Algebraic analysis of quantum search with pure and mixed states

Journal Article · Thu Mar 31 23:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.042320· OSTI ID:20653277

Shapira, Daniel; Shimoni, Yishai; Biham, Ofer ^[1]

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1. Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)

An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state vertical bar {psi}> of n qubits. This approach reveals the geometrical structure of the quantum search process, which turns out to be confined to a four-dimensional subspace of the Hilbert space. It unifies and generalizes earlier results on the time evolution of the amplitudes during the search, the optimal number of iterations, and the success probability. Furthermore, it enables a direct generalization to the case in which the initial state is a mixed state, providing an exact formula for the success probability.

• OSTI ID: 20653277
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 71; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
AMPLITUDES
ENERGY LEVELS
EVOLUTION
HILBERT SPACE
INFORMATION THEORY
ITERATIVE METHODS
MIXED STATE
PROBABILITY
QUANTUM MECHANICS
QUANTUM NUMBERS