[{"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>","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.","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>","short":"D. Kolisnyk, R.A. Medina Ramos, R. Vasseur, M. Serbyn, Quantum 10 (2026).","ista":"Kolisnyk D, Medina Ramos RA, Vasseur R, Serbyn M. 2026. Tensor cross interpolation of purities in quantum many-body systems. Quantum. 10, 2114.","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>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"2114","title":"Tensor cross interpolation of purities in quantum many-body systems","external_id":{"arxiv":["2503.17230"]},"publication_status":"published","publication_identifier":{"eissn":["2521-327X"]},"article_type":"original","arxiv":1,"type":"journal_article","has_accepted_license":"1","project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","grant_number":"850899","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","call_identifier":"H2020"}],"article_processing_charge":"Yes","day":"22","_id":"21917","fulldoi":"https://doi.org/10.22331/q-2026-05-22-2114","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.22331/q-2026-05-22-2114","file":[{"access_level":"open_access","date_updated":"2026-06-02T09:12:11Z","creator":"dernst","checksum":"f8ce78607ad06120cdf894dc8cef55da","success":1,"date_created":"2026-06-02T09:12:11Z","file_name":"2026_Quantum_Kolisnyk.pdf","content_type":"application/pdf","relation":"main_file","file_size":3284798,"file_id":"21939"}],"date_updated":"2026-06-02T09:15:13Z","department":[{"_id":"MaSe"},{"_id":"GradSch"}],"ec_funded":1,"date_created":"2026-05-26T19:39:12Z","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)","date_published":"2026-05-22T00:00:00Z","month":"05","OA_place":"publisher","publisher":"Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften","oa":1,"file_date_updated":"2026-06-02T09:12:11Z","author":[{"last_name":"Kolisnyk","first_name":"Dmytro","id":"530a7320-5355-11ee-ae5a-82a46997aaa7","orcid":"0000-0002-8612-8202","full_name":"Kolisnyk, Dmytro"},{"last_name":"Medina Ramos","first_name":"Raimel A","id":"CE680B90-D85A-11E9-B684-C920E6697425","orcid":"0000-0002-5383-2869","full_name":"Medina Ramos, Raimel A"},{"last_name":"Vasseur","full_name":"Vasseur, Romain","first_name":"Romain"},{"orcid":"0000-0002-2399-5827","first_name":"Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","full_name":"Serbyn, Maksym","last_name":"Serbyn"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"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.","lang":"eng"}],"corr_author":"1","PlanS_conform":"1","DOAJ_listed":"1","quality_controlled":"1","status":"public","OA_type":"gold","ddc":["530"],"intvolume":"        10","year":"2026","volume":10,"publication":"Quantum"},{"date_published":"2021-07-01T00:00:00Z","month":"07","date_updated":"2026-10-21T22:31:12Z","file":[{"checksum":"9706c2bb8e748e9b5b138381995a7f6f","file_name":"2021_Quantum_Sack.pdf","date_created":"2021-08-06T06:44:31Z","access_level":"open_access","date_updated":"2021-08-06T06:44:31Z","creator":"cchlebak","file_size":2312482,"file_id":"9774","content_type":"application/pdf","relation":"main_file"}],"ec_funded":1,"date_created":"2021-08-01T22:01:21Z","acknowledgement":"We would like to thank D. Abanin and R. Medina for fruitful discussions and A. Smith and I. Kim for valuable feedback on the manuscript. We acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899).","department":[{"_id":"GradSch"},{"_id":"MaSe"}],"intvolume":"         5","scopus_import":"1","status":"public","ddc":["530"],"quality_controlled":"1","year":"2021","volume":5,"publication":"Quantum","publisher":"Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"text":"The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in the QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with suboptimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent\r\nthe issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveal new connections between QAOA and quantum annealing.","lang":"eng"}],"corr_author":"1","oa":1,"file_date_updated":"2021-08-06T06:44:31Z","author":[{"full_name":"Sack, Stefan","orcid":"0000-0001-5400-8508","id":"dd622248-f6e0-11ea-865d-ce382a1c81a5","first_name":"Stefan","last_name":"Sack"},{"first_name":"Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827","full_name":"Serbyn, Maksym","last_name":"Serbyn"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"491","external_id":{"arxiv":["2101.05742"],"isi":["000669830600001"]},"publication_identifier":{"eissn":["2521-327X"]},"publication_status":"published","title":"Quantum annealing initialization of the quantum approximate optimization algorithm","citation":{"apa":"Sack, S., &#38; Serbyn, M. (2021). Quantum annealing initialization of the quantum approximate optimization algorithm. <i>Quantum</i>. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. <a href=\"https://doi.org/10.22331/Q-2021-07-01-491\">https://doi.org/10.22331/Q-2021-07-01-491</a>","ieee":"S. Sack and M. Serbyn, “Quantum annealing initialization of the quantum approximate optimization algorithm,” <i>Quantum</i>, vol. 5. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2021.","mla":"Sack, Stefan, and Maksym Serbyn. “Quantum Annealing Initialization of the Quantum Approximate Optimization Algorithm.” <i>Quantum</i>, vol. 5, 491, Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2021, doi:<a href=\"https://doi.org/10.22331/Q-2021-07-01-491\">10.22331/Q-2021-07-01-491</a>.","short":"S. Sack, M. Serbyn, Quantum 5 (2021).","ama":"Sack S, Serbyn M. Quantum annealing initialization of the quantum approximate optimization algorithm. <i>Quantum</i>. 2021;5. doi:<a href=\"https://doi.org/10.22331/Q-2021-07-01-491\">10.22331/Q-2021-07-01-491</a>","ista":"Sack S, Serbyn M. 2021. Quantum annealing initialization of the quantum approximate optimization algorithm. Quantum. 5, 491.","chicago":"Sack, Stefan, and Maksym Serbyn. “Quantum Annealing Initialization of the Quantum Approximate Optimization Algorithm.” <i>Quantum</i>. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2021. <a href=\"https://doi.org/10.22331/Q-2021-07-01-491\">https://doi.org/10.22331/Q-2021-07-01-491</a>."},"article_processing_charge":"Yes","doi":"10.22331/Q-2021-07-01-491","day":"01","_id":"9760","oa_version":"Published Version","fulldoi":"https://doi.org/10.22331/Q-2021-07-01-491","language":[{"iso":"eng"}],"arxiv":1,"isi":1,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"14622"}]},"article_type":"original","type":"journal_article","has_accepted_license":"1","project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","grant_number":"850899","call_identifier":"H2020","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E"}]}]