Efficiency of neural quantum states in light of the quantum geometric tensor

• URL: http://arxiv.org/abs/2402.01565v3
• Date: Tue, 24 Sep 2024 07:21:07 GMT
• Title: Efficiency of neural quantum states in light of the quantum geometric tensor
• Authors: Sidhartha Dash, Luca Gravina, Filippo Vicentini, Michel Ferrero, Antoine Georges,
• Abstract summary: Neural quantum state (NQS) ans"atze have shown promise in variational Monte Carlo algorithms. We study the efficiency of a shallow neural network to represent the ground states in different phases of the spin-1 bilinear-biquadratic chain.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural quantum state (NQS) ans\"atze have shown promise in variational Monte Carlo algorithms by their theoretical capability of representing any quantum state. However, the reason behind the practical improvement in their performance with an increase in the number of parameters is not fully understood. In this work, we systematically study the efficiency of a shallow neural network to represent the ground states in different phases of the spin-1 bilinear-biquadratic chain, as the number of parameters increases. We train our ansatz by a supervised learning procedure, minimizing the infidelity w.r.t. the exact ground state. We observe that the accuracy of our ansatz improves with the network width in most cases, and eventually saturates. We demonstrate that this can be explained by looking at the spectrum of the quantum geometric tensor (QGT), particularly its rank. By introducing an appropriate indicator, we establish that the QGT rank provides a useful diagnostic for the practical representation power of an NQS ansatz.

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