Grover's quantum search algorithm for an arbitrary initial mixed state

Journal Article · Sat Nov 30 23:00:00 EST 2002 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.66.062301· OSTI ID:20632409

Biham, Eli; Kenigsberg, Dan ^[1]

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1. Computer Science Department, Technion, Haifa 32000 (Israel)

The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The form of the function, though, remains as it is in the case of initial pure state. We study the role of the von Neumann entropy of the initial state, and show that the entropy cannot be a measure for the usefulness of the algorithm. We give few examples and show that for some extremely mixed initial states (carrying high entropy), the generalized Grover algorithm is considerably faster than any classical algorithm.

• OSTI ID: 20632409
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 66; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
ENERGY LEVELS
ENTROPY
INFORMATION THEORY
MIXED STATE
PROBABILITY
QUANTUM MECHANICS
TIME DEPENDENCE