Machine Learning Highly Entangled Quantum States

Artificial neural networks play a prominent role in the rapidly growing field of machine learning and are recently introduced to quantum many-body systems. This talk will focus on using a machine-learning model, the restricted Boltzmann machine (RBM) to describe entangled quantum states. Both short- and long-range coupled RBM will be discussed. For a short-range RBM, the associated quantum state satisfies an entanglement area law, regardless of spatial dimensions [1]. I will present our recently constructed exact RBM models for nontrivial topological phases, including a 1d cluster state and a 2d toric code [2]. For a long-range RBM, the captured entanglement entropy scales linearly with the number of variational parameters in the RBM model, in sharp contrast to the log-scaling in matrix product state representation [1].
[1] Dong-Ling Deng, Xiaopeng Li, S. Das Sarma, PRX 7, 021021 (2017)
[2] Dong-Ling Deng, Xiaopeng Li, S. Das Sarma, arXiv: 1609.09060 (2016)