# Overcoming barriers to scalability in variational quantum Monte Carlo

arXiv: https://arxiv.org/abs/2106.13308 · HTML: https://mlsanity.com/paper/2106.13308/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2021.

## Built on by (most cited first, 10 of 10)

- [Scalable neural quantum states architecture for quantum chemistry](https://mlsanity.com/paper/2208.05637/) (2022)
- [NNQS-Transformer: an Efficient and Scalable Neural Network Quantum States Approach for Ab initio Quantum Chemistry](https://mlsanity.com/paper/2306.16705/) (2023)
- [Retentive Neural Quantum States: Efficient Ans"atze for Ab Initio Quantum Chemistry](https://mlsanity.com/paper/2411.03900/) (2024)
- [Toward Neural Network Simulation of Variational Quantum Algorithms](https://mlsanity.com/paper/2211.02929/) (2022)
- [Numerical and geometrical aspects of flow-based variational quantum Monte Carlo](https://mlsanity.com/paper/2203.14824/) (2022)
- [Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry](https://mlsanity.com/paper/2509.12679/) (2025)
- [Probabilistic Computers for Neural Quantum States](https://mlsanity.com/paper/2512.24558/) (2025)
- [An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States](https://mlsanity.com/paper/2206.09241/) (2022)
- [Variational quantum and neural quantum states algorithms for the linear complementarity problem](https://mlsanity.com/paper/2504.08141/) (2025)
- [Neural Fourier Surrogates for Data Reuploading Quantum Neural Networks](https://mlsanity.com/paper/2610.00841/) (2026)

## Abstract (arXiv)

The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and the emerging hybrid quantum-classical computational paradigm of variational quantum algorithms. VQMC overcomes the curse of dimensionality by performing alternating steps of Monte Carlo sampling from a parametrized quantum state followed by gradient-based optimization. While VQMC has been applied to solve high-dimensional problems, it is known to be difficult to parallelize, primarily owing to the Markov Chain Monte Carlo (MCMC) sampling step. In this work, we explore the scalability of VQMC when autoregressive models, with exact sampling, are used in place of MCMC. This approach can exploit distributed-memory, shared-memory and/or GPU parallelism in the sampling task without any bottlenecks. In particular, we demonstrate the GPU-scalability of VQMC for solving up to ten-thousand dimensional combinatorial optimization problems.