title: Realization of a scalable Shor algorithm.
abstract: Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four "cache qubits" and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.
authors.affiliation: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria. thomas.monz@uibk.ac.at.
authors.forename: Thomas
authors.initials: T
authors.lastname: Monz
authors.affiliation: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria.
authors.forename: Daniel
authors.initials: D
authors.lastname: Nigg
authors.affiliation: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria.
authors.forename: Esteban A
authors.initials: EA
authors.lastname: Martinez
authors.affiliation: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria.
authors.forename: Matthias F
authors.initials: MF
authors.lastname: Brandl
authors.affiliation: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria.
authors.forename: Philipp
authors.initials: P
authors.lastname: Schindler
authors.affiliation: Center for Ultracold Atoms, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
authors.forename: Richard
authors.initials: R
authors.lastname: Rines
authors.affiliation: Center for Ultracold Atoms, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
authors.forename: Shannon X
authors.initials: SX
authors.lastname: Wang
authors.affiliation: Center for Ultracold Atoms, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
authors.forename: Isaac L
authors.initials: IL
authors.lastname: Chuang
authors.affiliation: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria.
authors.forename: Rainer
authors.initials: R
authors.lastname: Blatt