A quantum computing scheme for the Hamiltonian path problem

Details A quantum computing scheme for the Hamiltonian path problem A quantum computing scheme for the Hamiltonian path problem

2001-01-30

arxiv.org/abs/quant-ph/0101142v1

Physics

Quantum Physics

5 pages

Scientific paper

A quantum computing scheme that uses a single photon and multiple-slit gratings is suggested for the Hamiltonian path problem on a simple graph G of N vertices. The photon is input to an N-slit grating followed by an N x N matrix of `processing units'. A unit consists of a delay line followed by a grating with k slits (0 < k < N) whose outputs are directed to k units in the next row in a manner determined by the adjacency matrix of G. There is a one-to-one mapping between paths of length N-1 in the graph and physical paths through the matrix. The photon's path is a superposition of all these physical paths. The time taken by the photon along a physical path corresponding to a Hamiltonian path in G is a fixed value equal to the sum of N distinct delays, and is different from the time along any other path. The graph is Hamiltonian if any one of N detectors placed in the output of the N units in row N detects the photon at this fixed time.

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