Learning local and nonlocal quatum data via generative model over tensor network architechture*

Nonlocality lies at the heart of many striking features of quantum states such as entanglement. The Greenberger-Horne-Zeilinger (GHZ) states and Cluster states are known as an important category of highly entangled quantum states. They play key roles in various quantum-based technologies and are particularly of interest in benchmarking noisy quantum hardwares. A novel quantum inspired generative model known as Born Machine which leverages on probabilistic nature of quantum physics has shown a great success in learning classical and quantum data over tensor network (TN) architecture. To this end, we investigate the training of the Born Machine for learning both local and nonlocal data encoded in GHZ and Cluster states over various tensor network architectures. Our result indicates that gradient-based training schemes over TN Born Machine fails to learn the nonlocal information of the coherent superposition (or parity) of the GHZ state. Finally, we adapt a gradient free training algorithm similar to Density Matrix Renormalization Group. This opens a new direction of adapting quantum inspired gradient free training schemes in learning highly entangled and other exotic quantum states.