Photon-mediated interactions between atoms are of fundamental importance in quantum optics, quantum simulations, and quantum information processing. The exchange of real and virtual photons between atoms gives rise to nontrivial interactions, the strength of which decreases rapidly with distance in three dimensions. Here, we use two superconducting qubits in an open one-dimensional transmission line to study much stronger photon-mediated interactions. Making use of the possibility to tune these qubits by more than a quarter of their transition frequency, we observe both coherent exchange interactions at an effective separation of 3λ/4 and the creation of super- and subradiant states at a separation of one photon wavelength λ. In this system, collective atom-photon interactions and applications in quantum communication may be explored.

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 study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional superconducting transmission line. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super-and subradiance or to a coherent exchangetype interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms driven by a coherent state. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [A. F. van Loo et al.].

We experimentally demonstrate the in situ tunability of the minimum energy splitting (gap) of a superconducting flux qubit by means of an additional flux loop. Pulses applied via a local control line allow us to tune the gap over a range of several GHz on a nanosecond timescale. The strong flux sensitivity of the gap (up to ∼0.7 GHz/mΦ0) opens up the possibility to create different types of tunable couplings that are effective at the degeneracy point of the qubit. We investigate the dependence of the relaxation time and the Rabi frequency on the qubit gap.PACS numbers: 03.67. Lx, 85.25.Cp Superconducting circuits are promising candidates for the implementation of scalable quantum information processing [1]. To this purpose it is important to be able to selectively couple arbitrary quantum bits. Coupling multiple quantum two-level systems to a harmonic oscillator promises to be a successful strategy to create selective quantum gates in quantum optics and atomic physics [2], and in superconducting charge [3] and phase qubits [4]. In superconducting flux qubits single-qubit rotations [5], tunable qubit couplings [6] and two-qubit quantum gates [7] have been demonstrated as well as coupling between a flux qubit and a harmonic oscillator [8,9]. To controllably couple qubits via a harmonic oscillator bus requires the ability to tune the qubits in and out of resonance.In this Letter, we demonstrate the implementation of an additional flux loop to vary the minimum energy splitting, called the gap, of a superconducting flux qubit. In principle this control allows a fast change of the qubit resonance frequency while remaining at the point where the coherence properties of the qubit are optimal, i.e. at the gap. The large coupling makes this tunable qubit a good candidate to implement different types of qubit coupling besides σ z σ z , such as σ x σ z and σ x σ x [10].Commonly, a flux qubit consists of a small inductance superconducting loop intersected by three Josephson junctions ( Fig. 1(a)) [11]. If the flux penetrating the loop is close to half a superconducting flux quantum Φ 0 /2 (mod Φ 0 ), with Φ 0 = h/2e, the two lowest energy eigenstates can be used as a qubit (Fig. 1(b)). The qubit is characterized by the gap ∆ and by the persistent current I p . The energy eigenstates are linear combinations of clockwise and counterclockwise persistent-current states.In the persistent-current basis the qubit Hamiltonian can be written aswhere ǫ = 2I p (f ǫ − 1 2 )Φ 0 is the magnetic energy bias, with f ǫ the magnetic frustration of the qubit loop. σ z and σ x * Electronic address: j.e.mooij@tudelft.nl f fα fε fα

Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates, the creation of complex entangled states and the demonstration of algorithms or error correction. Using different variants of low-noise parametric amplifiers, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous and discrete feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 10(4) s(-1), exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.