As input for Grover's algorithm, suppose we have a function f : { 0 , 1 , … , N − 1 } → { 0 , 1 } {\displaystyle f\colon \{0,1,\ldots ,N-1\}\to \{0,1\}} . In the "unstructured database" analo… 展开

The steps of Grover's algorithm are given as follows: 1. Initialize the system to the uniform s… 展开

There is a geometric interpretation of Grover's algorithm, following from the observation that the quantum state of Grover's algorithm stays in a two-dimensional sub… 展开

To complete the algebraic analysis, we need to find out what happens when we repeatedly apply U s U ω {\displaystyle U_{s}U_{\omega }} . A natural way to do this is by eigenv… 展开

Multiple matching entries
If, instead of 1 matching entry, there are k matching entries, the same algorithm works, but the number of iterations must be π 4 ( N k ) 1 / 2 {… 展开