[{"PlanS_conform":"1","intvolume":"        10","file":[{"file_id":"21939","creator":"dernst","access_level":"open_access","file_name":"2026_Quantum_Kolisnyk.pdf","date_created":"2026-06-02T09:12:11Z","success":1,"content_type":"application/pdf","relation":"main_file","file_size":3284798,"date_updated":"2026-06-02T09:12:11Z","checksum":"f8ce78607ad06120cdf894dc8cef55da"}],"abstract":[{"lang":"eng","text":"A defining feature of quantum many-body systems is the exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders a complete state characterization, for instance via the complete set of bipartite Renyi entropies for all disjoint regions, a challenging task. Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed. Notably, the entanglement feature can be a simple object even for highly entangled quantum states. However the complexity and practical usage of the entanglement feature for general quantum states has not been explored. In this work, we demonstrate that the entanglement feature can be efficiently learned using only a polynomial amount of samples in the number of degrees of freedom through the so-called tensor cross interpolation (TCI) algorithm, assuming it is expressible as a finite bond dimension MPS. We benchmark this learning process on Haar and random MPS states, confirming analytic expectations. Applying the TCI algorithm to quantum eigenstates of various one dimensional quantum systems, we identify cases where eigenstates have entanglement feature learnable with TCI. We conclude with possible applications of the learned entanglement feature, such as quantifying the distance between different entanglement patterns and finding the optimal one-dimensional ordering of physical indices in a given state, highlighting the potential utility of the proposed purity interpolation method."}],"publication_status":"published","status":"public","article_processing_charge":"Yes","day":"22","publication":"Quantum","year":"2026","title":"Tensor cross interpolation of purities in quantum many-body systems","has_accepted_license":"1","ec_funded":1,"arxiv":1,"OA_type":"gold","volume":10,"article_number":"2114","department":[{"_id":"MaSe"},{"_id":"GradSch"}],"oa":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"date_updated":"2026-06-02T09:15:13Z","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","DOAJ_listed":"1","_id":"21917","OA_place":"publisher","author":[{"id":"530a7320-5355-11ee-ae5a-82a46997aaa7","last_name":"Kolisnyk","full_name":"Kolisnyk, Dmytro","first_name":"Dmytro","orcid":"0000-0002-8612-8202"},{"orcid":"0000-0002-5383-2869","first_name":"Raimel A","full_name":"Medina Ramos, Raimel A","last_name":"Medina Ramos","id":"CE680B90-D85A-11E9-B684-C920E6697425"},{"last_name":"Vasseur","first_name":"Romain","full_name":"Vasseur, Romain"},{"orcid":"0000-0002-2399-5827","full_name":"Serbyn, Maksym","first_name":"Maksym","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"citation":{"apa":"Kolisnyk, D., Medina Ramos, R. A., Vasseur, R., &#38; Serbyn, M. (2026). Tensor cross interpolation of purities in quantum many-body systems. <i>Quantum</i>. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. <a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">https://doi.org/10.22331/q-2026-05-22-2114</a>","mla":"Kolisnyk, Dmytro, et al. “Tensor Cross Interpolation of Purities in Quantum Many-Body Systems.” <i>Quantum</i>, vol. 10, 2114, Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2026, doi:<a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">10.22331/q-2026-05-22-2114</a>.","ama":"Kolisnyk D, Medina Ramos RA, Vasseur R, Serbyn M. Tensor cross interpolation of purities in quantum many-body systems. <i>Quantum</i>. 2026;10. doi:<a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">10.22331/q-2026-05-22-2114</a>","chicago":"Kolisnyk, Dmytro, Raimel A Medina Ramos, Romain Vasseur, and Maksym Serbyn. “Tensor Cross Interpolation of Purities in Quantum Many-Body Systems.” <i>Quantum</i>. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2026. <a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">https://doi.org/10.22331/q-2026-05-22-2114</a>.","ista":"Kolisnyk D, Medina Ramos RA, Vasseur R, Serbyn M. 2026. Tensor cross interpolation of purities in quantum many-body systems. Quantum. 10, 2114.","ieee":"D. Kolisnyk, R. A. Medina Ramos, R. Vasseur, and M. Serbyn, “Tensor cross interpolation of purities in quantum many-body systems,” <i>Quantum</i>, vol. 10. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2026.","short":"D. Kolisnyk, R.A. Medina Ramos, R. Vasseur, M. Serbyn, Quantum 10 (2026)."},"acknowledgement":"We acknowledge useful discussions with Richard Küng\r\non the interpolation methods and error spreading, Ilia\r\nA. Luchnikov, Margarita Davydova, and, in particular, Hiroshi Shinaoka, Marc Ritter, Yuriel Nuñez\r\nfor useful discussions about TCI and the various\r\nworkarounds within the TensorCrossInterpolation.jl\r\nlibrary. We also acknowledge the comments of anonymous Referee B, that encouraged us to expand the\r\nmanuscript with discussion of additional applications\r\nof entanglement feature in Section 4.3. M.S. acknowledges discussions with D. V. Savostyanov at the 2nd\r\nInternational Quantum Tensor Networks (IQTN) plenary meeting at Flatiron Institute’s Center for Computational Quantum Physics (CCQ) for introduction\r\nto the TCI approach. D.K and M.S. acknowledge support by the European Research Council (ERC) under We acknowledge useful discussions with Richard Küng\r\non the interpolation methods and error spreading, Ilia\r\nA. Luchnikov, Margarita Davydova, and, in particular, Hiroshi Shinaoka, Marc Ritter, Yuriel Nuñez\r\nfor useful discussions about TCI and the various\r\nworkarounds within the TensorCrossInterpolation.jl\r\nlibrary. We also acknowledge the comments of anonymous Referee B, that encouraged us to expand the\r\nmanuscript with discussion of additional applications\r\nof entanglement feature in Section 4.3. M.S. acknowledges discussions with D. V. Savostyanov at the 2nd\r\nInternational Quantum Tensor Networks (IQTN) plenary meeting at Flatiron Institute’s Center for Computational Quantum Physics (CCQ) for introduction\r\nto the TCI approach. D.K and M.S. acknowledge support by the European Research Council (ERC) under We acknowledge useful discussions with Richard Küng\r\non the interpolation methods and error spreading, Ilia\r\nA. Luchnikov, Margarita Davydova, and, in particular, Hiroshi Shinaoka, Marc Ritter, Yuriel Nuñez\r\nfor useful discussions about TCI and the various\r\nworkarounds within the TensorCrossInterpolation.jl\r\nlibrary. We also acknowledge the comments of anonymous Referee B, that encouraged us to expand the\r\nmanuscript with discussion of additional applications\r\nof entanglement feature in Section 4.3. M.S. acknowledges discussions with D. V. Savostyanov at the 2nd\r\nInternational Quantum Tensor Networks (IQTN) plenary meeting at Flatiron Institute’s Center for Computational Quantum Physics (CCQ) for introduction\r\nto the TCI approach. D.K and M.S. acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899).\r\nR.V. acknowledges partial support from the US Department of Energy, Office of Science, Basic Energy\r\nSciences, under award No. DE-SC0023999, and the\r\nSwiss National Science Foundation (grant 10008234).\r\nThis research was supported in part by grant NSF\r\nPHY-2309135 to the Kavli Institute for Theoretical\r\nPhysics (KITP)","external_id":{"arxiv":["2503.17230"]},"project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","call_identifier":"H2020","grant_number":"850899"}],"ddc":["530"],"publication_identifier":{"eissn":["2521-327X"]},"month":"05","oa_version":"Published Version","date_created":"2026-05-26T19:39:12Z","publisher":"Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften","date_published":"2026-05-22T00:00:00Z","language":[{"iso":"eng"}],"file_date_updated":"2026-06-02T09:12:11Z","doi":"10.22331/q-2026-05-22-2114","type":"journal_article"}]