Numerical simulations of a quantum algorithm for Hilbert's tenth problem

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/4309

Title: Numerical simulations of a quantum algorithm for Hilbert's tenth problem
Author(s): Kieu, Tien D.
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 Schrodinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.
Publication type: Conference paper
Research centre: Swinburne University of Technology. School of Biophysical Science and Electrical Engineering
Source: SPIE Technical Conference on Quantum Information and Computation, Orlando, Florida, USA, 21-22 April 2003., Proceedings of SPIE (v. 5105), pp 89-95.
Publication year: 2003
Publisher: SPIE - International Society for Optical Engineering
Format: pp 89-95
ISSN: 0277-786X
Publisher URL: http://dx.doi.org/10.1117/12.486889
Peer reviewed