Arkady Fedorov

Implementation of a Toffoli gate with superconducting circuits

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.

Photon-mediated interactions between distant artificial atoms

Artificial Complexity Quantum optics probes the interactions between light and matter. Building up from a simple, single-atom system, the exchange of virtual photons between systems of several (or many) atoms is expected to give rise to many exotic effects. Because controlling the separation of the atoms on the atomic scale is experimentally challenging, artificial atom systems may provide a more tractable route for systematic study, as described by van Loo et al. (p. 1494, published online 14 November). Using a system of two separate superconducting qubits in a microwave transmission line, they show how the interaction between the two qubits can be controlled and mediated by electromagnetic modes. The results illustrate a feasible route to probing the complexity of many-body effects that may otherwise be difficult to realize. Interaction between two separated superconducting qubits can be mediated and controlled by microwaves. 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.

Deterministic quantum teleportation with feed-forward in a solid state system

Transferring the state of an information carrier from a sender to a receiver is an essential primitive in both classical and quantum communication and information processing. In a quantum process known as teleportation the unknown state of a quantum bit can be relayed to a distant party using shared entanglement and classical information. Here we present experiments in a solid-state system based on superconducting quantum circuits demonstrating the teleportation of the state of a qubit at the macroscopic scale. In our experiments teleportation is realized deterministically with high efficiency and achieves a high rate of transferred qubit states. This constitutes a significant step towards the realization of repeaters for quantum communication at microwave frequencies and broadens the tool set for quantum information processing with superconducting circuits.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 104 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.

Error rate of a charge qubit coupled to an acoustic phonon reservoir

We analyze decoherence of an electron in a double-dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.

Tuning the Gap of a Superconducting Flux Qubit

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 time scale. The strong flux sensitivity of the gap (up to approximately 0.7 GHz/mPhi0) 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.

Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms

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 exchange-type 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 [van Loo (unpublished)].

Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point

A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit of which the gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-oscillator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency ν(osc) we find the largest vacuum Rabi splitting of ∼0.1 ν(osc). Here being at resonance coincides with the optimal coherence of the symmetry point.

Sisyphus cooling and amplification by a superconducting qubit

A superconducting qubit—a mesoscopic structure that behaves like a quantum two-level system—has been used to change the temperature of a resonant circuit, in close analogy to the so-called Sisyphus cooling and amplification protocols used in laser cooling of atoms.

Quantum-control approach to realizing a Toffoli gate in circuit QED

We study the realization of a Toffoli gate with superconducting qubits in a circuit-quantum-electrodynamics setup using quantum-control methods. Starting with optimized piecewise-constant control fields acting on all qubits and typical strengths of XY-type coupling between the qubits, we demonstrate that the optimal gate fidelities are affected only slightly by a ``low-pass`` filtering of these fields with the typical cutoff frequencies of microwave driving. Restricting ourselves to the range of control-field amplitudes for which the leakage to the noncomputational states of a physical qubit is heavily suppressed, we theoretically predict that in the absence of decoherence and leakage, within 75 ns a Toffoli gate can be realized with intrinsic fidelities higher than 90% while fidelities above 99% can be reached in about 140 ns.

Benchmarking a Quantum Teleportation Protocol in Superconducting Circuits Using Tomography and an Entanglement Witness

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three-qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 88%.