Scaling of neural-network quantum states for time evolution

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.

8 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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• Efficient quantum state tomography with convolutional neural networks
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics
• Can neural quantum states learn volume-law ground states?
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Quantum Gauge Networks: A New Kind of Tensor Network
• An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States
• Data-Driven Time Propagation of Quantum Systems with Neural Networks