Search on a hypercubic lattice using a quantum random walk. I. d>2
- Centre for High Energy Physics, Indian Institute of Science, Bangalore-560012 (India)
- Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore-560012 (India)
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d>2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d{yields}{infinity} limit). In particular, the scaling behavior for d=3 is only about 25% higher than the optimal d{yields}{infinity} value.
- OSTI ID:
- 21448668
- Journal Information:
- Physical Review. A, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevA.82.032330; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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