Synthesis of arbitrary unitary transformations of collective states of trapped ions by quantum Householder reflections

Peter A. Ivanov and Nikolay V. Vitanov
Phys. Rev. A 77, 012335 – Published 30 January 2008

Abstract

We propose an efficient technique for creation and manipulation of entangled states and for construction of arbitrary many-particle unitary transformations in a linear ion trap. We show that, under suitable conditions on the laser pulse areas and detunings, the propagator within the single-excitation manifold has the form of a Householder reflection (HR). We demonstrate that a single HR is sufficient to create an entangled W-type state or to transfer one entangled state into another. An arbitrary N-dimensional unitary transformation can be constructed by at most N1 HRs, i.e., significantly faster than O(N2) steps in previous proposals, which makes this technique less sensitive to heating and other types of decoherence. We present examples of synthesis of quantum Fourier transforms for four, five, and six ions, which are constructed using only two, three, and four HRs, respectively.

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  • Received 7 September 2007

DOI:https://doi.org/10.1103/PhysRevA.77.012335

©2008 American Physical Society

Authors & Affiliations

Peter A. Ivanov1,2 and Nikolay V. Vitanov2,3

  • 1Institute for Mathematical Sciences, Imperial College London, SW7 2PE, United Kingdom
  • 2Department of Physics, Sofia University, James Bourchier 5 boulevard 1164 Sofia, Bulgaria
  • 3Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko chaussée 72, 1784 Sofia, Bulgaria

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Vol. 77, Iss. 1 — January 2008

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