The Toffoli gate is a three-quantum-bit (three-qubit) operation that inverts the state of a target qubit conditioned on the state of two control qubits. It makes universal reversible classical computation possible and, together with a Hadamard gate, forms a universal set of gates in quantum computation. It is also a key element in quantum error correction schemes. The Toffoli gate has been implemented in nuclear magnetic resonance, linear optics and ion trap systems. Experiments with superconducting qubits have also shown significant progress recently: two-qubit algorithms and two-qubit process tomography have been implemented, three-qubit entangled states have been prepared, first steps towards quantum teleportation have been taken and work on quantum computing architectures has been done. Implementation of the Toffoli gate with only single- and two-qubit gates requires six controlled-NOT gates and ten single-qubit operations, and has not been realized in any system owing to current limits on coherence. Here we implement a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubits, we have significantly reduced the number of elementary gates needed for the implementation of the Toffoli gate, relative to that required in theoretical proposals using only two-level systems. Using full process tomography and Monte Carlo process certification, we completely characterize the Toffoli gate acting on three independent qubits, measuring a fidelity of 68.5 ± 0.5 per cent. A similar approach to realizing characteristic features of a Toffoli-class gate has been demonstrated with two qubits and a resonator and achieved a limited characterization considering only the phase fidelity. Our results reinforce the potential of macroscopic superconducting qubits for the implementation of complex quantum operations with the possibility of quantum error correction.

We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multi-qubit states and observe the discrete √ N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W -state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multi-atom quantum optics experiments with fixed atom numbers.PACS numbers: 42.50. Ct, 42.50.Pq, 03.67.Lx, 85.35.Gv In the early 1950's, Dicke realized that under certain conditions a gas of radiating molecules shows the collective behavior of a single quantum system [1]. The idealized situation in which N two-level systems with identical dipole coupling are resonantly interacting with a single mode of the electromagnetic field was analyzed by Tavis and Cummings [2]. This model predicts the collective N -atom interaction strength to be G N = g j √ N , where g j is the dipole coupling strength of each individual atom j. In fact, in first cavity QED experiments the normal mode splitting, observable in the cavity transmission spectrum [3,4], was demonstrated with on averageN > 1 atoms in optical [5,6] and microwave [7] cavities to overcome the relatively weak dipole coupling g j . The √ N scaling has been observed in the regime of a small mean number of atomsN with dilute atomic beams [7,8,9] and fountains [10] crossing a high-finesse cavity. In these experiments, spatial variations of the atom positions and Poissonian fluctuations in the atom number inherent to an atomic beam [4,8,11] are unavoidable. In a different limit where the cavity was populated with a very large number of ultra-cold 87 Rb atoms [12] and more recently with Bose-Einstein condensates [13,14] the √ N nonlinearity was also demonstrated. However, the number of interacting atoms is typically only known to about ∼ 10% [13].Here we present an experiment in which the TavisCummings model is studied for a discrete set of fully controllable artificial atoms at fixed positions and with virtually identical couplings to a resonant cavity mode. The investigated situation is sketched in Fig. 1 a, depicting an optical analog where three two-state atoms are deterministically positioned at electric field antinodes of a cavity mode where the coupling is maximum. In our circuit QED [15,16] realization of this configuration (Fig. 1 b), three transmon-type [17] superconducting qubits are embedded in a microwave resonator which contains a quantized radiation field. The cavity is realized as a coplanar waveguide resonator with a first harmonic full wavelength resonance frequency of ω r /2π = 6.729 GHz and a ...

Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured by using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.

We have designed and fabricated superconducting coplanar waveguide resonators with fundamental frequencies from 2 to 9 GHz and loaded quality factors ranging from a few hundreds to a several hundred thousands reached at temperatures of 20 mK. The loaded quality factors are controlled by appropriately designed input and output coupling capacitors. The measured transmission spectra are analyzed using both a lumped element model and a distributed element transmission matrix method. The experimentally determined resonance frequencies, quality factors and insertion losses are fully and consistently characterized by the two models for all measured devices. Such resonators find prominent applications in quantum optics and quantum information processing with superconducting electronic circuits and in single photon detectors and parametric amplifiers.

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