.

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Variational Monte Carlo with neural network quantum states has proven to be a promising avenue for evaluating the ground-state energy of spin Hamiltonians. However, despite continuous efforts the performance of the method on frustrated Hamiltonians remains significantly worse than those on stoquastic Hamiltonians that are sign free. We present a detailed and systematic study of restricted Boltzmann machine (RBM) based variational Monte Carlo for quantum spin chains, resolving how relevant stoquasticity is in this setting. We show that in most cases, when the Hamiltonian is phase connected with a stoquastic point, the complex RBM state can faithfully represent the ground state, and local quantities can be evaluated efficiently by sampling. On the other hand, we identify several new phases that are challenging for the RBM Ansatz, including nontopological robust nonstoquastic phases as well as stoquastic phases where sampling is nevertheless inefficient. We further find that, in contrast to the common belief, an accurate neural network representation of ground states in nonstoquastic phases is hindered not only by the sign structure but also by their amplitudes.

Item Type:Article
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URLURL TypeDescription
Park, Chae-Yeun0000-0003-4430-1000
Kastoryano, Michael J.0000-0001-5233-7957
Additional Information:The authors thank Prof. Simon Trebst, Dr. Ciarán Hickey, and Dr. Markus Schmitt for helpful discussions. This project was funded by the Deutsche Forschungsgemeinschaft under Germany's Excellence Strategy - Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 - 390534769 and within the CRC network TR 183 (Project Grant No. 277101999) as part of Project No. B01. The numerical simulations were performed on the JUWELS and JUWELS Booster clusters at the Forschungszentrum Juelich. This work presented in the manuscript was completed while both authors were at the University of Cologne. Source code used in this paper is available at Ref. [60].
Group:AWS Center for Quantum Computing
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EXC 2004/1-390534769
Deutsche Forschungsgemeinschaft (DFG)277101999
Issue or Number:13
Record Number:CaltechAUTHORS:20230113-705133800.4
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118792
Deposited By: Research Services Depository
Deposited On:01 Feb 2023 18:18
Last Modified:01 Feb 2023 18:18

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