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.

翻译：科学计算长期以来依赖双精度（64位浮点）算术来保证对现实世界现象模拟的准确性。然而，随着图形处理器（GPU）等硬件加速器的日益普及，低精度格式因其卓越性能、更低内存占用和更高能效而变得极具吸引力。在本工作中，我们研究了混合精度算术在基于神经网络的变分蒙特卡洛（VMC）方法中的作用，VMC是求解计算上难以处理的量子多体系统的一种广泛应用的方法。我们首先推导了降低精度对Metropolis-Hastings MCMC算法引入误差的一般解析界，随后在VMC的实际用例中对这些界进行了实证验证。我们证明该算法的关键部分，特别是量子态采样，可以在半精度下执行而不损失精度。更广泛而言，本工作为评估混合精度算术在依赖MCMC采样的机器学习方法中的适用性提供了一个理论框架。在VMC的背景下，我们进一步展示了混合精度策略的实际有效性，从而能够实现更具可扩展性和更高能效的量子多体系统模拟。