Quantum snake walk on graphs
- David R. Cheriton School of Computer Science and Institute for Quantum Computing, University of Waterloo, West Waterloo, Ontario, N2L 3G1 (Canada)
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
- OSTI ID:
- 21537121
- Journal Information:
- Physical Review. A, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevA.83.022304; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quantum stochastic walks: A generalization of classical random walks and quantum walks
Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks