# A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo

## TL;DR

This paper introduces a memory-efficient modification to the linear method in variational Monte Carlo, enabling large parameter optimizations on modern supercomputers and demonstrating its effectiveness on molecular and condensed matter systems.

## Contribution

A novel blocked linear method that significantly reduces memory requirements for large-scale variational Monte Carlo optimizations, compatible with excited state principles.

## Key findings

- Reduces memory per process from tens of GB to hundreds of MB.
- Successfully applied to small molecules with complex wave functions.
- Integrated into QMCPACK for practical large-scale quantum simulations.

## Abstract

We present a modification to variational Monte Carlo's linear method optimization scheme that addresses a critical memory bottleneck while maintaining compatibility with both the traditional ground state variational principle and our recently-introduced variational principle for excited states. For wave function ansatzes with tens of thousands of variables, our modification reduces the required memory per parallel process from tens of gigabytes to hundreds of megabytes, making the methodology a much better fit for modern supercomputer architectures in which data communication and per-process memory consumption are primary concerns. We verify the efficacy of the new optimization scheme in small molecule tests involving both the Hilbert space Jastrow antisymmetric geminal power ansatz and real space multi-Slater Jastrow expansions. Satisfied with its performance, we have added the optimizer to the QMCPACK software package, with which we demonstrate on a hydrogen ring a prototype approach for making systematically convergent, non-perturbative predictions of Mott-insulators' optical band gaps.