TTNOpt: Tree tensor network package for high-rank tensor compression

Watanabe, Ryo; Manabe, Hidetaka; Hikihara, Toshiya; Ueda, Hiroshi

doi:https://doi.org/10.1016/j.cpc.2025.109918

TTNOpt: Tree tensor network package for high-rank tensor compression

Watanabe, Ryo; Manabe, Hidetaka; Hikihara, Toshiya et al.

Computer Physics Communications, 2025, 319, 109918

アクセス数:65件（2026-02-16 16:45 集計）

固定URL: https://hdl.handle.net/11094/103523

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タイトル	TTNOpt: Tree tensor network package for high-rank tensor compression
著者	著者名 Watanabe, Ryo
	ORCID 0009-0002-2302-0357 0009-0002-2302-0357 Scopus Author ID 57713094700 57713094700 著者名 Manabe, Hidetaka
	NRID 1000000373358 1000000373358 著者名 Hikihara, Toshiya
	NRID 1000040632758 1000040632758 ORCID 0000-0001-9561-0933 0000-0001-9561-0933 researchmap permalink hiroshi_ueda hiroshi_ueda Scopus Author ID 57210940815 57210940815 著者名 Ueda, Hiroshi
キーワード等	Data analysis
	Quantum spin system
	Tensor decomposition
	Tensor network method
	Tree tensor network
内容	Watanabe R., Manabe H., Hikihara T., et al. TTNOpt: Tree tensor network package for high-rank tensor compression. Computer Physics Communications 319, 109918 (2026); https://doi.org/10.1016/j.cpc.2025.109918.
抄録	We have developed TTNOpt, a software package that utilizes tree tensor networks (TTNs) for quantum spin systems and high-dimensional data analysis. TTNOpt provides efficient and powerful TTN computations by locally optimizing the network structure, guided by the entanglement pattern of the target tensors. For quantum spin systems, TTNOpt searches for the ground state of Hamiltonians with bilinear spin interactions and magnetic fields, and computes physical properties of these states, including the variational energy, bipartite entanglement entropy (EE), single-site expectation values, and two-site correlation functions. Additionally, TTNOpt can target the lowest-energy state within a specified subspace, provided that the Hamiltonian conserves total magnetization. For high-dimensional data analysis, TTNOpt factorizes complex tensors into TTN states that maximize fidelity to the original tensors by optimizing the tensors and the network. When a TTN is provided as input, TTNOpt reconstructs the network based on the EE without referencing the fidelity of the original state. We present three demonstrations of TTNOpt: (1) Ground-state search for the hierarchical chain model with a system size of 256. The entanglement patterns of the ground state manifest themselves in a tree structure, and TTNOpt successfully identifies the tree. (2) Factorization of a quantic tensor of the 2²⁴ dimensions representing a three-variable function where each variant has a weak bit-wise correlation. The optimized TTN shows that its structure isolates the variables from each other. (3) Reconstruction of the matrix product network representing a 16-variable normal distribution characterized by a tree-like correlation structure. TTNOpt can reveal hidden correlation structures of the covariance matrix.
出版者	Elsevier B.V.
収録物名	Computer Physics Communications
巻(号)	319
ページ	109918
刊行年月	2025-11-04
言語	英語
ハンドルURL	https://hdl.handle.net/11094/103523
PISSN	00104655
関連情報 (isIdenticalTo)	DOI (出版社版) https://doi.org/10.1016/j.cpc.2025.109918
アクセス権	open access
権利情報	This article is licensed under a Creative Commons Attribution 4.0 International License.
出版タイプ	Version of Record
カテゴリ	学術雑誌論文 Journal Article

資源タイプ	学術雑誌論文
ローカル資源タイプ	学術雑誌論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Computer Physics Communications. 2025, 319, p. 109918
DC.title	TTNOpt: Tree tensor network package for high-rank tensor compression
DC.creator	Watanabe, Ryo
	Manabe, Hidetaka
	Hikihara, Toshiya
	Ueda, Hiroshi
DC.publisher	Elsevier B.V.
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2025-11-04
DC.identifier	https://doi.org/10.1016/j.cpc.2025.109918
DC.subject	Data analysis
	Quantum spin system
	Tensor decomposition
	Tensor network method
	Tree tensor network
DC.description	Watanabe R., Manabe H., Hikihara T., et al. TTNOpt: Tree tensor network package for high-rank tensor compression. Computer Physics Communications 319, 109918 (2026); https://doi.org/10.1016/j.cpc.2025.109918.
DCTERMS.abstract	We have developed TTNOpt, a software package that utilizes tree tensor networks (TTNs) for quantum spin systems and high-dimensional data analysis. TTNOpt provides efficient and powerful TTN computations by locally optimizing the network structure, guided by the entanglement pattern of the target tensors. For quantum spin systems, TTNOpt searches for the ground state of Hamiltonians with bilinear spin interactions and magnetic fields, and computes physical properties of these states, including the variational energy, bipartite entanglement entropy (EE), single-site expectation values, and two-site correlation functions. Additionally, TTNOpt can target the lowest-energy state within a specified subspace, provided that the Hamiltonian conserves total magnetization. For high-dimensional data analysis, TTNOpt factorizes complex tensors into TTN states that maximize fidelity to the original tensors by optimizing the tensors and the network. When a TTN is provided as input, TTNOpt reconstructs the network based on the EE without referencing the fidelity of the original state. We present three demonstrations of TTNOpt: (1) Ground-state search for the hierarchical chain model with a system size of 256. The entanglement patterns of the ground state manifest themselves in a tree structure, and TTNOpt successfully identifies the tree. (2) Factorization of a quantic tensor of the 2²⁴ dimensions representing a three-variable function where each variant has a weak bit-wise correlation. The optimized TTN shows that its structure isolates the variables from each other. (3) Reconstruction of the matrix product network representing a 16-variable normal distribution characterized by a tree-like correlation structure. TTNOpt can reveal hidden correlation structures of the covariance matrix.
DC.rights	This article is licensed under a Creative Commons Attribution 4.0 International License.
DC.format	103523
citation_title	TTNOpt: Tree tensor network package for high-rank tensor compression
citation_author	Watanabe, Ryo
	Manabe, Hidetaka
	Hikihara, Toshiya
	Ueda, Hiroshi
citation_publisher	Elsevier B.V.
citation_language	英語
citation_date	2025-11-04
citation_journal_title	Computer Physics Communications
citation_volume	319
citation_firstpage	109918
citation_doi	https://doi.org/10.1016/j.cpc.2025.109918
citation_public_url	https://hdl.handle.net/11094/103523

TTNOpt: Tree tensor network package for high-rank tensor compression

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