Minds and Machines 16 (1):87-93 (2006)

Amit Hagar
Indiana University, Bloomington
Alexandre Korolev
University of British Columbia
A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.
Keywords Diophantine equations   Halting problem   Hilbert 10th problem   adiabatic algorithm   hypercomputation   quantum computing   undecidability
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DOI 10.1007/s11023-005-9006-y
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References found in this work BETA

Hypercomputation.B. Jack Copeland - 2002 - Minds and Machines 12 (4):461-502.
Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:126-138.
Quantum Hypercomputation.Tien D. Kieu - 2002 - Minds and Machines 12 (4):541-561.

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Quantum Algorithms: Philosophical Lessons.Amit Hagar - 2007 - Minds and Machines 17 (2):233-247.
A Brief Critique of Pure Hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.

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