Quantum Dynamic Simulations with Autoregressive Neural Networks

The theory of quantum dynamics is crucial for quantum science and engineering. The computation cost for exact quantum simulation is expensive due to the exponential growth of the dimension of the Hilbert space. There are recent attempts that utilize neural networks to simulate long-time quantum dynamics. We conduct a comparative study on different approaches that simulate dynamics based on parameterizing the quantum states with state-of-the-art autoregressive neural networks. Pixel Convolution Neural Networks, Recurrent Neural Networks, and Transformer models are examined for their representability and accuracy. We identify that Recurrent Neural Networks and Transformers are superior to Pixel Convolution Neural Networks. In addition, we compare the performance of different algorithms to simulate quantum dynamics, which include the Euler’s method, the forward-backward trapezoid method, the stochastic reconfiguration method, and the spacetime method. We found that the spacetime method performs better than the other algorithms, the Euler’s method and the forward-backward method are comparable, while the SR method exhibits stability issues. Our study is performed on the transverse-field Ising model on one-dimensional systems.U of I OnlyUndergraduate senior thesis not recommended for open acces