Synthesis of arbitrary unitary transformations of collective states of trapped ions by quantum Householder reflections
Peter A. Ivanov and Nikolay V. Vitanov

We propose a novel 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 $N-1$ HRs, i.e., significantly faster than $O(N^2)$ 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 4, 5, and 6 ions, which are constructed by only 2, 3, and 4 HRs, respectively.

© 2008 The American Physical Society.