Collective decoherence of the superpositional entangled states in the quantum Shor algorithm

Journal Article · Tue Mar 01 00:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.032346· OSTI ID:20650384

Berman, G P ^[1]; Kamenev, D I ^[2]; Tsifrinovich, V I ^[3]

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1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. IDS Department, Polytechnic University, Brooklyn, New York 11201 (United States)

We consider collective decoherence for the quantum Shor algorithm. A quantum computer which interacts with its environment is modeled by a spin-1/2 chain interacting with harmonic oscillators at a given temperature. We calculate the nondiagonal matrix elements of the density matrix which are important for implementation of the quantum Shor algorithm, and study the decay rate and the Lamb phase shift for these elements. It is shown that the probability of superdecoherence in the quantum Shor algorithm is extremely small. The conditions for preserving quantum entanglement are formulated.

• OSTI ID: 20650384
• Journal Information: Physical Review. A, Vol. 71, Issue 3; Other Information: DOI: 10.1103/PhysRevA.71.032346; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
36 MATERIALS SCIENCE
ALGEBRA
ALGORITHMS
CORRELATIONS
DECAY
DENSITY MATRIX
ENERGY LEVELS
HARMONIC OSCILLATORS
IMPLEMENTATION
INFORMATION THEORY
LAMB SHIFT
MATRIX ELEMENTS
PHASE SHIFT
PROBABILITY
QUANTUM MECHANICS
QUANTUM NUMBERS
SPIN