TY - JOUR
T1 - Grover’s quantum search algorithm for an arbitrary initial amplitude distribution
AU - Biham, Eli
AU - Biham, Ofer
AU - Biron, David
AU - Grassl, Markus
AU - Lidar, Daniel A.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0000314365&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.60.2742
DO - 10.1103/PhysRevA.60.2742
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AN - SCOPUS:0000314365
SN - 1050-2947
VL - 60
SP - 2742
EP - 2745
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 4
ER -