dorsal/arxiv
View SchemaClassical spin models and the quantum stabilizer formalism
| Authors | M. Van den Nest, W. Dür, H. J. Briegel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610157 |
| URL | https://arxiv.org/abs/quant-ph/0610157 |
| DOI | 10.1103/PhysRevLett.98.117207 |
| Journal | Phys. Rev. Lett. 98, 117207 (2007) |
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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"abstract": "We relate a large class of classical spin models, including the inhomogeneous\nIsing, Potts, and clock models of q-state spins on arbitrary graphs, to\nproblems in quantum physics. More precisely, we show how to express partition\nfunctions as inner products between certain quantum stabilizer states and\nproduct states. This connection allows us to use powerful techniques developed\nin quantum information theory, such as the stabilizer formalism and classical\nsimulation techniques, to gain general insights into these models in a unified\nway. We recover and generalize several symmetries and high-low temperature\ndualities, and we provide an efficient classical evaluation of partition\nfunctions for all interaction graphs with a bounded tree-width.",
"arxiv_id": "quant-ph/0610157",
"authors": [
"M. Van den Nest",
"W. D\u00fcr",
"H. J. Briegel"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevLett.98.117207",
"journal_ref": "Phys. Rev. Lett. 98, 117207 (2007)",
"title": "Classical spin models and the quantum stabilizer formalism",
"url": "https://arxiv.org/abs/quant-ph/0610157"
},
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