Scaling of neural-network quantum states for time evolution
This work addresses the problem of exponential scaling in quantum simulations for researchers in quantum physics and machine learning, but it is incremental as it benchmarks existing methods without introducing new paradigms.
The authors tackled the challenge of simulating quantum many-body dynamics by benchmarking neural-network quantum states for time evolution in a non-integrable quantum Ising chain, finding that the number of parameters needed for a given accuracy increases exponentially over time, with minimal impact from network architecture variations.
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.