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arXiv · 2310.05715

A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States

Riccardo Rende·Luciano Loris Viteritti·Lorenzo Bardone·Federico Becca·Sebastian Goldt
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Abstract

Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are challenging to optimize using traditional methods, as gradient descent. Stochastic Reconfiguration (SR) has been effective with a limited number of parameters, but becomes impractical beyond a few thousand parameters. Here, we leverage a simple linear algebra identity to show that SR can be employed even in the deep learning scenario. We demonstrate the effectiveness of our method by optimizing a Deep Transformer architecture with $3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square lattice, a challenging benchmark in highly-frustrated magnetism. This work marks a significant step forward in the scalability and efficiency of SR for Neural-Network Quantum States, making them a promising method to investigate unknown quantum phases of matter, where other methods struggle.

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Riccardo Rende, Luciano Loris Viteritti, Lorenzo Bardone, Federico Becca, Sebastian Goldt. 2023-10-09. A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States. https://doi.org/10.1038/s42005-024-01732-4

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