Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm

Details Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm

2003-10-08

arxiv.org/abs/quant-ph/0310052v2

Physics

Quantum Physics

Typos fixed, substantial results added in Section III, new reference and footnotes added. Now 22 pages, one figure

Scientific paper

We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for any input of Diophantine equation; (ii) the final ground state which contains the answer for the Diophantine equation can be identified as the component state having better-than-even probability to be found by measurement at the end time--even though probability for the final ground state in a quantum adiabatic process need not monotonically increase towards one in general. Presented finally are the reasons why our algorithm is outside the jurisdiction of no-go arguments previously employed to show that Hilbert's tenth problem is recursively non-computable.

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