Two notes on Grover’s search: Programming and discriminating
In this work we address two questions concerning Grover’s algorithm. In the first part we give an answer to the question on how to employ Grover’s algorithm for actual search over database. We introduce a quantum model of an unordered phone book (quantum database) with programmable queries to search in the phone book either for a number or for a name. In the second part we investigate how successful the algorithm can be if the number of elements of the database is not known precisely. This question reduces to analysis of the distinguishability of states occurring during Grover’s algorithm. We found that using an unambiguous discrimination scheme even a seemingly good guess that is close to the optimal one, can result in a rather small success rate.
KeywordsSuccess Probability Phone Number Quantum Search Quantum Query Phone Book
- 4.M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).Google Scholar
- 17.O. Regev, L. Schiff, Impossibility of a Quantum Speed-Up with a Faulty Oracle, in Proceedings of the 35th International Colloquium on Automata, Languages and Programming, Vol. 1 (2008) p. 773.Google Scholar