Towards Neural Variational Monte Carlo That Scales Linearly with System Size

• URL: http://arxiv.org/abs/2212.11296v1
• Date: Wed, 21 Dec 2022 19:00:04 GMT
• Title: Towards Neural Variational Monte Carlo That Scales Linearly with System Size
• Authors: Or Sharir, Garnet Kin-Lic Chan and Anima Anandkumar
• Abstract summary: Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
• Score: 67.09349921751341
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum many-body problems are some of the most challenging problems in science and are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, coupled with the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. However, the run-time of this approach scales quadratically with the number of simulated particles, constraining the practically usable NN to - in machine learning terms - minuscule sizes (<10M parameters). Considering the many breakthroughs brought by extreme NN in the +1B parameters scale to other domains, lifting this constraint could significantly expand the set of quantum systems we can accurately simulate on classical computers, both in size and complexity. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm - the source of the quadratic scaling. In our preliminary experiments, we demonstrate VQ-NQS ability to reproduce the ground state of the 2D Heisenberg model across various system sizes, while reporting a significant reduction of about ${\times}10$ in the number of FLOPs in the local-energy calculation.

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