Greenberger-Horne-Zeilinger state protocols for fully connected qubit networks

Andrei Galiautdinov, Mark W. Coffey, and Ron Deiotte
Phys. Rev. A 80, 062302 – Published 2 December 2009

Abstract

We generalize the recently proposed Greenberger-Horne-Zeilinger tripartite protocol [A. Galiautdinov and J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)] to fully connected networks of weakly coupled qubits interacting by way of anisotropic Heisenberg exchange g(XX+YY)+g̃ZZ. Our model differs from the more familiar Ising-Heisenberg chain in that here every qubit interacts with every other qubit in the circuit. The assumption of identical couplings on all qubit pairs allows an elegant proof of the protocol for arbitrary N. In order to further make contact with experiment, we study fidelity degradation due to coupling imperfections by numerically simulating the N=3 and 4 cases. Our simulations indicate that the best fidelity at unequal couplings is achieved when (a) the system is initially prepared in the uniform superposition state (similarly to how it is done in the ideal case) and (b) the entangling time and the final rotations on each of the qubits are appropriately adjusted.

  • Figure
  • Received 12 July 2009

DOI:https://doi.org/10.1103/PhysRevA.80.062302

©2009 American Physical Society

Authors & Affiliations

Andrei Galiautdinov*

  • Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA

Mark W. Coffey and Ron Deiotte

  • Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA

  • *ag@physast.uga.edu
  • mcoffey@mines.edu

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Vol. 80, Iss. 6 — December 2009

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