Scaling of neural-network quantum states for time evolution

TL;DR

This paper investigates the effectiveness of various neural network architectures in simulating quantum many-body dynamics, revealing exponential growth in parameters needed over time regardless of network design.

Contribution

It benchmarks different neural network architectures for quantum state simulation, showing their limitations in representing time-evolved states efficiently.

Findings

Number of parameters grows exponentially with time for accurate state representation.

Network architecture variations have minimal impact on the exponential growth rate.

Shallow and deep networks, with various design choices, perform similarly in terms of parameter scaling.

Abstract

Simulating quantum many-body dynamics on classical computers is a challenging problem due to the exponential growth of the Hilbert space. Artificial neural networks have recently been introduced as a new tool to approximate quantum-many body states. We benchmark the variational power of the restricted Boltzmann machine quantum states and different shallow and deep neural autoregressive quantum states to simulate global quench dynamics of a non-integrable quantum Ising chain. We find that the number of parameters required to represent the quantum state at a given accuracy increases exponentially in time. The growth rate is only slightly affected by the network architecture over a wide range of different design choices: shallow and deep networks, small and large filter sizes, dilated and normal convolutions, with and without shortcut connections.