Grover’s quantum search algorithm for an arbitrary initial amplitude distribution

Eli Biham, Ofer Biham, David Biron, Markus Grassl, Daniel A. Lidar

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


Grover’s algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First-order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked states. These equations are solved exactly. New expressions are derived for the optimal time of measurement and the maximal probability of success. They are found to depend on the averages and variances of the initial amplitude distributions of the marked and unmarked states, but not on higher moments. Our results imply that Grover’s algorithm is robust against modest noise in the amplitude initialization procedure.

Original languageAmerican English
Pages (from-to)2742-2745
Number of pages4
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
StatePublished - 1999


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