Quantum simulations of classical annealing processes.

@article{Somma2008QuantumSO,
  title={Quantum simulations of classical annealing processes.},
  author={Rolando D. Somma and Sergio Boixo and Howard Barnum and E Knill},
  journal={Physical review letters},
  year={2008},
  volume={101 13},
  pages={130504}
}
We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order 1/sqrt delta steps to find an optimal solution with bounded error probability, where delta is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.
Showing 1-10 of 23 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 13 references

Proceedings of the 45th Symposium on Foundations of Computer Science

A. Ambainis
22 (2004). M. Szegedy, Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 32 (2004). F. Magniez, A. Nayak, J. Roland, and M. Santha, Proceedings of the 39th Annual ACM Symposium on Theory of Computing, 575 • 2007
View 5 Excerpts
Highly Influenced

Phys

R. D. Somma, C. D. Batista, G. Ortiz
Rev. Lett. 99, 030603 • 2007

Proceedings of the 35th Annual Symposium on the Theory of Computation (STOC)

D. Aharonov, A. Ta-Shma
20-29 (2003); SIAM J. Comput. 37, 47 • 2007
View 1 Excerpt

and D

B. Apolloni, N. Cesa-Bianchi
de Falco, in Stochastic Processes, Physics and Geometry, World Scientific (1990). T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998); E. Farhi, et al., Science 292, 472 (2001); G.E. Santoro et al., Science 295, 2427 (2002); G.E. Santoro and E. Tosatti, Nature Physics 3, 593 • 2007
View 1 Excerpt

An Introduction to Markov Processes

D. W. Stroock
Springer-Verlag, Berlin • 2005
View 1 Excerpt

arXiv:quant-ph/0303081 for a review and references therein

J. Kempe
Proceedings of the 33th Annual ACM Symposium on Theory of Computing, • 2001
View 1 Excerpt

Combinatorial Optimization

W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, A. Schrijver
J. Wiley and Sons, New York • 1998
View 1 Excerpt

Proceedings of the 35th Annual Symp

P. Shor
Found. Comp. Science, 116 (1994); L.K. Grover, Proceedings of the 28th Annual ACM Symp. on the Th. Comp., 212 • 1996
View 1 Excerpt

Siam J

M. Jerrum, A. Sinclair
of Comp. 22, 1087 • 1993
View 1 Excerpt

Similar Papers

Loading similar papers…