Neural Quantum States in Mixed Precision

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.

💡 Research Summary

The paper investigates the use of mixed‑precision arithmetic in neural‑network based Variational Monte Carlo (VMC), focusing on the Metropolis‑Hastings (MH) sampling step that dominates the computational cost of quantum many‑body simulations. The authors first construct a theoretical model for the numerical error introduced by reduced‑precision evaluation of the log‑probability: they treat the perturbation δ(x) as an additive Gaussian random variable with mean μ and variance σ². Under this model, the Kullback‑Leibler divergence between the exact target distribution π and the perturbed distribution π̃ is σ²/2, which via Pinsker’s inequality yields a total‑variation (TV) distance bound of σ/2. This provides a conservative estimate of the bias that finite‑precision arithmetic can induce in any bounded observable, such as the VMC energy.

Recognizing that this bound ignores the dynamics of the Markov chain, the authors incorporate mixing properties using the Doeblin minorization condition. Assuming the exact MH kernel P satisfies P(x,·) ≥ ξ ν(·) for all states, the chain contracts in TV distance with rate r = 1 − ξ. They then prove that the stationary distribution π̃ of the perturbed kernel P̃ deviates from π by at most ‖π̃ ΔP‖₁ / (1 − r), where ΔP = P̃ − P. This tighter bound shows that fast‑mixing chains (small r) are robust to small kernel perturbations caused by low‑precision errors.

The analysis of ΔP reveals three regimes for the acceptance ratio s(x,y) = exp