Lower Bounds for Quantum Search and Derandomization
| dc.creator | Buhrman, Harry | |
| dc.creator | de Wolf, Ronald | |
| dc.date | 1998-11-18 | |
| dc.date.accessioned | 2026-07-07T06:15:50Z | |
| dc.date.available | 2026-07-07T06:15:50Z | |
| dc.description | We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a constant. If we want error <1/2^N then we need T=Omega(N) queries. We apply this to show that a quantum computer cannot do much better than a classical computer when amplifying the success probability of an RP-machine. A classical computer can achieve error <=1/2^k using k applications of the RP-machine, a quantum computer still needs at least ck applications for this (when treating the machine as a black-box), where c>0 is a constant independent of k. Furthermore, we prove a lower bound of Omega(sqrt{log N}/loglog N) queries for quantum bounded-error search of an ordered list of N items. | |
| dc.description | 12 pages LaTeX. Submitted to CCC'99 (formerly Structures) | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9811046 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9811046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/93880 | |
| dc.subject | Quantum Physics | |
| dc.subject | Computational Complexity | |
| dc.title | Lower Bounds for Quantum Search and Derandomization | |
| dc.type | text |