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Cited by 139Quantum many-body systemsQuantum Computing Algorithms and ArchitectureCold Atom Physics and Bose-Einstein Condensates

Contraction of fermionic operator circuits and the simulation of strongly correlated fermions

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Barthel, Thomas, Pineda, Carlos, Eisert, Jens·2009·Physical Review A
DOI 10.1103/physreva.80.042333
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Abstract

A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented framework allows for the introduction of fermionic versions of known qudit operator circuits (QUOC), important for the simulation of strongly correlated $d$-dimensional systems: the multiscale entanglement renormalization ans\"atze (MERA), tree tensor networks (TTN), projected entangled pair states (PEPS), or their infinite-size versions (iPEPS etc.). After the definition of a FOC, we present a method to contract it with the same computation and memory requirements as a corresponding QUOC, for which all fermionic operators are replaced by qudit operators of identical dimension. A given scheme for contracting the QUOC relates to an analogous scheme for the corresponding fermionic circuit, where additional marginal computational costs arise only from reordering of modes for operators occurring in intermediate stages of the contraction. Our result hence generalizes efficient schemes for the simulation of $d$-dimensional spin systems, as MERA, TTN, or PEPS to the fermionic case.

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  • Levitov's formula relates traces of operators in the fermionic Hilbert space to determinants of much smaller matrices.

    “For computing fidelities, we use the convenient Levitov's formula [204, 205], which relates traces of operators in the Hilbert space of the fermions to determinants of much smaller matrices (like H ).”

    From Can one trust quantum simulators? (2012) · cites this paper as [204]

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Research works printed but not linked: 5

  1. [29]P. Corboz, G. Evenbly, F. Verstraete, and G. Vidal, arXiv:0904.4151v1 (2009). · arXiv
  2. [30]C. Pineda, T. Barthel, and J. Eisert, arXiv:0905.0669 (2009). · arXiv
  3. [31]C. V. Kraus, N. Schuch, F. Verstraete, and J. I. Cirac, arXiv:0904.4667 (2009). · arXiv
  4. [42]J. Eisert, M. Cramer, and M. B. Plenio, arXiv:0808.3773 (2008). · arXiv
  5. [43]J. I. Latorre and A. Riera, arXiv:0906.1499 (2009). · arXiv

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Authors
Barthel, T., Pineda, C., & Eisert, J.
Affiliations
  • University of Potsdam (DE)
  • Universidad Nacional Autónoma de México (MX)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2009-10-30
Volume
80
Issue
4
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.80.042333
OpenAlex
W1976666892
Cited by
139
References
38
Citations by year
2026: 2 · 2025: 9 · 2024: 9 · 2023: 7 · 2022: 14 · 2021: 9 · 2020: 10 · 2019: 11 · 2018: 1 · 2017: 6 · 2016: 7 · 2015: 5 · 2014: 11 · 2013: 4 · 2012: 11
FWCI
6.32
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • publish.UP (University of Potsdam) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
Keywords
strongly correlated fermions, multiscale entanglement renormalization ansatz, tree tensor networks, projected entangled pair states, infinite projected entangled pair states, tensor network contraction

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