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={Joseph Geraci and D. Lidar}, journal={Communications in Mathematical Physics}, year={2008}, volume={279}, pages={735-768} }
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… CONTINUE READING
27 Citations
A theorem on the quantum evaluation of Weight Enumerators for a certain class of Cyclic Codes with a note on Cyclotomic cosets
- Mathematics, Computer Science
- 2007
- 2
- PDF
Possible quantum algorithms for the Bollobas-Riordan-Tutte polynomial of a ribbon graph
- Mathematics, Engineering
- SPIE Defense + Commercial Sensing
- 2008
- 2
Completeness of classical spin models and universal quantum computation
- Mathematics, Physics
- 2009
- 14
- PDF
References
SHOWING 1-10 OF 61 REFERENCES
Polynomial Quantum Algorithms for Additive approximations of the Potts model and other Points of the Tutte Plane
- Mathematics, Physics
- 2007
- 66
- Highly Influential
- PDF
On the quantum computational complexity of the Ising spin glass partition function and of knot invariants
- Physics, Mathematics
- 2004
- 22
- PDF
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
- Mathematics, Physics
- Quantum Inf. Comput.
- 2008
- 77
- PDF
On Some Polynomials Related to Weight Enumerators of Linear Codes
- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 2002
- 8
- PDF
Quantum computation of zeta functions of curves
- Mathematics, Computer Science
- computational complexity
- 2006
- 27
- PDF
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial
- Mathematics, Computer Science
- Algorithmica
- 2008
- 153
- PDF
$q$ - Deformed Spin Networks, Knot Polynomials and Anyonic Topological Quantum Computation
- Mathematics, Physics
- 2006
- 74
- PDF
Exact Potts Model Partition Functions on Ladder Graphs
- Mathematics, Physics
- 2000
- 59
- Highly Influential
- PDF