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Cited by 56Quantum Computing Algorithms and ArchitectureQuantum many-body systemsTheoretical and Computational Physics

Classical Spin Models and the Quantum-Stabilizer Formalism

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den Nest, M. Van, Dür, W., Briegel, H. J.·2007·Physical Review Letters
DOI 10.1103/physrevlett.98.117207
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Abstract

We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum-stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum-information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and high-low temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded tree-width.

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  • The Ising model on an arbitrary lattice L can be mapped to an MQC model in which the entangled resource is determined by the geometry of L.

    “The connection between MQC and the Ising model is given by a mapping of the Ising model on an arbitrary lattice L to an MQC model where the entangled resource is determined by the geometry of L ,”

    From Measurement-based quantum computation (2009) · cites this paper as [96]

  • These connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting.

    “For one, these connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting 87,92,95,96,99-102 .”

    From Measurement-based quantum computation (2009) · cites this paper as [96]

  • The efficient classical simulation of MQC on stabilizer states with bounded tree-width yields a novel classical algorithm to efficiently calculate the partition function on (inhomogeneous) q-state spin models on tree-like graphs with or without magnetic fields.

    “In turn, the efficient classical simulation of MQC on stabilizer states with bounded tree-width 94 , as demonstrated in 91 , yields a novel classical algorithm to efficiently calculate the partition function on (inhomogenous) q -state spin models on tree-like-graphs with or without magnetic fields 95,96 .”

    From Measurement-based quantum computation (2009) · cites this paper as [96]

  • The partition function Z_L is identified with a quantum mechanical amplitude obtained as an overlap between two quantum states.

    “This expression states that the partition function Z L is identified with a quantum mechanical amplitude which is obtained as an overlap between two quantum states 92,95,96 (see also 99 ).”

    From Measurement-based quantum computation (2009) · cites this paper as [96]

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Authors
den Nest, M. V., Dür, W., & Briegel, H. J.
Affiliations
Austrian Academy of Sciences (AT)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2007-03-16
Volume
98
Issue
11
Pages
117207-117207
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.98.117207
OpenAlex
W1993557942
Cited by
56
References
15
Citations by year
2026: 1 · 2024: 2 · 2023: 2 · 2022: 3 · 2021: 2 · 2020: 4 · 2019: 3 · 2018: 3 · 2017: 2 · 2016: 1 · 2015: 2 · 2014: 3 · 2013: 3 · 2012: 3
FWCI
8.29
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
Keywords
classical spin systems, partition function, Potts model, clock model, quantum-classical correspondence

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