Tensor tree learns hidden relational structures in data to construct generative models
Generative modeling is a significant machine learning technique that constructs the probability distribution of a dataset, owing to its wide range of applications across various problems. Recently, there has been extensive research into generative modeling on quantum computers, referred to as Born machines [1-8]. This approach utilizes the output of projective measurement of quantum states for stochastic samplings.
We propose a general method for constructing a generative model based on the tree tensor network within the Born machine framework [9]. The core idea is to optimize the tree structure dynamically to minimize the bond mutual information. We demonstrate potential applications with four examples:
(1) Random bit sequences with long-range correlation
(2) Images of handwritten digits from the QMNIST dataset
(3) Bayesian networks
(4) Stock price fluctuations in the S&P 500
Our method significantly enhances performance and reveals hidden relational structures in the target data, paving the way for future improvements and advancements.
[2] J.-G. Liu and L. Wang. Physical Review A, 98, 062324 (2018).
[3] M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz. npj Quantum Information, 5, 45 (2019).
[4] S. Cheng, L. Wang, T. Xiang, and P. Zhang. Physical Review B, 99, 155131(2019).
[5] B. Coyle, D. Mills, V. Danos, and E. Kashefi. npj Quantum Information, 6, 60 (2020).
[6] M. Benedetti, B. Coyle, M. Fiorentini, M. Lubasch, and M. Rosenkranz. Physical Review Applied, 16, 044057 (2021).
[7] M.S. Rudolph, J. Miller, D. Motlagh, J. Chen, A. Acharya, and A. Perdomo-Ortiz. Nature Communications, 14, 8367 (2023).
[8] M. Hibat-Allah, M. Mauri, J. Carrasquilla, and A. Perdomo-Ortiz. Communications Physics, 7, 68 (2024).
[9] K. Harada, T. Okubo, and N. Kawashima. arXiv:2408.10669 (2024).