TY - JOUR

T1 - Investigating Network Parameters in Neural-Network Quantum States

AU - Nomura, Yusuke

N1 - Funding Information:
Acknowledgment We are grateful for the helpful discussions with Nobuyuki Yoshioka. This work was supported by Grant-in-Aids for Scientific Research (JSPS KAKENHI) (Grants Nos. 16H06345, 20K14423, and 21H01041) and MEXT as “Program for Promoting Researches on the Supercomputer Fugaku” (Basic Science for Emergence and Functionality in Quantum Matter —Innovative Strongly-Correlated Electron Science by Integration of “Fugaku” and Frontier Experiments—, JPMXP1020200104).
Publisher Copyright:
© 2022 The Physical Society of Japan

PY - 2022/5/15

Y1 - 2022/5/15

N2 - Recently, quantum-state representation using artificial neural networks has started to be recognized as a powerful tool. However, due to the black-box nature of machine learning, it is difficult to analyze what machine learns or why it is powerful. Here, by applying one of the simplest neural networks, the restricted Boltzmann machine (RBM), to the ground-state representation of the one-dimensional (1D) transverse-field Ising (TFI) model, we make an attempt to directly analyze the optimized network parameters. In the RBM optimization, a zero-temperature quantum state is mapped onto a finite-temperature classical state of the extended Ising spins that constitute the RBM. We find that the quantum phase transition from the ordered phase to the disordered phase in the 1D TFI model by increasing the transverse field is clearly reflected in the behaviors of the optimized RBM parameters and hence in the finite-temperature phase diagram of the classical RBM Ising system. The present finding of a correspondence between the neural-network parameters and quantum phases suggests that a careful investigation of the neural-network parameters may provide a new route to extracting nontrivial physical insights from the neural-network wave functions.

AB - Recently, quantum-state representation using artificial neural networks has started to be recognized as a powerful tool. However, due to the black-box nature of machine learning, it is difficult to analyze what machine learns or why it is powerful. Here, by applying one of the simplest neural networks, the restricted Boltzmann machine (RBM), to the ground-state representation of the one-dimensional (1D) transverse-field Ising (TFI) model, we make an attempt to directly analyze the optimized network parameters. In the RBM optimization, a zero-temperature quantum state is mapped onto a finite-temperature classical state of the extended Ising spins that constitute the RBM. We find that the quantum phase transition from the ordered phase to the disordered phase in the 1D TFI model by increasing the transverse field is clearly reflected in the behaviors of the optimized RBM parameters and hence in the finite-temperature phase diagram of the classical RBM Ising system. The present finding of a correspondence between the neural-network parameters and quantum phases suggests that a careful investigation of the neural-network parameters may provide a new route to extracting nontrivial physical insights from the neural-network wave functions.

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U2 - 10.7566/JPSJ.91.054709

DO - 10.7566/JPSJ.91.054709

M3 - Article

AN - SCOPUS:85129586405

SN - 0031-9015

VL - 91

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

IS - 5

M1 - 054709

ER -