Probabilistic Computing on FPGAs Enables Fast Sampling of Neural Quantum States

Simulating the behaviour of complex quantum systems presents a significant computational challenge, particularly when dealing with many interacting particles, and researchers continually seek methods to overcome these limitations. Shuvro Chowdhury, Jasper Pieterse, and Navid Anjum Aadit, along with colleagues from the University of California, Santa Barbara, and Radboud University, now demonstrate a powerful new approach using probabilistic computers to model these intricate systems. The team successfully implements a specialised computer on field programmable gate arrays, effectively accelerating the process of sampling neural states, which represent the quantum behaviour of many-body systems. This innovation allows them to accurately calculate ground-state energies for systems containing up to 6400 spins, and to train deeper, more efficient neural networks, representing a substantial step towards simulating increasingly complex quantum phenomena and potentially unlocking new discoveries in materials science and fundamental physics.

Monte Carlo sampling limits their scaling to large system sizes. Here, we address this challenge by combining sparse Boltzmann machine architectures with probabilistic computing hardware. We implement a probabilistic computer on field-programmable gate arrays (FPGAs) and use it as a fast sampler for energy-based neural quantum states. For the two-dimensional transverse-field Ising model at criticality, we obtain accurate ground-state energies for lattices up to 80×80 (6400 spins) using a custom multi-FPGA cluster.

Deep Boltzmann Machines on FPGA Accelerators

This document provides extensive supporting details for a research paper demonstrating the use of Deep Boltzmann Machines (DBMs) for variational Monte Carlo simulations of quantum systems, and the acceleration of these simulations using FPGA-based probabilistic computing. It covers training details, parameter counting, connectivity definitions, and computational cost analysis. The authors enforce a locality constraint, limiting connections between neurons based on a distance metric, which is essential for FPGA implementation. The parameter ‘k’ controls the range of this locality, balancing connections and complexity.

Sparse DBMs demonstrate increased expressiveness compared to Restricted Boltzmann Machines (RBMs) while maintaining reasonable parameter counts. A detailed computational cost model reveals that the dual sampling algorithm, involving outer loop sampling of visible configurations and inner loop sampling of auxiliary units, dramatically reduces sampling time on FPGA-based probabilistic computers. The parallel update capability of FPGAs overcomes the bottleneck of sequential sampling on conventional processors, with sampling time independent of the number of stochastic units for fixed sampling budgets and bounded degree sparsity. This is a core claim of the paper. The combination of sparse connectivity and probabilistic computing makes it possible to simulate larger quantum systems than would be feasible with traditional methods. This work demonstrates the potential of neural networks as efficient and accurate variational wavefunctions for quantum systems, and represents a hardware-aware approach to machine learning.

Large Scale Quantum Simulation via Probabilistic Computing

Scientists have achieved a significant breakthrough in simulating complex quantum systems by combining sparse Boltzmann machine architectures with custom-built probabilistic computing hardware. The team implemented a probabilistic computer using field programmable gate arrays (FPGAs), creating a fast sampler for energy-based neural states and overcoming limitations in scaling to larger system sizes. Experiments revealed the ability to obtain accurate ground-state energies for two-dimensional transverse-field Ising models on lattices up to 80×80, encompassing a total of 6400 spins, using a multi-FPGA cluster. This represents a substantial increase in the scale of simulations possible with this approach.

The research also introduces a novel dual-sampling algorithm designed to train deep Boltzmann machines, effectively replacing computationally challenging marginalization with conditional sampling over auxiliary layers. This innovation allows for the training of sparse deep models, improving parameter efficiency, and facilitated the training of a deep Boltzmann machine for a system of 35×35 spins, or 1225 spins total. The method significantly reduces the sampling bottleneck traditionally encountered in variational simulation of many-body systems, paving the way for even larger and more complex architectures. The breakthrough delivers a pathway to explore quantum systems with unprecedented scale and depth, as the FPGA-based probabilistic computer demonstrates high-throughput sampling capabilities. Tests prove the efficacy of mapping sparse Boltzmann machines directly onto the FPGA fabric, exploiting spatial parallelism and low-precision arithmetic to accelerate simulations. The results demonstrate that probabilistic hardware can effectively address the computational demands of simulating quantum phenomena, opening new avenues for research in condensed matter physics, quantum chemistry, and quantum information science.

Neural Networks Accelerate Quantum System Simulation

This research demonstrates a significant advance in simulating complex quantum systems, achieved by integrating neural networks with specialized probabilistic computing hardware. Scientists successfully constructed a probabilistic computer using field programmable gate arrays, and applied it to accurately determine ground-state energies for the two-dimensional transverse-field Ising model, extending simulations to lattices containing up to 6400 spins, a substantial increase over previous software-based methods. This achievement overcomes a key limitation in neural quantum state simulations, which is the computational cost of sampling many-body wavefunctions. Furthermore, the team developed a novel algorithm called dual-sampling, which streamlines the training of deep Boltzmann machines.

This technique replaces computationally intensive calculations with more efficient conditional sampling, allowing for the creation of deeper, more parameter-efficient models for these quantum systems. The researchers trained deep Boltzmann machines to represent systems with 1225 spins, demonstrating the potential for scaling these models to even larger and more complex scenarios. While the hardware significantly reduces sampling time, the overall training process still exhibits a linear dependence on system size due to updates performed by a conventional processor. Future work could focus on accelerating these optimization routines with dedicated hardware, potentially leading to even greater performance gains. These results highlight the benefits of spatial locality and parallel processing for variational Monte Carlo simulations, and suggest that probabilistic computing offers a promising pathway toward classically simulating quantum matter at unprecedented scales.