Grover's algorithm

Etymology
Named after Indian-American computer scientist, who devised the algorithm in 1996.

Proper noun

 * 1)  A quantum algorithm that finds with high probability the unique input to a black-box function that produces a particular output value.
 * 2) * 2006, E. Arikan, 22: An Upper Bound on the Rate of Information Transfer by Grover's Algorithm, Rudolf Ahlswede et al. (editors), General Theory of Information Transfer and Combinatorics, Springer, 4123, page 452,
 * Thus, Grover's algorithm has optimal order of complexity. Here, we present an information-theoretic analysis of Grover's algorithm and show that the square-root speed-up by Grover's algorithm is the best possible by any algorithm using the same quantum oracle.
 * 1) * 2018, Joseph F. Fitzsimons, Eleanor G. Rieffel, Valerio Scarani, 11: Quantum Frontier, Justyna Zander, Pieter J. Mosterman (editors), Computation for Humanity, Taylor & Francis (CRC Press), page 286,
 * The best possible classical algorithm uses $$O(N)$$ time. This speed up is only polynomial, but, unlike for Shor's algorithm, it has been proven that Grover's algorithm outperforms any possible classical approach.
 * 1) * 2022 [2008 Morgan & Claypool], Marco Lanzagorta, Jeffrey Uhlmann, Quantum Computer Science, Springer Nature, page 49,
 * However, we cannot output the entire solution dataset using a single application of Grover's algorithm. Indeed, the superposition of states for the last iteration of Grover's algorithm, with known $$k$$, looks like:
 * $$\left\vert Q_A \right\rangle = G^r\left\vert \Psi(0)\right\rangle \approx \sin((2r+1)\phi)\frac{1}{\sqrt{k}} \sum_\mathit{solutions}\left\vert y\right\rangle$$     (3.59)
 * where the probability of finding a nonsolution is presumed to be small and has been neglected in the equation.

Translations

 * French: algorithme de Grover
 * German: Grover-Algorithmus
 * Italian: