Physics – Quantum Physics
Scientific paper
2002-03-07
Contemporary Physics 44 (2003) 51- 71
Physics
Quantum Physics
Extensively revised and enlarged with: 2 new subsections, 4 new figures, 1 new reference, and a short biography as requested b
Scientific paper
10.1080/00107510302712
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered for the Hilbert's tenth problem, which is equivalent to the Turing halting problem and known to be mathematically noncomputable. Generalised quantum algorithms are also considered for some other mathematical noncomputables in the same and of different noncomputability classes. The key element of all these algorithms is the measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values. It is argued that computability, and thus the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by physical principles.
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