## Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

Marin Bukov, Markus Schmitt, Maxime Dupont

SciPost Phys. 10, 147 (2021) · published 17 June 2021

- doi: 10.21468/SciPostPhys.10.6.147
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### Abstract

Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

### Cited by 42

### Authors / Affiliations: mappings to Contributors and Organizations

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^{1}^{2}Marin Bukov, -
^{1}Markus Schmitt, -
^{1}^{3}Maxime Dupont

^{1}University of California, Berkeley [UCBL]^{2}Софийски университет / Sofia University^{3}Lawrence Berkeley National Laboratory [LBNL]

- Bulgarian National Science Fund (through Organization: Bulgarian Science Fund [BSF])
- Deutsche Akademie der Naturforscher Leopoldina - Nationale Akademie der Wissenschaften (through Organization: Nationale Akademie der Wissenschaften Leopoldina / German National Academy of Sciences Leopoldina)
- Gordon and Betty Moore Foundation
- Horizon 2020 (through Organization: European Commission [EC])
- Simons Foundation
- United States Department of Energy [DOE]