Spatial search by quantum walk

Journal Article · Sun Aug 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.022314· OSTI ID:20645859

Childs, Andrew M; Goldstone, Jeffrey ^[1]

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1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

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 {radical}(N) for d>2, and in time of order {radical}(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 {radical}(N) speedup can also be achieved on the hypercube. We show that full {radical}(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 {radical}(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.

• OSTI ID: 20645859
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
CORRELATIONS
ENERGY LEVELS
GRAPH THEORY
INFORMATION THEORY
PERIODICITY
QUANTUM MECHANICS
VELOCITY