Quantum Random Walks without a Coin Toss

Details Quantum Random Walks without a Coin Toss Quantum Random Walks without a Coin Toss

2005-06-27

arxiv.org/abs/quant-ph/0506221v1

Physics

Quantum Physics

8 pages, RevTeX4, 5 figures. Invited lecture at the Workshop on Quantum Information, Computation and Communication (QICC-2005)

Scientific paper

We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of classical randomised algorithms. We use this algorithm to search for a marked vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and analytical results match the scaling behaviour of earlier algorithms that use a coin toss instruction.

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