Meaning of Grover's algorithm | Babel Free

Definitions

A quantum algorithm that finds with high probability the unique input to a black-box function that produces a particular output value.

Equivalents

Examples

“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, LNCS 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.”

“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⟳.”

“|Q_A⟩=Gʳ|Ψ(0)⟩≈ sin ((2r+1)ϕ)1/√∑_( mathit )solutions|y⟩ (3.59) where the probability of finding a nonsolution is presumed to be small and has been neglected in the equation.”

CEFR level