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Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution | | David Biron
; Ofer Biham
; Eli Biham
; Markus Grassl
; Daniel A. Lidar
; | | Date: |
28 Dec 1997 | | Journal: | "Quantum Computing & Quantum Communications; First NASA International Conference; selected papers, QCQC’98", C.P. Williams (ed.), Lecture Notes in Computer Science vol. 1509, pp. 140-147 (Springer, 1998). | | Subject: | quant-ph | | Affiliation: | Racah Institute of Physics, The Hebrew University, Israel, Computer Science Department, Technion, Israel, Institut fur Algorithmen und Kognitive Systeme, Universitat Karlsruhe, Germany, Department of Chemistry, University of California, Berkeley, U | | Abstract: | Grover’s algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r unmarked states. These equations are solved exactly. An expression for the optimal measurement time T sim O(sqrt{N/r}) is derived which is shown to depend only on the initial average amplitudes of the marked and unmarked states. A bound on the probability of measuring a marked state is derived, which depends only on the standard deviation of the initial amplitude distributions of the marked or unmarked states. | | Source: | arXiv, quant-ph/9801066 | | Services: | Forum | Review | PDF | Favorites | |
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