Neural Operator Learning in Quantum Simulations

Synopsis

Simulating the real-time operator dynamics is crucial to characterize quantum many-body systems. The simulation can be performed efficiently using quantum computers and potentially exhibiting a practical quantum advantage over classical computers. However, due to decoherence in quantum simulators, the operator dynamics is limited within a short evolution time, such that the quantum systems are characterized with low accuracy. On the other hand, given the short-time data, neural networks with physics priors can potentially learn the operator dynamics and predict the long-time behavior. In this work, we implement neural ordinary differential equations (Neural ODEs) to learn the intrinsic dynamics from the short-time signal and extract physical kernels. By exploiting physical symmetries and locality, it reduces complexity while retaining essential operator dynamics. Our method provides a scalable and data-efficient avenue to characterize quantum many-body systems using noisy quantum computers where long-time dynamics is unavailable.