---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '21917'
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.
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)"
article_number: '2114'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Dmytro
full_name: Kolisnyk, Dmytro
id: 530a7320-5355-11ee-ae5a-82a46997aaa7
last_name: Kolisnyk
orcid: 0000-0002-8612-8202
- first_name: Raimel A
full_name: Medina Ramos, Raimel A
id: CE680B90-D85A-11E9-B684-C920E6697425
last_name: Medina Ramos
orcid: 0000-0002-5383-2869
- first_name: Romain
full_name: Vasseur, Romain
last_name: Vasseur
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
citation:
ama: Kolisnyk D, Medina Ramos RA, Vasseur R, Serbyn M. Tensor cross interpolation
of purities in quantum many-body systems. Quantum. 2026;10. doi:10.22331/q-2026-05-22-2114
apa: Kolisnyk, D., Medina Ramos, R. A., Vasseur, R., & Serbyn, M. (2026). Tensor
cross interpolation of purities in quantum many-body systems. Quantum.
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften.
https://doi.org/10.22331/q-2026-05-22-2114
chicago: Kolisnyk, Dmytro, Raimel A Medina Ramos, Romain Vasseur, and Maksym Serbyn.
“Tensor Cross Interpolation of Purities in Quantum Many-Body Systems.” Quantum.
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften,
2026. https://doi.org/10.22331/q-2026-05-22-2114.
ieee: D. Kolisnyk, R. A. Medina Ramos, R. Vasseur, and M. Serbyn, “Tensor cross
interpolation of purities in quantum many-body systems,” Quantum, vol.
10. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften,
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.
mla: Kolisnyk, Dmytro, et al. “Tensor Cross Interpolation of Purities in Quantum
Many-Body Systems.” Quantum, vol. 10, 2114, Verein zur Förderung des Open
Access Publizierens in den Quantenwissenschaften, 2026, doi:10.22331/q-2026-05-22-2114.
short: D. Kolisnyk, R.A. Medina Ramos, R. Vasseur, M. Serbyn, Quantum 10 (2026).
corr_author: '1'
date_created: 2026-05-26T19:39:12Z
date_published: 2026-05-22T00:00:00Z
date_updated: 2026-06-02T09:15:13Z
day: '22'
ddc:
- '530'
department:
- _id: MaSe
- _id: GradSch
doi: 10.22331/q-2026-05-22-2114
ec_funded: 1
external_id:
arxiv:
- '2503.17230'
file:
- access_level: open_access
checksum: f8ce78607ad06120cdf894dc8cef55da
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creator: dernst
date_created: 2026-06-02T09:12:11Z
date_updated: 2026-06-02T09:12:11Z
file_id: '21939'
file_name: 2026_Quantum_Kolisnyk.pdf
file_size: 3284798
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has_accepted_license: '1'
intvolume: ' 10'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: Quantum
publication_identifier:
eissn:
- 2521-327X
publication_status: published
publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
quality_controlled: '1'
status: public
title: Tensor cross interpolation of purities in quantum many-body systems
tmp:
image: /images/cc_by.png
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)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '2026'
...