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Inducing interactions between individual photons is essential for applications in photonic quantum information processing and fundamental research on many-body photon states. A field that is well suited to combine strong interactions and low losses is microwave quantum optics with superconducting circuits. Photons are typically stored in an $LC$ circuit, and interactions appear when the circuit is shunted by a Josephson tunnel junction. Importantly, the zero-point fluctuations of the superconducting phase across the junction control the strength and order of the induced interactions. Superconducting circuits have almost exclusively operated in the regime where phase fluctuations are smaller than unity, and two-photon interactions, known as the Kerr effect, dominate. In this experiment, we shunt a high-impedance $LC$ oscillator by a dipole that only allows pairs of Cooper pairs to tunnel. Phase fluctuations, which are effectively doubled by this pairing, reach the value of 3.4. In this regime of extreme fluctuations, we observe transition frequencies that shift non-monotonically as we climb the anharmonic ladder. From this spectroscopic measurement, we extract two-, three- and four-photon interaction energies of comparable amplitude, and all exceeding the photon loss rate. This work explores a new regime of high-order photon interactions in microwave quantum optics, with applications ranging from multi-photon quantum logic to the study of highly correlated microwave radiation., Comment: 12 pages, 10 figures

Owing to their strong dipole moment and long coherence times, superconducting qubits have demonstrated remarkable success in hybrid quantum circuits. However, most qubit architectures are limited to the GHz frequency range, severely constraining the class of systems they can interact with. The fluxonium qubit, on the other hand, can be biased to very low frequency while being manipulated and read out with standard microwave techniques. Here, we design and operate a heavy fluxonium with an unprecedentedly low transition frequency of $1.8~\mathrm{MHz}$. We demonstrate resolved sideband cooling of the ``hot'' qubit transition with a final ground state population of $97.7~\%$, corresponding to an effective temperature of $23~\mu\mathrm{K}$. We further demonstrate coherent manipulation with coherence times $T_1=34~\mu\mathrm{s}$, $T_2^*=39~\mu\mathrm{s}$, and single-shot readout of the qubit state. Importantly, by directly addressing the qubit transition with a capacitively coupled waveguide, we showcase its high sensitivity to a radio-frequency field. Through cyclic qubit preparation and interrogation, we transform this low-frequency fluxonium qubit into a frequency-resolved charge sensor. This method results in a charge sensitivity of $33~\mu\mathrm{e}/\sqrt{\mathrm{Hz}}$, or an energy sensitivity (in joules per hertz) of $2.8~\hbar$. This method rivals state-of-the-art transport-based devices, while maintaining inherent insensitivity to DC charge noise. The high charge sensitivity combined with large capacitive shunt unlocks new avenues for exploring quantum phenomena in the $1-10~\mathrm{MHz}$ range, such as the strong-coupling regime with a resonant macroscopic mechanical resonator.

The interaction strength of an oscillator to a qubit grows with the oscillator's vacuum field fluctuations. The well known degenerate parametric oscillator has revived interest in the regime of strongly detuned squeezing, where its eigenstates are squeezed Fock states. Owing to these amplified field fluctuations, it was recently proposed that squeezing this oscillator would dynamically boost qubit-photon interactions. In a superconducting circuit experiment, we observe a two-fold increase in the dispersive interaction between a qubit and an oscillator at 5.5 dB of squeezing, demonstrating in-situ dynamical control of qubit-photon interactions. This work initiates the experimental coupling of oscillators of squeezed photons to qubits, and cautiously motivates their dissemination in experimental platforms seeking enhanced interactions., Comment: 22 pages, 15 figures

Current implementations of quantum bits (qubits) continue to undergo too many errors to be scaled into useful quantum machines. An emerging strategy is to encode quantum information in the two meta-stable pointer states of an oscillator exchanging pairs of photons with its environment, a mechanism shown to provide stability without inducing decoherence. Adding photons in these states increases their separation, and macroscopic bit-flip times are expected even for a handful of photons, a range suitable to implement a qubit. However, previous experimental realizations have saturated in the millisecond range. In this work, we aim for the maximum bit-flip time we could achieve in a two-photon dissipative oscillator. To this end, we design a Josephson circuit in a regime that circumvents all suspected dynamical instabilities, and employ a minimally invasive fluorescence detection tool, at the cost of a two-photon exchange rate dominated by single-photon loss. We attain bit-flip times of the order of 100 seconds for states pinned by two-photon dissipation and containing about 40 photons. This experiment lays a solid foundation from which the two-photon exchange rate can be gradually increased, thus gaining access to the preparation and measurement of quantum superposition states, and pursuing the route towards a logical qubit with built-in bit-flip protection.

The coupling of the spin and the motion of charge carriers stems directly from the atomic structure of a conductor. It has become an important ingredient for the emergence of topological matter, and, in particular, topological superconductivity which could host non-abelian excitations such as Majorana modes or parafermions. These modes are sought after mostly in semiconducting platforms which are made of heavy atoms and therefore exhibit naturally a large spin-orbit interaction. Creating domain walls in the spin orbit interaction at the nanoscale may turn out to be a crucial resource for engineering topological excitations suitable for universal topological quantum computing. For example, it has been proposed for exploring exotic electronic states or for creating hinge states. Realizing this in natural platforms remains a challenge. In this work, we show how this can be alternatively implemented by using a synthetic spin orbit interaction induced by two lithographically patterned magnetically textured gates. By using a double quantum dot in a light material -- a carbon nanotube -- embedded in a microwave cavity, we trigger hopping between two adjacent orbitals with the microwave photons and directly compare the wave functions separated by the domain wall via the light-matter coupling. We show that we can achieve an engineered staggered spin-orbit interaction with a change of strength larger than the hopping energy between the two sites., Comment: comments/questions are highly welcome

Remarkably, complex assemblies of superconducting wires, electrodes, and Josephson junctions are compactly described by a handful of collective phase degrees of freedom that behave like quantum particles in a potential. The inductive wires contribute a parabolic confinement, while the tunnel junctions add a cosinusoidal corrugation. Usually, the ground state wavefunction is localized within a single potential well -- that is, quantum phase fluctuations are small -- although entering the regime of delocalization holds promise for metrology and qubit protection. A direct route is to loosen the inductive confinement and let the ground state phase spread over multiple Josephson periods, but this requires a circuit impedance vastly exceeding the resistance quantum and constitutes an ongoing experimental challenge. Here we take a complementary approach and fabricate a generalized Josephson element that can be tuned in situ between one- and two-Cooper-pair tunneling, doubling the frequency of the corrugation and thereby magnifying the number of wells probed by the ground state. We measure a tenfold suppression of flux sensitivity of the first transition energy, implying a twofold increase in the vacuum phase fluctuations., Comment: 11 pages, 8 figures

Spins confined in quantum dots are considered as a promising platform for quantum information processing. While many advanced quantum operations have been demonstrated, experimental as well as theoretical efforts are now focusing on the development of scalable spin quantum bit architectures. One particularly promising method relies on the coupling of spin quantum bits to microwave cavity photons. This would enable the coupling of distant spins via the exchange of virtual photons for two qubit gate applications, which still remains to be demonstrated with spin qubits. Here, we use a circuit QED spin-photon interface to drive a single electronic spin in a carbon nanotube based double quantum dot using cavity photons. The microwave spectroscopy allows us to identify an electrically controlled spin transition with a decoherence rate which can be tuned to be as low as $250kHz$. We show that this value is consistent with the expected hyperfine coupling in carbon nanotubes. These coherence properties, which can be attributed to the use of pristine carbon nanotubes stapled inside the cavity, should enable coherent spin-spin interaction via cavity photons and compare favourably to the ones recently demonstrated in Si-based circuit QED experiments.

In quantum mechanics, continuously measuring an observable steers the system into one eigenstate of that observable. This property has interesting and useful consequences when the observable is a joint property of two remotely separated qubits. In particular, if the measurement of the two-qubit joint observable is performed in a way that is blind to single-qubit information, quantum back-action generates correlation of the discord type even if the measurement is weak and inefficient. We demonstrate the ability to generate these quantum correlations in a circuit-QED setup by performing a weak joint readout of two remote, non-interacting, superconducting transmon qubits using the two non-degenerate modes of a Josephson Parametric Converter (JPC). Single-qubit information is erased from the output in the limit of large gain and with properly tailored cavity drive pulses. Our results of the measurement of discord are in quantitative agreement with theoretical predictions, and demonstrate the utility of the JPC as a which-qubit information eraser.

Decoherence originates from the leakage of quantum information into external degrees of freedom. For a qubit the two main decoherence channels are relaxation and dephasing. Here, we report an experiment on a superconducting qubit where we retrieve part of the lost information in both of these channels. We demonstrate that raw averaging the corresponding measurement records provides a full quantum tomography of the qubit state where all three components of the effective spin-1/2 are simultaneously measured. From single realizations of the experiment, it is possible to infer the quantum trajectories followed by the qubit state conditioned on relaxation and/or dephasing channels. The incompatibility between these quantum measurements of the qubit leads to observable consequences in the statistics of quantum states. The high level of controllability of superconducting circuits enables us to explore many regimes from the Zeno effect to underdamped Rabi oscillations depending on the relative strengths of driving, dephasing and relaxation., Comment: Supplemental videos can be found at http://physinfo.fr/publications/Ficheux1710.html and supplemental information can be found as an ancillary file on arxiv

Manipulating the state of a logical quantum bit usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schroedinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase-flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits.

Entangling two remote quantum systems which never interact directly is an essential primitive in quantum information science and forms the basis for the modular architecture of quantum computing. When protocols to generate these remote entangled pairs rely on using traveling single photon states as carriers of quantum information, they can be made robust to photon losses, unlike schemes that rely on continuous variable states. However, efficiently detecting single photons is challenging in the domain of superconducting quantum circuits because of the low energy of microwave quanta. Here, we report the realization of a robust form of concurrent remote entanglement based on a novel microwave photon detector implemented in the superconducting circuit quantum electrodynamics (cQED) platform of quantum information. Remote entangled pairs with a fidelity of $0.57\pm0.01$ are generated at $200$ Hz. Our experiment opens the way for the implementation of the modular architecture of quantum computation with superconducting qubits., Comment: Main paper: 7 pages, 4 figures; Appendices: 14 pages, 9 figures

Experimental quantum information processing with superconducting circuits is rapidly advancing, driven by innovation in two classes of devices, one involving planar micro-fabricated (2D) resonators, and the other involving machined three-dimensional (3D) cavities. We demonstrate that circuit quantum electrodynamics can be implemented in a multilayer superconducting structure that combines 2D and 3D advantages. We employ standard micro-fabrication techniques to pattern each layer, and rely on a vacuum gap between the layers to store the electromagnetic energy. Planar qubits are lithographically defined as an aperture in a conducting boundary of the resonators. We demonstrate the aperture concept by implementing an integrated, two cavity-modes, one transmon-qubit system.

Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying active feedback conditioned on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single photon resolved cross-Kerr effect between the two cavities enabling a photon number dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function., Comment: 8 pages, 6 figures

Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as , must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions, electrons, cavity quantum electrodynamics (QED), nitrogen-vacancy (NV) centers, and superconducting qubits. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schr\"{o}dinger cat states in a harmonic oscillator. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of quantum information in cat states realized earlier, our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit., Comment: 6 pages with 4 figures for the main text, 14 pages with 9 figures for supplementary material

Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors, but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a non-equilibrium state of a simple quantum system such as a qubit or a cavity mode in the presence of decoherence. Several groups have recently accomplished this goal using measurement-based feedback schemes. A next step is to prepare and stabilize a state of a composite system. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have recently been used for qubit reset and the stabilization of a single qubit state, as well as for creating and stabilizing states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach counter-intuitively uses engineered dissipation to fight decoherence, obviating the need for a complicated external feedback loop to correct errors, simplifying implementation. Instead the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building-block state for quantum information processing. Such autonomous schemes, broadly applicable to a variety of physical systems as demonstrated by a concurrent publication with trapped ion qubits, will be an essential tool for the implementation of quantum-error correction., Comment: 39 pages, 7 figures

We propose a dissipation engineering scheme that prepares and protects a maximally entangled state of a pair of superconducting qubits. This is done by off-resonantly coupling the two qubits to a low-Q cavity mode playing the role of a dissipative reservoir. We engineer this coupling by applying six continuous-wave microwave drives with appropriate frequencies. The two qubits need not be identical. We show that our approach does not require any fine-tuning of the parameters and requires only that certain ratios between them be large. With currently achievable coherence times, simulations indicate that a Bell state can be maintained over arbitrary long times with fidelities above 94%. Such performance leads to a significant violation of Bell's inequality (CHSH correlation larger than 2.6) for arbitrary long times., Comment: 5 pages, 4 figures

Qubit reset is crucial at the start of and during quantum information algorithms. We present the experimental demonstration of a practical method to force qubits into their ground state, based on driving certain qubit and cavity transitions. Our protocol, called the double drive reset of population is tested on a superconducting transmon qubit in a three-dimensional cavity. Using a new method for measuring population, we show that we can prepare the ground state with a fidelity of at least 99.5 % in less than 3 microseconds; faster times and higher fidelity are predicted upon parameter optimization., Comment: 5 pages, 4 figures

We analyze a quantum reservoir engineering method, originally introduced by [Sarlette et al. in Phys. Rev. Lett. 107, 010402 (2011) -- arXiv 1011.5057], for the stabilization of non-classical field states in high quality cavities. We generalize the method to the protection of mesoscopic entangled field states shared by two non-degenerate field modes. The reservoir is made up of a stream of atoms undergoing successive composite interactions with the cavity, each combining resonant with non-resonant parts. We get a detailed insight into the competition between the engineered reservoir and decoherence. We show that the operation is quite insensitive to experimental imperfections and that it could thus be implemented in the near future, either in the context of microwave Cavity Quantum Electrodynamics or in that of circuit-QED., Comment: submitted to Physical Review A