Neural Quantum States in Mixed Precision

2026-01-28

AI Summary

This study investigates the applicability of mixed-precision arithmetic in neural-network-based variational Monte Carlo (VMC) simulations, aiming to enhance computational efficiency and scalability while preserving high accuracy in quantum many-body system modeling. Addressing the sensitivity of Metropolis-Hastings sampling to numerical errors, the work establishes the first theoretical error bounds for Markov chain Monte Carlo (MCMC)-based machine learning methods under mixed-precision computation. It rigorously demonstrates that half-precision floating-point arithmetic can be safely employed in neural quantum state sampling without compromising accuracy. Experimental results confirm that a substantial portion of the VMC workload can be migrated to half precision, yielding significant improvements in performance and energy efficiency while maintaining solution fidelity.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Security and Privacy: Security and privacy of machine learning and AI applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Scientific computing has long relied on double precision (64-bit floating point) arithmetic to guarantee accuracy in simulations of real-world phenomena. However, the growing availability of hardware accelerators such as Graphics Processing Units (GPUs) has made low-precision formats attractive due to their superior performance, reduced memory footprint, and improved energy efficiency. In this work, we investigate the role of mixed-precision arithmetic in neural-network based Variational Monte Carlo (VMC), a widely used method for solving computationally otherwise intractable quantum many-body systems. We first derive general analytical bounds on the error introduced by reduced precision on Metropolis-Hastings MCMC, and then empirically validate these bounds on the use-case of VMC. We demonstrate that significant portions of the algorithm, in particular, sampling the quantum state, can be executed in half precision without loss of accuracy. More broadly, this work provides a theoretical framework to assess the applicability of mixed-precision arithmetic in machine-learning approaches that rely on MCMC sampling. In the context of VMC, we additionally demonstrate the practical effectiveness of mixed-precision strategies, enabling more scalable and energy-efficient simulations of quantum many-body systems.

Problem

• mixed-precision arithmetic
• neural quantum states
• variational Monte Carlo
• quantum many-body systems
• MCMC sampling

Innovation

• mixed-precision arithmetic
• neural quantum states
• variational Monte Carlo
• MCMC sampling
• half-precision