info:eu-repo/semantics/conferencePaper
A possible hypercomputational quantum algorithm
Fecha
2005-01-01Registro en:
0277786X
1996756X
WOS;000231558600025
10.1117/12.602254
Autor
Sicard, A
Velez, M
Ospina, J
Sicard, A
Velez, M
Ospina, J
Institución
Resumen
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.