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Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
Open accessAbstract
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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“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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Metadata
- Authors
- Barthel, T., Pineda, C., & Eisert, J.
- Affiliations
- University of Potsdam (DE)
- Universidad Nacional Autónoma de México (MX)
- 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
- 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
- green
- arxiv.org
- 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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