dorsal/arxiv
View SchemaNumerical simulations of a quantum algorithm for Hilbert's tenth problem
| Authors | Tien D Kieu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304114 |
| URL | https://arxiv.org/abs/quant-ph/0304114 |
| DOI | 10.1117/12.486889 |
| Journal | in Proceedings of SPIE Vol. 5105 Quantum Information and Computation, edited by Eric Donkor, Andrew R. Pirich, Howard E. Brandt, (SPIE, Bellingham, WA, 2003), pp. 89-95. |
Abstract
We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem enables us to establish a connection between the solution for this class of problems and the asymptotic behaviour of solutions of a particular type of time-dependent Schr\"odinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.
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"abstract": "We employ quantum mechanical principles in the computability exploration of\nthe class of classically noncomputable Hilbert\u0027s tenth problem which is\nequivalent to the Turing halting problem in Computer Science. The Quantum\nAdiabatic Theorem enables us to establish a connection between the solution for\nthis class of problems and the asymptotic behaviour of solutions of a\nparticular type of time-dependent Schr\\\"odinger equations. We then present some\npreliminary numerical simulation results for the quantum adiabatic processes\ncorresponding to various Diophantine equations.",
"arxiv_id": "quant-ph/0304114",
"authors": [
"Tien D Kieu"
],
"categories": [
"quant-ph",
"cs.LO",
"math.LO",
"math.NT"
],
"doi": "10.1117/12.486889",
"journal_ref": "in Proceedings of SPIE Vol. 5105 Quantum Information and\n Computation, edited by Eric Donkor, Andrew R. Pirich, Howard E. Brandt,\n (SPIE, Bellingham, WA, 2003), pp. 89-95.",
"title": "Numerical simulations of a quantum algorithm for Hilbert\u0027s tenth problem",
"url": "https://arxiv.org/abs/quant-ph/0304114"
},
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