The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
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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Cites
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597
Verstraete, F., Murg, V., & Cirac, J. I. (2008) · Advances In Physics · doi:10.1080/14789940801912366 · Cited by 1,841
Vidal, G. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.220405 · Cited by 1,206
Bravyi, S. B., & Kitaev, A. Y. (2002) · Annals of Physics · doi:10.1006/aphy.2002.6254 · Cited by 1,033
Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions
Jordan, J., Orús, R., Vidal, G., Verstraete, F., & Cirac, J. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.250602 · Cited by 710
The Complexity of the Local Hamiltonian Problem
Kempe, J., Kitaev, A., & Regev, O. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704445226 · Cited by 648
Classical simulation of quantum many-body systems with a tree tensor network
Shi, Y.-Y., Duan, L.-M., & Vidal, G. (2006) · Physical Review A · doi:10.1103/physreva.74.022320 · Cited by 577
Research works printed but not linked: 1
- R. Oliveira, 2008, Quantum Inf. Comput., 8, 0900
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Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
Cirac, J. I., Pérez-Garcı́a, D., Schuch, N., & Verstraete, F. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.045003 · Cited by 1,025
Tensor networks for complex quantum systems
Orús, R. (2019) · Nature Reviews Physics · doi:10.1038/s42254-019-0086-7 · Cited by 734
Competing States in the t - J Model: Uniform d -Wave State versus Stripe State
Corboz, P., Rice, T. M., & Troyer, M. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.046402 · Cited by 493
Corboz, P., Orús, R., Bauer, B., & Vidal, G. (2010) · Physical Review B · doi:10.1103/physrevb.81.165104 · Cited by 334
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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