Towards Neural Variational Monte Carlo That Scales Linearly with System Size
Abstract
Quantum manybody problems are some of the most challenging problems in science and are central to demystifying some exotic quantum phenomena, e.g., hightemperature 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 runtime 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 VectorQuantized Neural Quantum States (VQNQS) that utilizes vectorquantization techniques to leverage redundancies in the localenergy calculations of the VMC algorithm  the source of the quadratic scaling. In our preliminary experiments, we demonstrate VQNQS 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 localenergy calculation.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2212.11296
 arXiv:
 arXiv:2212.11296
 Bibcode:
 2022arXiv221211296S
 Keywords:

 Quantum Physics;
 Computer Science  Machine Learning;
 Computer Science  Neural and Evolutionary Computing
 EPrint:
 Appeared on NeurIPS 2022 AI for Science Workshop (a nonarchival poster presentation)