Abstract
Grover’s quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of items laid out in spatial dimensions can be searched in time of order for , and in time of order for . We consider an alternative search algorithm based on a continuous-time quantum walk on a graph. The case of the complete graph gives the continuous-time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that speedup can also be achieved on the hypercube. We show that full speedup can be achieved on a -dimensional periodic lattice for . In , the quantum walk search algorithm takes time of order , and in , the algorithm does not provide substantial speedup.
- Received 16 June 2003
DOI:https://doi.org/10.1103/PhysRevA.70.022314
©2004 American Physical Society