2001/01/30 by G. Sampath, Sampath, G.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0101142
5 pages
arxiv created 2001/01/30 · openalex publication_date 2001/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.