Hardware Acceleration of Frustrated Lattice Systems using Convolutional Restricted Boltzmann Machine

Abstract

Geometric frustration gives rise to emergent quantum phenomena and exotic phases of matter. While Monte Carlo methods are traditionally used to simulate such systems, their sampling efficiency is limited by the complexity of interactions and ground-state properties. Restricted Boltzmann Machines (RBMs), a class of probabilistic neural networks, offer improved sampling by incorporating machine learning techniques. However, fully-connected bipartite RBMs are inefficient for representing physical lattices with sparse interactions. To address this, we implement Convolutional Restricted Boltzmann Machines (CRBMs) that leverage translational symmetry inherent to lattices. Using the classical Shastry-Sutherland (SS) Ising lattice, we demonstrate (i) CRBM formulation that captures SS interactions, and (ii) digital hardware accelerator to enhance sampling performance. We simulate lattices with up to 324 spins, recovering all known phases of the SS Ising model, including the long range ordered fractional plateau. Our hardware characterizes spin behavior at critical points and within spin liquid phases. This implementation achieves a speedup of 3 to 5 orders of magnitude (33 ns to 120 ms) over GPU-based implementations. Moreover, the time-to-solution is within two orders of magnitude of quantum annealers, while offering superior scalability, room-temperature operation and reprogrammability. This work paves a pathway for scalable digital hardware that embeds physical symmetries to enable large scale simulations of material systems.