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Numerical simulations of a quantum algorithm for Hilbert's tenth problem | | Tien D Kieu
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16 Apr 2003 | | 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. | | Subject: | Quantum Physics; Number Theory; Logic in Computer Science; Logic | quant-ph cs.LO math.LO math.NT | | 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 Schrödinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations. | | Source: | arXiv, quant-ph/0304114 | | Services: | Forum | Review | PDF | Favorites | |
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