Scaling of neural-network quantum states for time evolution
arXiv:2104.10696 · doi:10.1002/pssb.202100172
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.
arXiv comment8 pages, 6 figures (+appendix: 5 pages, 8 figures); v2: adding data for SGD optimization on MPS; v3: including results for RBM NQS. Code is available at https://github.com/ShHsLin/Neural-Network-Quantum-State
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