Unsupervised Generative Modeling Using Matrix Product States

2017/09/30 by Zhaoyu Han, Zhao-Yu Han, Jun Wang +3 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Complex system #Computational Physics and Python Applications #Computer science #Generative grammar #Generative model #Machine learning #Mathematics #Physics #Probability distribution #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Statistical physics #Unsupervised learning #cond-mat.stat-mech #cs.LG #quant-ph #stat.ML

paper · pdf · doi:10.1103/physrevx.8.031012

published as Phys. Rev. X 8, 031012 (2018) · 11 pages, 12 figures (not including the TNs) GitHub Page: https://congzlwag.github.io/UnsupGenModbyMPS/

openalex publication_date 2018/07/17 · arxiv created 2018/07/19 · arxiv updated 2018/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Modeling the probability distribution of complex data using insights from quantum physics is a fresh approach to generative modeling in machine learning, and shows great potential compared to conventional neural network approaches.

Citations

• A Practical Guide to Training Restricted Boltzmann Machines
• Adam: A Method for Stochastic Optimization
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• NICE: Non-linear Independent Components Estimation
• Tensorizing Neural Networks
• Colloquium: Area laws for the entanglement entropy
• Auto-Encoding Variational Bayes
• On Information and Sufficiency
• Preparing Projected Entangled Pair States on a Quantum Computer
• Zur Quantenmechanik der Sto�vorg�nge
• The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• The density-matrix renormalization group in the age of matrix product states
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Deep learning
• Variational Inference with Normalizing Flows
• Generative Adversarial Nets

Cited by

• Tensor network solvers for ultra-large tight-binding Hamiltonians: algorithms and applications
• Polyformer: a generative framework for thermodynamic modeling of polymeric molecules
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Quantum self-learning Monte Carlo and quantum-inspired Fourier transform sampler

Related

• A Matrix Product State Model for Simultaneous Classification and Generation
• Generative Learning of Continuous Data by Tensor Networks
• Generative Quantum Machine Learning
• Investigating Quantum Many-Body Systems with Tensor Networks, Machine Learning and Quantum Computers
• Distributive Pre-Training of Generative Modeling Using Matrix-Product States