Machine learning quantum states and many-body entanglement

Leonardo Banchi

Yusuke Nomura, Yamaji Yohei, Imada Masatoshi

Douglas Hendry, Adrian E. Feiguin

Ding Liu, Shi-Ju Ran, Peter Wittek +4 more

Abstract The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional TNs in image recognition, showing limited scalability and flexibilities. In this work, we train two-dimensional hierarchical TNs to solve image recognition problems, using a training algorithm derived from the multi-scale entanglement renormalization ansatz. This approach introduces mathematical connections among quantum many-body physics, quantum information theory, and machine learning. While keeping the TN unitary in the training phase, TN states are defined, which encode classes of images into quantum many-body states. We study the quantum features of the TN states, including quantum entanglement and fidelity. We find these quantities could be properties that characterize the image classes, as well as the machine learning tasks.

Dong-Ling Deng, Xiaopeng Li, S. Das Sarma

Machine learning has recently gained attention as a possible way to understand phase transitions in many-body quantum systems. A new entanglement analysis reveals crucial properties of the data structures that encode quantum states in a neural network, opening new inroads in applying machine learning to quantum many-body physics.

Yusuke Nomura