15131514 KANN ET AL.Vol. 720 ABSTRACT We have gathered optical photometry data from the literature on a large sample of Swift-era gamma-ray burst (GRB) afterglows including GRBs up to 2009 September, for a total of 76 GRBs, and present an additional three pre-Swift GRBs not included in an earlier sample. Furthermore, we publish 840 additional new photometry data points on a total of 42 GRB afterglows, including large data sets for GRBs 050319, 050408, 050802, 050820A, 050922C, 060418, 080413A, and 080810. We analyzed the light curves of all GRBs in the sample and derived spectral energy distributions for the sample with the best data quality, allowing us to estimate the host-galaxy extinction. We transformed the afterglow light curves into an extinction-corrected z = 1 system and compared their luminosities with a sample of pre-Swift afterglows. The results of a former study, which showed that GRB afterglows clustered and exhibited a bimodal distribution in luminosity space, are weakened by the larger sample. We found that the luminosity distribution of the two afterglow samples (Swift-era and pre-Swift) is very similar, and that a subsample for which we were not able to estimate the extinction, which is fainter than the main sample, can be explained by assuming a moderate amount of line-of-sight host extinction. We derived bolometric isotropic energies for all GRBs in our sample, and found only a tentative correlation between the prompt energy release and the optical afterglow luminosity at 1 day after the GRB in the z = 1 system. A comparative study of the optical luminosities of GRB afterglows with echelle spectra (which show a high number of foreground absorbing systems) and those without, reveals no indication that the former are statistically significantly more luminous. Furthermore, we propose the existence of an upper ceiling on afterglow luminosities and study the luminosity distribution at early times, which was not accessible before the advent of the Swift satellite. Most GRBs feature afterglows that are dominated by the forward shock from early times on. Finally, we present the first indications of a class of long GRBs, which form a bridge between the typical highluminosity, high-redshift events and nearby low-luminosity events (which are also associated with spectroscopic supernovae) in terms of energetics and observed redshift distribution, indicating a continuous distribution overall.

The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models. Realizations of harmonic oscillators in the quantum regime include electromagnetic fields in a cavity and the mechanical modes of a trapped atom or macroscopic solid. Quantized interaction between two motional modes of an individual trapped ion has been achieved by coupling through optical fields, and entangled motion of two ions in separate locations has been accomplished indirectly through their internal states. However, direct controllable coupling between quantized mechanical oscillators held in separate locations has not been realized previously. Here we implement such coupling through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40 μm (similar work is reported in a related paper). By tuning the confining wells into resonance, energy is exchanged between the ions at the quantum level, establishing that direct coherent motional coupling is possible for separately trapped ions. The system demonstrates a building block for quantum information processing and quantum simulation. More broadly, this work is a natural precursor to experiments in hybrid quantum systems, such as coupling a trapped ion to a quantized macroscopic mechanical or electrical oscillator.

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With a 9 Be + trapped-ion hyperfine-states qubit, we demonstrate an error probability per randomized singlequbit gate of 2.0(2) × 10 −5 , below the threshold estimate of 10 −4 commonly considered sufficient for faulttolerant quantum computing. The 9 Be + ion is trapped above a microfabricated surface-electrode ion trap and is manipulated with microwaves applied to a trap electrode. The achievement of low single-qubit-gate errors is an essential step toward the construction of a scalable quantum computer.In theory, quantum computers can solve certain problems much more efficiently than classical computers [1]. This has motivated experimental efforts to construct and to verify devices that manipulate quantum bits (qubits) in a variety of physical systems [2]. The power of quantum computers depends on the ability to accurately control sensitive superposition amplitudes by means of quantum gates, and errors in these gates are a chief obstacle to building quantum computers [3]. Small gate errors would enable fault-tolerant operation through the use of quantum error correction protocols [4]. While the maximum tolerable error varies between correction strategies, there is a consensus that 10 −4 is an important threshold to breach [4,5]. Single-qubit gates with errors slightly above this level have been achieved with nuclear spins in liquid-state nuclear-magnetic resonance experiments [6] and with neutral atoms confined in optical lattices [7]; here we demonstrate single-qubit error probabilities of 2.0(2) × 10 −5 , substantially below the threshold. Reaching fault-tolerance still requires reducing two-qubit-gate errors from the current state of the art (7 × 10 −3 for laser-based [8] and 0.24 for microwave-based gates [9]) to similar levels.To determine the average error per gate (EPG), we use the method of randomized benchmarking [10]. Compared to other methods for evaluating gate performance, such as quantum process tomography [11], randomized benchmarking offers the advantage that it efficiently and separately can determine the EPG and the combined state-preparation and measurement errors. Because it involves long sequences of random gates, it is sensitive to errors occurring when gates are used in arbitrary computations. In randomized benchmarking, the qubit, initialized close to a pure quantum state, is subjected to predetermined sequences of randomly selected Clifford gates [12] for which, in the absence of errors, the measurement outcome is deterministic and efficiently predictable. Clifford gates include the basic unitary gates of most proposed fault-tolerant quantum computing architectures. Together with certain single-qubit states and measurements, they suffice for universal quantum computing [12,13]. To establish the EPG, the actual measurement and predicted outcome are compared for many random sequences of different lengths. Under assumptions presented in Ref.[10], this yields an average fidelity as a function of the number of gates that decreases exponentially to 1/2 and determines the EPG. Randomized bench...