{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T13:08:58Z","timestamp":1778936938607,"version":"3.51.4"},"reference-count":79,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001459","name":"Government of Singapore Ministry of Education","doi-asserted-by":"publisher","award":["A- 8002392-00-00"],"award-info":[{"award-number":["A- 8002392-00-00"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer Physics Communications"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.cpc.2026.110164","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T08:47:10Z","timestamp":1776242830000},"page":"110164","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Accelerated inchworm method with tensor-train bath influence functional"],"prefix":"10.1016","volume":"325","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7890-2758","authenticated-orcid":false,"given":"Geshuo","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5808-166X","authenticated-orcid":false,"given":"Yixiao","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6651-6224","authenticated-orcid":false,"given":"Siyao","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7086-7983","authenticated-orcid":false,"given":"Zhenning","family":"Cai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"1-2","key":"10.1016\/j.cpc.2026.110164_bib0001","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0378-4371(98)00076-4","article-title":"Decoherence and dissipation in quantum two-state systems","volume":"256","author":"Grigorescu","year":"1998","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"10.1016\/j.cpc.2026.110164_bib0002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2019.10.001","article-title":"Quantum decoherence","volume":"831","author":"Schlosshauer","year":"2019","journal-title":"Phys. Rep."},{"key":"10.1016\/j.cpc.2026.110164_bib0003","series-title":"The Theory of Open Quantum Systems","author":"Breuer","year":"2002"},{"key":"10.1016\/j.cpc.2026.110164_bib0004","series-title":"Quantum Dissipative Systems","volume":"13","author":"Weiss","year":"2012"},{"key":"10.1016\/j.cpc.2026.110164_bib0005","series-title":"Quantum computation and quantum information","author":"Nielsen","year":"2010"},{"issue":"6","key":"10.1016\/j.cpc.2026.110164_bib0006","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1143\/PTP.20.948","article-title":"On quantum theory of transport phenomena: steady diffusion","volume":"20","author":"Nakajima","year":"1958","journal-title":"Prog. Theor. Phys."},{"issue":"5","key":"10.1016\/j.cpc.2026.110164_bib0007","doi-asserted-by":"crossref","first-page":"1338","DOI":"10.1063\/1.1731409","article-title":"Ensemble method in the theory of irreversibility","volume":"33","author":"Zwanzig","year":"1960","journal-title":"J. Chem. Phys."},{"issue":"23","key":"10.1016\/j.cpc.2026.110164_bib0008","doi-asserted-by":"crossref","DOI":"10.1063\/5.0124028","article-title":"Quasiclassical approaches to the generalized quantum master equation","volume":"157","author":"Amati","year":"2022","journal-title":"J. Chem. Phys."},{"issue":"18","key":"10.1016\/j.cpc.2026.110164_bib0009","doi-asserted-by":"crossref","DOI":"10.1063\/1.4948408","article-title":"Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics","volume":"144","author":"Montoya-Castillo","year":"2016","journal-title":"J. Chem. Phys."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0010","doi-asserted-by":"crossref","DOI":"10.1063\/1.4812355","article-title":"Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics","volume":"139","author":"Kelly","year":"2013","journal-title":"J. Chem. Phys."},{"issue":"2","key":"10.1016\/j.cpc.2026.110164_bib0011","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF01608499","article-title":"On the generators of quantum dynamical semigroups","volume":"48","author":"Lindblad","year":"1976","journal-title":"Commun. Math. Phys."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0012","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-024-02707-x","article-title":"Structure-preserving numerical schemes for Lindblad equations","volume":"102","author":"Cao","year":"2025","journal-title":"J. Sci. Comput."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0013","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1063\/1.1580111","article-title":"Multilayer formulation of the multiconfiguration time-dependent Hartree theory","volume":"119","author":"Wang","year":"2003","journal-title":"J. Chem. Phys."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0014","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(99)00047-2","article-title":"The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets","volume":"324","author":"Beck","year":"2000","journal-title":"Phys. Rep."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0015","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0009-2614(90)87014-I","article-title":"The multi-configurational time-dependent Hartree approach","volume":"165","author":"Meyer","year":"1990","journal-title":"Chem. Phys. Lett."},{"issue":"11","key":"10.1016\/j.cpc.2026.110164_bib0016","doi-asserted-by":"crossref","first-page":"4611","DOI":"10.1063\/1.469509","article-title":"Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology","volume":"102","author":"Makri","year":"1995","journal-title":"J. Chem. Phys."},{"issue":"11","key":"10.1016\/j.cpc.2026.110164_bib0017","doi-asserted-by":"crossref","first-page":"4600","DOI":"10.1063\/1.469508","article-title":"Tensor propagator for iterative quantum time evolution of reduced density matrices. I theory","volume":"102","author":"Makri","year":"1995","journal-title":"J. Chem. Phys."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0018","doi-asserted-by":"crossref","first-page":"B771","DOI":"10.1137\/21M1439833","article-title":"Differential equation based path integral for open quantum systems","volume":"44","author":"Wang","year":"2022","journal-title":"SIAM J. Sci. Comput."},{"issue":"7","key":"10.1016\/j.cpc.2026.110164_bib0019","doi-asserted-by":"crossref","first-page":"4038","DOI":"10.1021\/acs.jctc.0c00039","article-title":"Small matrix path integral for system-bath dynamics","volume":"16","author":"Makri","year":"2020","journal-title":"J. Chem. Theory Comput."},{"issue":"48","key":"10.1016\/j.cpc.2026.110164_bib0020","doi-asserted-by":"crossref","first-page":"10500","DOI":"10.1021\/acs.jpca.1c08230","article-title":"Small matrix path integral for driven dissipative dynamics","volume":"125","author":"Makri","year":"2021","journal-title":"J. Phys. Chem. A"},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0021","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1021\/acs.jctc.0c00987","article-title":"Small matrix path integral with extended memory","volume":"17","author":"Makri","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"10.1016\/j.cpc.2026.110164_bib0022","doi-asserted-by":"crossref","first-page":"389","DOI":"10.4208\/cicp.OA-2023-0329","article-title":"Tree-based implementation of the small matrix path integral for system-bath dynamics","volume":"36","author":"Wang","year":"2024","journal-title":"Commun. Comput. Phys."},{"issue":"13","key":"10.1016\/j.cpc.2026.110164_bib0023","doi-asserted-by":"crossref","DOI":"10.1063\/1.4896736","article-title":"Blip decomposition of the path integral: exponential acceleration of real-time calculations on quantum dissipative systems","volume":"141","author":"Makri","year":"2014","journal-title":"J. Chem. Phys."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0024","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1038\/s42005-023-01427-2","article-title":"An efficient Julia framework for hierarchical equations of motion in open quantum systems","volume":"6","author":"Huang","year":"2023","journal-title":"Commun. Phys."},{"issue":"17","key":"10.1016\/j.cpc.2026.110164_bib0025","doi-asserted-by":"crossref","DOI":"10.1063\/1.5026753","article-title":"Efficient propagation of the hierarchical equations of motion using the matrix product state method","volume":"148","author":"Shi","year":"2018","journal-title":"J. Chem. Phys."},{"issue":"20","key":"10.1016\/j.cpc.2026.110164_bib0026","doi-asserted-by":"crossref","first-page":"3209","DOI":"10.1140\/epjs\/s11734-023-01000-6","article-title":"About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach","volume":"232","author":"Xu","year":"2023","journal-title":"Eur. Phys. J. Spec. Top."},{"issue":"9","key":"10.1016\/j.cpc.2026.110164_bib0027","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/aa8744","article-title":"Efficient real-time path integrals for non-Markovian spin-boson models","volume":"19","author":"Strathearn","year":"2017","journal-title":"New J. Phys."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0028","doi-asserted-by":"crossref","first-page":"3322","DOI":"10.1038\/s41467-018-05617-3","article-title":"Efficient non-Markovian quantum dynamics using time-evolving matrix product operators","volume":"9","author":"Strathearn","year":"2018","journal-title":"Nat. Commun."},{"issue":"24","key":"10.1016\/j.cpc.2026.110164_bib0029","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.123.240602","article-title":"Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals","volume":"123","author":"J\u00f8rgensen","year":"2019","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0030","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevResearch.2.013265","article-title":"Exact quantum dynamics in structured environments","volume":"2","author":"Gribben","year":"2020","journal-title":"Phys. Rev. Res."},{"issue":"2","key":"10.1016\/j.cpc.2026.110164_bib0031","doi-asserted-by":"crossref","DOI":"10.1063\/5.0073234","article-title":"A multisite decomposition of the tensor network path integrals","volume":"156","author":"Bose","year":"2022","journal-title":"J. Chem. Phys."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0032","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1103\/PhysRev.75.486","article-title":"The radiation theories of Tomonaga, Schwinger, and Feynman","volume":"75","author":"Dyson","year":"1949","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cpc.2026.110164_bib0033","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.phpro.2010.09.034","article-title":"Diagrammatic Monte Carlo","volume":"6","author":"Van Houcke","year":"2010","journal-title":"Phys. Procedia"},{"issue":"13","key":"10.1016\/j.cpc.2026.110164_bib0034","doi-asserted-by":"crossref","first-page":"9301","DOI":"10.1103\/PhysRevB.41.9301","article-title":"Sign problem in the numerical simulation of many-electron systems","volume":"41","author":"Loh","year":"1990","journal-title":"Phys. Rev. B"},{"issue":"25","key":"10.1016\/j.cpc.2026.110164_bib0035","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.99.250201","article-title":"Bold diagrammatic Monte Carlo technique: when the sign problem is welcome","volume":"99","author":"Prokof\u2019ev","year":"2007","journal-title":"Phys. Rev. Lett."},{"issue":"12","key":"10.1016\/j.cpc.2026.110164_bib0036","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.77.125101","article-title":"Bold diagrammatic Monte Carlo: a generic sign-problem tolerant technique for polaron models and possibly interacting many-body problems","volume":"77","author":"Prokof\u2019ev","year":"2008","journal-title":"Phys. Rev. B"},{"issue":"5","key":"10.1016\/j.cpc.2026.110164_bib0037","doi-asserted-by":"crossref","DOI":"10.1063\/1.4974329","article-title":"Inchworm Monte Carlo for exact non-adiabatic dynamics. I. Theory and algorithms","volume":"146","author":"Chen","year":"2017","journal-title":"J. Chem. Phys."},{"issue":"11","key":"10.1016\/j.cpc.2026.110164_bib0038","doi-asserted-by":"crossref","first-page":"2430","DOI":"10.1002\/cpa.21888","article-title":"Inchworm Monte Carlo method for open quantum systems","volume":"73","author":"Cai","year":"2020","journal-title":"Commun. Pure Appl. Math."},{"issue":"341","key":"10.1016\/j.cpc.2026.110164_bib0039","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1090\/mcom\/3785","article-title":"Numerical analysis for inchworm Monte Carlo method: sign problem and error growth","volume":"92","author":"Cai","year":"2023","journal-title":"Math. Comput."},{"issue":"5","key":"10.1016\/j.cpc.2026.110164_bib0040","doi-asserted-by":"crossref","DOI":"10.1063\/1.4974329","article-title":"Inchworm Monte Carlo for exact non-adiabatic dynamics. II. Benchmarks and comparison with established methods","volume":"146","author":"Chen","year":"2017","journal-title":"J. Chem. Phys."},{"issue":"6","key":"10.1016\/j.cpc.2026.110164_bib0041","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/ac02e1","article-title":"Inclusion\u2013exclusion principle for open quantum systems with bosonic bath","volume":"23","author":"Yang","year":"2021","journal-title":"New J. Phys."},{"issue":"4","key":"10.1016\/j.cpc.2026.110164_bib0042","article-title":"Learning Feynman diagrams with tensor trains","volume":"12","author":"N\u00fa\u00f1ez Fern\u00e1ndez","year":"2022","journal-title":"Phys. Rev. X"},{"issue":"24","key":"10.1016\/j.cpc.2026.110164_bib0043","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.107.245135","article-title":"Tensor train continuous time solver for quantum impurity models","volume":"107","author":"Erpenbeck","year":"2023","journal-title":"Phys. Rev. B"},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0044","doi-asserted-by":"crossref","first-page":"063","DOI":"10.21468\/SciPostPhysCore.7.3.063","article-title":"Efficient construction of the Feynman-Vernon influence functional as matrix product states","volume":"7","author":"Guo","year":"2024","journal-title":"SciPost Phys. Core"},{"issue":"8","key":"10.1016\/j.cpc.2026.110164_bib0045","doi-asserted-by":"crossref","DOI":"10.1103\/yt8p-vr1v","article-title":"Inchworm tensor train hybridization expansion quantum impurity solver","volume":"112","author":"Yu","year":"2025","journal-title":"Phys. Rev. B"},{"issue":"2","key":"10.1016\/j.cpc.2026.110164_bib0046","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1103\/PhysRev.80.268","article-title":"The evaluation of the collision matrix","volume":"80","author":"Wick","year":"1950","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cpc.2026.110164_bib0047","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.22331\/q-2025-10-28-1896","article-title":"Error bounds for open quantum systems with harmonic bosonic bath","volume":"9","author":"Liu","year":"2025","journal-title":"Quantum"},{"key":"10.1016\/j.cpc.2026.110164_bib0048","unstructured":"Z. Huang, L. Lin, G. Park, Y. Zhu, Unified analysis of non-Markovian open quantum systems in Gaussian environment using superoperator formalism, 2024, arXiv: 2411.08741."},{"issue":"5","key":"10.1016\/j.cpc.2026.110164_bib0049","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.1137\/090752286","article-title":"Tensor-train decomposition","volume":"33","author":"Oseledets","year":"2011","journal-title":"SIAM J. Sci. Comput."},{"issue":"21","key":"10.1016\/j.cpc.2026.110164_bib0050","doi-asserted-by":"crossref","first-page":"9269","DOI":"10.1021\/acs.jctc.4c00864","article-title":"Simulation of spin chains with off-diagonal coupling using the inchworm method","volume":"20","author":"Sun","year":"2024","journal-title":"J. Chem. Theory Comput."},{"key":"10.1016\/j.cpc.2026.110164_bib0051","unstructured":"Y. Sun, BIF-TT (source code), 2025, (https:\/\/github.com\/syixiao\/BIF-TT.git)."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0052","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.79.035320","article-title":"Diagrammatic Monte Carlo simulation of nonequilibrium systems","volume":"79","author":"Werner","year":"2009","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110164_bib0053","doi-asserted-by":"crossref","DOI":"10.1016\/j.cpc.2022.108417","article-title":"Fast algorithms of bath calculations in simulations of quantum system-bath dynamics","author":"Cai","year":"2022","journal-title":"Comput. Phys. Commun."},{"issue":"4","key":"10.1016\/j.cpc.2026.110164_bib0054","doi-asserted-by":"crossref","first-page":"A1812","DOI":"10.1137\/22M1499297","article-title":"The bold-thin-bold diagrammatic Monte Carlo method for open quantum systems","volume":"45","author":"Cai","year":"2023","journal-title":"SIAM J. Sci. Comput."},{"issue":"15","key":"10.1016\/j.cpc.2026.110164_bib0055","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.96.155126","article-title":"Quantum Monte Carlo solution of the dynamical mean field equations in real time","volume":"96","author":"Dong","year":"2017","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110164_bib0056","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.95.085144","article-title":"Currents and Green\u2019s functions of impurities out of equilibrium: results from inchworm quantum Monte Carlo","volume":"95","author":"Antipov","year":"2017","journal-title":"Phys. Rev. B"},{"issue":"12","key":"10.1016\/j.cpc.2026.110164_bib0057","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.110.L121120","article-title":"Inchworm quasi Monte Carlo for quantum impurities","volume":"110","author":"Strand","year":"2024","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.cpc.2026.110164_bib0058","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.22331\/q-2025-03-24-1667","article-title":"Solving Caldeira-Leggett model by inchworm method with frozen Gaussian approximation","volume":"9","author":"Wang","year":"2025","journal-title":"Quantum"},{"issue":"23","key":"10.1016\/j.cpc.2026.110164_bib0059","doi-asserted-by":"crossref","first-page":"8523","DOI":"10.1021\/acs.jctc.3c00751","article-title":"Real-time simulation of open quantum spin chains with the inchworm method","volume":"19","author":"Wang","year":"2023","journal-title":"J. Chem. Theory Comput."},{"issue":"26","key":"10.1016\/j.cpc.2026.110164_bib0060","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.115.266802","article-title":"Taming the dynamical sign problem in real-time evolution of quantum many-body problems","volume":"115","author":"Cohen","year":"2015","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0061","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0012-365X(78)90162-0","article-title":"On a class of linked diagrams II. asymptotics","volume":"21","author":"Stein","year":"1978","journal-title":"Discrete Math."},{"issue":"2","key":"10.1016\/j.cpc.2026.110164_bib0062","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1103\/RevModPhys.20.367","article-title":"Space-time approach to non-relativistic quantum mechanics","volume":"20","author":"Feynman","year":"1948","journal-title":"Rev. Mod. Phys."},{"key":"10.1016\/j.cpc.2026.110164_bib0063","series-title":"Doklady Mathematics","first-page":"495","article-title":"A new tensor decomposition","volume":"80","author":"Oseledets","year":"2009"},{"key":"10.1016\/j.cpc.2026.110164_bib0064","article-title":"Compact matrix form of the d-dimensional tensor decomposition","volume":"43","author":"Oseledets","year":"2009"},{"issue":"19","key":"10.1016\/j.cpc.2026.110164_bib0065","doi-asserted-by":"crossref","first-page":"2863","DOI":"10.1103\/PhysRevLett.69.2863","article-title":"Density matrix formulation for quantum renormalization groups","volume":"69","author":"White","year":"1992","journal-title":"Phys. Rev. Lett."},{"issue":"14","key":"10.1016\/j.cpc.2026.110164_bib0066","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.48.10345","article-title":"Density-matrix algorithms for quantum renormalization groups","volume":"48","author":"White","year":"1993","journal-title":"Phys. Rev. B"},{"issue":"1","key":"10.1016\/j.cpc.2026.110164_bib0067","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.laa.2009.07.024","article-title":"TT-cross approximation for multidimensional arrays","volume":"432","author":"Oseledets","year":"2010","journal-title":"Lin. Algebra Appl."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0068","doi-asserted-by":"crossref","DOI":"10.1088\/2632-2153\/ab8731","article-title":"Modeling sequences with quantum states: a look under the hood","volume":"1","author":"Bradley","year":"2020","journal-title":"Mach. Learn. Sci. Technol."},{"issue":"3","key":"10.1016\/j.cpc.2026.110164_bib0069","article-title":"Unsupervised generative modeling using matrix product states","volume":"8","author":"Han","year":"2018","journal-title":"Phys. Rev. X"},{"key":"10.1016\/j.cpc.2026.110164_bib0070","series-title":"Uncertainty in Artificial Intelligence","first-page":"1321","article-title":"Tensor-train density estimation","author":"Novikov","year":"2021"},{"key":"10.1016\/j.cpc.2026.110164_bib0071","doi-asserted-by":"crossref","unstructured":"Y. Peng, S. Yang, Y. Khoo, D. Wang, Tensor density estimator by convolution-deconvolution, 2024, arXiv: 2412.18964.","DOI":"10.2139\/ssrn.5717603"},{"key":"10.1016\/j.cpc.2026.110164_bib0072","doi-asserted-by":"crossref","DOI":"10.1016\/j.acha.2023.101575","article-title":"Generative modeling via tensor train sketching","volume":"67","author":"Hur","year":"2023","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"4","key":"10.1016\/j.cpc.2026.110164_bib0073","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s00211-011-0419-7","article-title":"On manifolds of tensors of fixed TT-rank","volume":"120","author":"Holtz","year":"2012","journal-title":"Numer. Math."},{"key":"10.1016\/j.cpc.2026.110164_bib0074","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1007\/s11045-017-0481-0","article-title":"Fundamental tensor operations for large-scale data analysis using tensor network formats","volume":"29","author":"Lee","year":"2018","journal-title":"Multidim. Syst. Signal Process."},{"issue":"11","key":"10.1016\/j.cpc.2026.110164_bib0075","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevB.98.115152","article-title":"Inclusion-exclusion principle for many-body diagrammatics","volume":"98","author":"Boag","year":"2018","journal-title":"Phys. Rev. B"},{"issue":"15","key":"10.1016\/j.cpc.2026.110164_bib0076","doi-asserted-by":"crossref","first-page":"2823","DOI":"10.1021\/jp9847540","article-title":"The linear response approximation and its lowest order corrections: an influence functional approach","volume":"103","author":"Makri","year":"1999","journal-title":"J. Phys. Chem. B"},{"issue":"11","key":"10.1016\/j.cpc.2026.110164_bib0077","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.112.110401","article-title":"Non-Markovian dynamical maps: numerical processing of open quantum trajectories","volume":"112","author":"Cerrillo","year":"2014","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"10.1016\/j.cpc.2026.110164_bib0078","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/18\/2\/023035","article-title":"Efficient simulation of non-Markovian system-environment interaction","volume":"18","author":"Rosenbach","year":"2016","journal-title":"New J. Phys."},{"key":"10.1016\/j.cpc.2026.110164_bib0079","unstructured":"Z. Sun, J. Huang, C. Xiao, C. Yang, HaTT: Hadamard avoiding TT recompression, 2024, arXiv: 2410.04385."}],"container-title":["Computer Physics Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010465526001463?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010465526001463?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T12:37:44Z","timestamp":1778935064000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0010465526001463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":79,"alternative-id":["S0010465526001463"],"URL":"https:\/\/doi.org\/10.1016\/j.cpc.2026.110164","relation":{},"ISSN":["0010-4655"],"issn-type":[{"value":"0010-4655","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Accelerated inchworm method with tensor-train bath influence functional","name":"articletitle","label":"Article Title"},{"value":"Computer Physics Communications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cpc.2026.110164","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110164"}}