NEWS
- Title
- Improving the accuracy of the tree-tensor network approach by optimization of network structure
- Author
- Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, and Tomotoshi Nishino
- Abstract
- Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state crucially depends on the spatial structure of the network. In the previous work [T. Hikihara et al., Phys. Rev. Res. 5, 013031 (2023)], we proposed an algorithm based on tree-tensor networks (TTNs) that automatically optimizes the structure of a TTN according to the spatial profile of entanglement in the state of interest. In this paper, we apply the algorithm to the random 𝑋𝑌 -exchange model under random magnetic fields and the Richardson model in order to analyze how the performance of the algorithm depends on the detailed updating schemes of the structural optimization. We then find that for the random 𝑋𝑌 model, on the one hand, the algorithm achieves improved accuracy, and the stochastic algorithm, which selects the local network structure probabilistically, is notably effective. For the Richardson model, on the other hand, the resulting numerical accuracy subtly depends on the initial TTN and the updating schemes. In particular, the algorithm without the stochastic updating scheme certainly improves the accuracy, while the one with the stochastic updates results in poor accuracy due to the effect of randomizing the network structure at the early stage of the calculation. These results indicate that the algorithm successfully improves the accuracy of the numerical calculations for quantum many-body states, while it is essential to appropriately choose the updating scheme as well as the initial TTN structure, depending on the systems treated.
- Comments
- 19 pages, 17 figures, 2 tables
- Citation
- Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Tomotoshi Nishino, ``Improving the accuracy of the tree-tensor network approach by optimization of network structure'', Phys. Rev. B 112, 134427 (2025)
- DOI
- 10.1103/ljj8-tkpc
- Code
- Demo code
- Dates
- August 25-29, 2025
- Conference
- SQAI-NCTS Workshop on Quantum Technologies and Machine Learning (National Taiwan University, Taipei, Taiwan)
- Title
- Adaptive Tensor Tree Method with Annealing of Mini-batch Samples for Generative Modeling on Quantum Devices
- Abstract
- We proposed the Adaptive Tensor Tree (ATT) method, which uses the tensor tree network within the Born machine framework to construct a generative model. This method expresses the target distribution function as the squared amplitude of a quantum wave function represented by a tensor tree. The core concept of the ATT method involves dynamically optimizing the tree structure to minimize the bond mutual information. In this presentation, we introduce a new technique that utilizes an annealing process on mini-batch samples to enhance the performance of the ATT method. We will demonstrate the effectiveness of this new ATT approach using various datasets.
- Title
- Tensor tree learns hidden relational structures in data to construct generative models
- Author
- Kenji Harada, Tsuyoshi Okubo, Naoki Kawashima
- Abstract
- Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S\&P500. In (i) and (ii), the strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and in (iv), a structure corresponding to the eleven sectors emerged.
- Comments
- 10 pages, 3 figures
- Citation
- Kenji Harada, Tsuyoshi Okubo, and Naoki Kawashima, Machine Learning: Science and Technology 6 025002(2025)
- DOI
- 10.1088/2632-2153/adc2c7
- Code
- Adaptive Tensor Tree Generative Modeling
- Date
- December 13th, 2024
- Seminar
- Theory seminar at ISSP, Univ. of Tokyo
- Title
- Tensor tree learns hidden relational structure in data to construct generative models
- Abstract
-
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. 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. 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.
- Reference
- arXiv:2408.10669
- Code
- Adaptive Tensor Tree Generative Modeling
- Dates
- March 25-29, 2024
- Conference
- SQAI-NCTS Workshop on Tensor Network and Quantum Embedding (Hongo Campus, The University of Tokyo)
- Title
- Optimizing the structure of tree tensor network for quantum generative modeling using mutual information-based approach
- Abstract
- Generative modeling is a crucial task in the field of machine learning. Recently, there have been several proposals for generative models on quantum devices. We can efficiently optimize generative models defined by tensor network states, but their performance largely depends on the geometrical structure of the tensor network. To tackle this issue, we have proposed an optimization method for the network structure in the tree tensor network class, based on the least mutual information principle. Generative modeling with an optimized network structure has better performance than a fixed network structure. Moreover, by embedding data dependencies into the tree structure based on the least mutual information principle, we can geometrically represent the correlations in the data.
- Book title
- Advanced Mathematical Science for Mobility Society
- Editors
- Kazushi Ikeda, Yoshiumi Kawamura, Kazuhisa Makino, Satoshi Tsujimoto, Nobuo Yamashita, Shintaro Yoshizawa, Hanna Sumita
- Publisher
- Springer Singapore
- Reference
- ISBN 978-981-99-9771-8 ISBN 978-981-99-9772-5 (eBook)
- Title
- Chapter 5 "Application of Tensor Network Formalism for Processing Tensor Data"
- Authors
- Kenji Harada, Hiroaki Matsueda, and Tsuyoshi Okubo
- Web page
- Open access
TOPICS
Toolkit of Bayesian Scaling Analysis
Reference application software of a new scaling analysis method of critical phenomena based on Bayesian inference.
To demo To detailsToolkit of Adaptive Tensor Tree Generative Modeling
Reference application software of adaptive tensor tree generative modeling.
To GitHubMonte Carlo simulations
This demonstration shows a Monte Carlo simulation of the two-dimensional Ising model by three algorithms: Metropolis, Swendsen-Wang, and Wolff algorithms.
To demoABOUT
Kenji Harada
(
原田健自
)
Assistant Professor,
Graduate School of Informatics, Kyoto University, Japan.
harada.kenji.8e@kyoto-u.ac.jp
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 606-8501, Japan.
Map (No.59)
orcid.org/0000-0003-0231-7880