Real time evolution with neural network quantum states

The Hilbert space of a quantum system grows exponentially with system size, which makes many-body quantum systems challenging to simulate on a classical computer. One approach is to use tensor network methods, but these require an increasing bond dimension to capture the growth in entanglement during real time evolution, which limits their application to short time intervals. An alternative method proposed recently uses a neural network as a variational Ansatz to describe the quantum wave function. However, its application for real time evolution has not been extensively explored. In this work, we propose the use of standard machine learning optimization techniques, combined with a modified backpropagation for a neural network with complex parameters, to tackle the time evolution of an example system: the Ising model in 1 and 2-D. Our preliminary results show that our method performs comparably as well as stochastic reconfiguration, while avoiding a sensitivity issue related to the pseudo-inverse of the covariance matrix.