Fourier neural operators for learning dynamics in quantum spin systems

Abstract Fourier Neural Operators (FNOs) excel on functional data tasks, such as those originating from partial differential equations. This renders them effective at simulating the time evolution of quantum wavefunctions, a computationally challenging, yet coveted task. In this manuscript, we use FNOs to model the evolution of random quantum spin systems, chosen due to their representative dynamics. We find that traditional neural networks, such as U-Net, exhibit limited extrapolation beyond the training time interval, whereas FNOs capture the underlying time-evolution operator, generalizing to unseen times. Additionally, we apply FNOs to a compact set of Hamiltonian observables (~ poly( n )) instead of 2 n -component wavefunctions, greatly reducing the size of our inputs, outputs, and FNO models. This Hamiltonian observable-based method demonstrates that FNOs can distill information from high to low-dimensional spaces. We perform numerical experiments on a 20-qubit system, extrapolating Hamiltonian observables to twice the training time with a relative error of 5.8%. Notably, relative to numerical time-evolution methods, FNO achieves an inference speedup of approximately 10 4 × for 20-qubit systems, underscoring its computational efficiency. This extrapolation of observables past training times stands to fundamentally increase the simulatability of quantum systems beyond the limitations of quantum device coherence and tensor network circuit-depth.