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

G. P. Berman, D. I. Kamenev, and V. I. Tsifrinovich

Phys. Rev. A 71, 032346 – Published 28 March 2005

Abstract

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.

Received 8 November 2004

DOI:https://doi.org/10.1103/PhysRevA.71.032346

Authors & Affiliations

G. P. Berman¹, D. I. Kamenev², and V. I. Tsifrinovich³

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

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Vol. 71, Iss. 3 — March 2005

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