On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants

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dc.creatorLidar, Daniel A.
dc.date2003-09-08
dc.date2004-08-18
dc.date.accessioned2026-07-07T06:07:47Z
dc.date.available2026-07-07T06:07:47Z
dc.descriptionIt is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed weight enumerators (QWGTs). On the other hand it is known that quantum computing is polynomially equivalent to classical probabilistic computing with an oracle for estimating QWGTs. This suggests a connection between the partition function estimation problem for spin glasses and quantum computation. This connection extends to knots and graph theory via the equivalence of the Kauffman polynomial and the partition function for the Potts model.
dc.description8 pages, incl. 2 figures. v2: Substantially rewritten
dc.identifierhttps://arxiv.org/abs/quant-ph/0309064
dc.identifierhttp://arxiv.org/abs/quant-ph/0309064
dc.identifierNew J. Phys. 6 (2004) 167
dc.identifierdoi:10.1088/1367-2630/6/1/167
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91414
dc.subjectQuantum Physics
dc.subjectCondensed Matter
dc.subjectMathematical Physics
dc.titleOn the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
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