dorsal/arxiv
View SchemaA possible hypercomputational quantum algorithm
| Authors | Andrés Sicard, Mario Vélez, Juan Ospina |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406137 |
| URL | https://arxiv.org/abs/quant-ph/0406137 |
| DOI | 10.1117/12.602254 |
| Journal | In E. J. Donkor, A. R. Pirich, and H. E. Brandt, editors, "Quantum Information and Computation III", volume 5815 of Proc. of SPIE. SPIE, Bellingham, WA, 2005. p. 219-226 |
Abstract
The term `hypermachine' denotes any data processing device (theoretical or that can be implemented) capable of carrying out tasks that cannot be performed by a Turing machine. We present a possible quantum algorithm for a classically non-computable decision problem, Hilbert's tenth problem; more specifically, we present a possible hypercomputation model based on quantum computation. Our algorithm is inspired by the one proposed by Tien D. Kieu, but we have selected the infinite square well instead of the (one-dimensional) simple harmonic oscillator as the underlying physical system. Our model exploits the quantum adiabatic process and the characteristics of the representation of the dynamical Lie algebra su(1,1) associated to the infinite square well.
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"abstract": "The term `hypermachine\u0027 denotes any data processing device (theoretical or\nthat can be implemented) capable of carrying out tasks that cannot be performed\nby a Turing machine. We present a possible quantum algorithm for a classically\nnon-computable decision problem, Hilbert\u0027s tenth problem; more specifically, we\npresent a possible hypercomputation model based on quantum computation. Our\nalgorithm is inspired by the one proposed by Tien D. Kieu, but we have selected\nthe infinite square well instead of the (one-dimensional) simple harmonic\noscillator as the underlying physical system. Our model exploits the quantum\nadiabatic process and the characteristics of the representation of the\ndynamical Lie algebra su(1,1) associated to the infinite square well.",
"arxiv_id": "quant-ph/0406137",
"authors": [
"Andr\u00e9s Sicard",
"Mario V\u00e9lez",
"Juan Ospina"
],
"categories": [
"quant-ph",
"cs.LO"
],
"doi": "10.1117/12.602254",
"journal_ref": "In E. J. Donkor, A. R. Pirich, and H. E. Brandt, editors, \"Quantum\n Information and Computation III\", volume 5815 of Proc. of SPIE. SPIE,\n Bellingham, WA, 2005. p. 219-226",
"title": "A possible hypercomputational quantum algorithm",
"url": "https://arxiv.org/abs/quant-ph/0406137"
},
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