  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.
