An Example of the Difference Between Quantum and Classical Random Walks
- 887 Downloads
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analog. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case.
Unable to display preview. Download preview PDF.
- 1.E. Farhi and S. Gutmann, Phys. Rev. A 58, 915 (1998).Google Scholar
- 2.E. Farhi and S. Gutmann, Ann. Phys. 213, 182 (1992).Google Scholar
- 3.D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, quant-ph/0012090.Google Scholar
- 4.Y. Aharonov, L. Davidovich, and N. Zagury, Phys. Rev. A 48, 1687 (1993).Google Scholar
- 5.A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, in Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing (ACM Press, New York, 2001), p. 37.Google Scholar
- 6.D. A. Meyer, Phys. Lett. A 223, 337 (1996).Google Scholar