title: Implementation of the semiclassical quantum Fourier transform in a scalable system.
abstract: We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.
authors.affiliation: National Institute of Standards and Technology, Boulder, CO 80305, USA. john.chiaverini@boulder.nist.gov
authors.forename: J
authors.initials: J
authors.lastname: Chiaverini
authors.forename: J
authors.initials: J
authors.lastname: Britton
authors.forename: D
authors.initials: D
authors.lastname: Leibfried
authors.forename: E
authors.initials: E
authors.lastname: Knill
authors.forename: M D
authors.initials: MD
authors.lastname: Barrett
authors.forename: R B
authors.initials: RB
authors.lastname: Blakestad
authors.forename: W M
authors.initials: WM
authors.lastname: Itano
authors.forename: J D
authors.initials: JD
authors.lastname: Jost
authors.forename: C
authors.initials: C
authors.lastname: Langer
authors.forename: R
authors.initials: R
authors.lastname: Ozeri
authors.forename: T
authors.initials: T
authors.lastname: Schaetz
authors.forename: D J
authors.initials: DJ
authors.lastname: Wineland