Variational real-time dynamics of Josephson junction arrays

Numerical simulation of quantum systems with continuous degrees of freedom out of equilibrium is a key challenge for modern computational chemistry, optics and materials. We study the case of real-time dynamics of two-dimensional Josephson junction arrays, a vital component of modern quantum computing hardware based on superconducting architectures. Our approach is based on custom neural-network many-body quantum states. We simulate large experimentally-relevant system sizes by representing a trial state in a continuous basis and using state-of-the-art sampling approaches based on Hamiltonian Monte Carlo. Using this method, we observe key phenomena like fidelity decay and vorticity oscillations at long time scales for two-dimensional systems of up to 64 junctions. Our approach can be used for accurate non-equilibrium simulations of continuous systems at previously unexplored system sizes and evolution times, bridging the gap between simulation and experiment.