Physics – Quantum Physics
Scientific paper
2003-06-06
Phys. Rev. A 70, 022314 (2004)
Physics
Quantum Physics
v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fails
Scientific paper
10.1103/PhysRevA.70.022314
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 N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. 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 sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.
Childs Andrew M.
Goldstone Jeffrey
No associations
LandOfFree
Spatial search by quantum walk does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spatial search by quantum walk, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spatial search by quantum walk will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-435200