dorsal/arxiv
View SchemaA quantum computing scheme for the Hamiltonian path problem
| Authors | G. Sampath |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101142 |
| URL | https://arxiv.org/abs/quant-ph/0101142 |
Abstract
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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"abstract": "A quantum computing scheme that uses a single photon and multiple-slit\ngratings is suggested for the Hamiltonian path problem on a simple graph G of N\nvertices. The photon is input to an N-slit grating followed by an N x N matrix\nof `processing units\u0027. A unit consists of a delay line followed by a grating\nwith k slits (0 \u003c k \u003c N) whose outputs are directed to k units in the next row\nin a manner determined by the adjacency matrix of G. There is a one-to-one\nmapping between paths of length N-1 in the graph and physical paths through the\nmatrix. The photon\u0027s path is a superposition of all these physical paths. The\ntime taken by the photon along a physical path corresponding to a Hamiltonian\npath in G is a fixed value equal to the sum of N distinct delays, and is\ndifferent from the time along any other path. The graph is Hamiltonian if any\none of N detectors placed in the output of the N units in row N detects the\nphoton at this fixed time.",
"arxiv_id": "quant-ph/0101142",
"authors": [
"G. Sampath"
],
"categories": [
"quant-ph"
],
"title": "A quantum computing scheme for the Hamiltonian path problem",
"url": "https://arxiv.org/abs/quant-ph/0101142"
},
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