Abstract
The rapid development of machine learning and artificial intelligence has significantly altered the landscape of daily life and work. In particular, the use of artificial neural networks shows tremendous potential in solving highly complicated problems with high-dimensional data. Quantum physics is a natural testbed of the machine-learning-based approach due to its exponential growth of complexity. Recent studies show a wide range of applications of artificial neural networks in quantum mechanics. A particular family of methods, known as the neural network quantum states, is to use artificial neural networks to represent wavefunctions to solve many-body quantum systems. In this thesis, we focus on two interesting problems: the ground state search and the dynamics of many-body quantum systems. We use the restricted Boltzmann machine and feedforward neural network as the neural network quantum states. In ground state search, by considering the neural network quantum states as trial wave functions for variation Monte Carlo method, we propose a local optimization procedure which, when integrated with stochastic reconfiguration, outperforms previously used global optimization approaches. Specifically, we analyze both the ground state energy and the correlations for the non-integrable tilted Ising model with restricted Boltzmann machines. To study quantum dynamics, we introduce the concept of infidelity as the loss function, and we utilize the Suzuki–Trotter decomposition to separate the unitary operator into smaller blocks. Our findings indicate a significant improvement in the stability of our results as compared to conventional approaches. To summarize, we study the applications of neural network quantum states in solving many-body quantum systems. Our new training protocols show improved performance, demonstrating the potential in this multidisciplinary emerging field.