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In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has important implications in quantum information processing, where errors can be interpreted as measurements. Therefore, it seems that it is impossible to correct errors in a quantum information processor, but protocols exist that are capable of eliminating them if they affect only part of the system. In this work we present the deterministic reversal of a fully projective measurement on a single particle, enabled by a quantum error-correction protocol in a trapped ion quantum information processor. We further introduce an in-sequence, single-species recooling procedure to counteract the motional heating of the ion string due to the measurement.

We report on the implementation of a quantum process tomography (QPT) technique known as direct characterization of quantum dynamics (DCQD) applied on coherent and incoherent single- qubit processes in a system of trapped calcium 40 ions. Using quantum correlations with an ancilla qubit, DCQD reduces exponentially the number of experimental configurations required for standard QPT. With this technique, the system's relaxation times T1 and T2 were measured with a single experimental configuration. We further show the first complete characterization of single-qubit processes using a single generalized measurement realized through multi-body correlations with three ancilla qubits., (7 pages, 4 figures) This is part of a joint submission with an implementation with hyperentangled photons: "Hyperentanglement-enabled Direct Characterization of Quantum Dynamics" by T.M. Graham, J.T. Barreiro, M. Mohseni and P.G. Kwiat

When experimental errors are ignored in an experiment, the subsequent analysis of its results becomes questionable. We develop tests to detect systematic errors in quantum experiments where only a finite amount of data is recorded and apply these tests to tomographic data taken in an ion trap experiment. We put particular emphasis on quantum state tomography and present three detection methods: the first two employ linear inequalities while the third is based on the generalized likelihood ratio.

We report the creation of Greenberger-Horne-Zeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology., Comment: 4 pages, 2 figures, 1 table

Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum computation, gates acting on more than two qubits can simplify the implementation of complex quantum algorithms[2]. Thus, a single three-qubit operation can replace a complex sequence of two-qubit gates, which in turn promises faster execution with potentially higher Fidelity. One important three-qubit operation is the quantum Toffoli gate which performs a NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer. Our implementation is particular effcient as we directly encode the relevant logic information in the motion of the ion string. [1] DiVincenzo, D. P. Two-bit gates are universal for quantum computation. cond-mat/9407022, Phys.Rev. A 51, 1015-1022 (1995). [2] Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602-605 (2004)., 11 pages, 2 figures

We report on the first absolute transition frequency measurement at the ${10}^{\ensuremath{-}15}$ level with a single, laser-cooled $^{40}\mathrm{Ca}^{+}$ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the $^{40}\mathrm{Ca}^{+}$ $4s\text{ }^{2}S_{1/2}\ensuremath{-}3d\text{ }^{2}D_{5/2}$ electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency ${\ensuremath{\nu}}_{{\mathrm{Ca}}^{+}}=411\text{ }042\text{ }129\text{ }776\text{ }393.2(1.0)\text{ }\text{ }\mathrm{Hz}$ is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Land\'e $g$ factor of the $3d^{2}D_{5/2}$ level to be ${g}_{5/2}=1.200\text{ }334\text{ }0(3)$.

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude--shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.