On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

@article{Geraci2008OnTE,
  title={On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers},
  author={J. Geraci and D. Lidar},
  journal={Communications in Mathematical Physics},
  year={2008},
  volume={279},
  pages={735-768}
}
  • J. Geraci, D. Lidar
  • Published 2008
  • Mathematics, Physics
  • Communications in Mathematical Physics
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to… Expand
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