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28 March 2024
 
  » arxiv » quant-ph/0309064

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On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
Daniel A. Lidar ;
Date 8 Sep 2003
Journal New J. Phys. 6 (2004) 167 DOI: 10.1088/1367-2630/6/1/167
Subject Quantum Physics; Mathematical Physics | quant-ph cond-mat math-ph math.MP
AffiliationCenter for Quantum Information and Quantum Control, University of Toronto
AbstractIt 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.
Source arXiv, quant-ph/0309064
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