Fast Prediction of Full Quantum Dynamics with Deep Recurrent Neural Networks

Abstract

Numerical simulations of interacting quantum systems are computationally very intensive, typically requiring resources that scale exponentially in the number of particles. A plausible approach to overcoming this unfavorable simulation time is to train deep neural networks over short timescales and use them to infer dynamics over much longer timescales. We demonstrate that such a speedup is possible using deep recurrent neural networks, including LSTM and Transformer-based networks, by predicting the quantum dynamics of multiple ’classic’ systems - the Ising, Heisenberg, and Hubbard models, with up to 9 spins, at most. We observe up to 3 orders of magnitude of data generation speedup for systems that can still be simulated with full system evolution. We observe this same performance - O(0.1) seconds - to generate data samples that cannot be generated with the resources we have available to use. Unique to our work, we predict the full wavefunction dynamics of the systems, which can then be used to calculate the evolution of measurable and theoretical observables over time. We present sample predictions for our models and compare the efficacy of the different approaches with varying context-length for prediction, spin count, and Hamiltonian parameters (mixing, interaction strength, etc.), at best accurately predicting (< 10−6 mean square error - MSE) up to 90% of a single period with 10% of a period for context. We probe a number of frustrations, including square and triangular interaction lattices, more complex next-nearest neighbor interactions, etc. to understand what currently limits strong machine learning - ML - results in this space. Our results indicate that the primary inhibitor to fast prediction at scale is the system scale, not the complexity of the dynamics. We anticipate that our work will provide insights towards extending the coherence time of quantum systems such as qubits and spins by determining the issues that stand in the way of network training and prediction on realistic Hamiltonians. We further believe that this work has immediate application in the simulation of large-scale neutral atom arrays, like Yt-171, under so-called Lieb-Robinson bounds.