Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm
| dc.creator | Kieu, Tien D. | |
| dc.date | 2003-10-08 | |
| dc.date | 2003-10-17 | |
| dc.date.accessioned | 2026-07-07T06:08:01Z | |
| dc.date.available | 2026-07-07T06:08:01Z | |
| dc.description | 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. | |
| dc.description | Typos fixed, substantial results added in Section III, new reference and footnotes added. Now 22 pages, one figure | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0310052 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0310052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/91494 | |
| dc.subject | Quantum Physics | |
| dc.title | Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm | |
| dc.type | text |