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Generalized Grover's Algorithm for Multiple Phase Inversion States. | LitMetric

Generalized Grover's Algorithm for Multiple Phase Inversion States.

Phys Rev Lett

New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China.

Published: February 2018

AI Article Synopsis

Article Abstract

Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator inverts the sign on only one state. Here we provide an exact solution to the problem of performing Grover's search where the Grover operator inverts the sign on N states. We show the underlying structure in terms of the eigenspectrum of the generalized Hamiltonian, and derive an appropriate initial state to perform the Grover evolution. This allows us to use the quantum phase estimation algorithm to solve the search problem in this generalized case, completely bypassing the Grover algorithm altogether. We obtain a time complexity of this case of sqrt[D/M^{α}], where D is the search space dimension, M is the number of target states, and α≈1, which is close to the optimal scaling.

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Source
http://dx.doi.org/10.1103/PhysRevLett.120.060501DOI Listing

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