Furthering Quantum Systems with Neural Operators

Fourier Neural Operators (FNOs) excel on various high-dimensional tasks, such as those generated by partial differential equations. We demonstrate that this renders them an effective approach for simulating the time evolution of quantum wavefunctions, which is a computationally challenging, yet central task for understanding quantum systems. In this talk, we use FNOs to model the evolution of random quantum spin systems, so chosen due to their representative quantum dynamics and minimal symmetry. We explore two distinct FNO architectures and examine their performance for learning and predicting time evolution using both random and low-energy input states. Additionally, we apply FNOs to a compact set of Hamiltonian observables, rather than the entire quantum wavefunction, which greatly reduces the size of our inputs and outputs and, consequently, the requisite dimensions of the resulting FNOs. The extrapolation of Hamiltonian observables to times later than those used in training is of particular interest, as this stands to fundamentally increase the simulatability of quantum systems past both the coherence times of contemporary quantum architectures and the circuit-depths of tractable tensor networks.