---
APC_amount: 3711,01 EUR
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18488'
abstract:
- lang: eng
  text: The advancement of quantum simulators motivates the development of a theoretical
    framework to assist with efficient state preparation in quantum many-body systems.
    Generally, preparing a target entangled state via unitary evolution with time-dependent
    couplings is a challenging task and very little is known about the existence of
    solutions and their properties. In this work we develop a constructive approach
    for preparing matrix product states (MPS) via continuous unitary evolution. We
    provide an explicit construction of the operator that exactly implements the evolution
    of a given MPS along a specified direction in its tangent space. This operator
    can be written as a sum of local terms of finite range, yet it is in general non-Hermitian.
    Relying on the explicit construction of the non-Hermitian generator of the dynamics,
    we demonstrate the existence of a Hermitian sequence of operators that implements
    the desired MPS evolution with an error that decreases exponentially with the
    operator range. The construction is benchmarked on an explicit periodic trajectory
    in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary
    generating the dynamics over one period of the trajectory features an approximate
    MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results
    show that our construction is not only useful for state preparation and control
    of many-body systems, but also provides a generic route towards Floquet scars—periodically
    driven models with quasilocal generators of dynamics that have exact MPS eigenstates
    in their spectrum.
acknowledgement: We thank L. Piroli, S. Garratt, and A. Molnár for insightful discussions.
  This research was funded in part by the European Research Council (ERC) under the
  European Union’s Horizon 2020 research and innovation programme (Grant Agreements
  No. 850899 and No. 863476), the Austrian Science Fund (FWF) (Grant DOIs 10.55776/COE1,
  10.55776/P36305, and 10.55776/F71), and the European Union (NextGenerationEU). This
  work was performed in part at the Aspen Center for Physics, which is supported by
  National Science Foundation Grant PHY-2210452. This research was supported in part
  by NSF Grant PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).
article_number: '040311'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Marko
  full_name: Ljubotina, Marko
  id: F75EE9BE-5C90-11EA-905D-16643DDC885E
  last_name: Ljubotina
  orcid: 0000-0003-0038-7068
- first_name: Elena
  full_name: Petrova, Elena
  id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
  last_name: Petrova
- first_name: Norbert
  full_name: Schuch, Norbert
  last_name: Schuch
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
citation:
  ama: Ljubotina M, Petrova E, Schuch N, Serbyn M. Tangent space generators of matrix
    product states and exact floquet quantum scars. <i>PRX Quantum</i>. 2024;5(4).
    doi:<a href="https://doi.org/10.1103/prxquantum.5.040311">10.1103/prxquantum.5.040311</a>
  apa: Ljubotina, M., Petrova, E., Schuch, N., &#38; Serbyn, M. (2024). Tangent space
    generators of matrix product states and exact floquet quantum scars. <i>PRX Quantum</i>.
    American Physical Society. <a href="https://doi.org/10.1103/prxquantum.5.040311">https://doi.org/10.1103/prxquantum.5.040311</a>
  chicago: Ljubotina, Marko, Elena Petrova, Norbert Schuch, and Maksym Serbyn. “Tangent
    Space Generators of Matrix Product States and Exact Floquet Quantum Scars.” <i>PRX
    Quantum</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/prxquantum.5.040311">https://doi.org/10.1103/prxquantum.5.040311</a>.
  ieee: M. Ljubotina, E. Petrova, N. Schuch, and M. Serbyn, “Tangent space generators
    of matrix product states and exact floquet quantum scars,” <i>PRX Quantum</i>,
    vol. 5, no. 4. American Physical Society, 2024.
  ista: Ljubotina M, Petrova E, Schuch N, Serbyn M. 2024. Tangent space generators
    of matrix product states and exact floquet quantum scars. PRX Quantum. 5(4), 040311.
  mla: Ljubotina, Marko, et al. “Tangent Space Generators of Matrix Product States
    and Exact Floquet Quantum Scars.” <i>PRX Quantum</i>, vol. 5, no. 4, 040311, American
    Physical Society, 2024, doi:<a href="https://doi.org/10.1103/prxquantum.5.040311">10.1103/prxquantum.5.040311</a>.
  short: M. Ljubotina, E. Petrova, N. Schuch, M. Serbyn, PRX Quantum 5 (2024).
corr_author: '1'
date_created: 2024-10-29T16:04:05Z
date_published: 2024-10-23T00:00:00Z
date_updated: 2025-09-08T14:26:29Z
day: '23'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1103/prxquantum.5.040311
ec_funded: 1
external_id:
  arxiv:
  - '2403.12325'
  isi:
  - '001346198800001'
file:
- access_level: open_access
  checksum: 2e057ba021744d0a74602517935326b3
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  creator: dernst
  date_created: 2024-10-30T08:59:09Z
  date_updated: 2024-10-30T08:59:09Z
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file_date_updated: 2024-10-30T08:59:09Z
fulldoi: https://doi.org/10.1103/prxquantum.5.040311
has_accepted_license: '1'
intvolume: '         5'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
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: PRX Quantum
publication_identifier:
  eissn:
  - 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tangent space generators of matrix product states and exact floquet quantum
  scars
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 5
year: '2024'
...