Quantum control of a cat qubit with bit-flip times exceeding ten seconds.

Quantum bits (qubits) are prone to several types of error as the result of uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads1. One possible solution is to build qubits that are inherently protected against certain types of error, so the overhead required to correct the remaining errors is greatly reduced2-7. However, this strategy relies on one condition: any quantum manipulations of the qubit must not break the protection that has been so carefully engineered5,8. A type of qubit known as a cat qubit is encoded in the manifold of metastable states of a quantum dynamical system, and thereby acquires continuous and autonomous protection against bit-flips. Here, in a superconducting-circuit experiment, we implemented a cat qubit with bit-flip times exceeding 10 s. This is an improvement of four orders of magnitude over previously published cat-qubit implementations. We prepared and imaged quantum superposition states, and measured phase-flip times greater than 490 ns. Most importantly, we controlled the phase of these quantum superpositions without breaking the bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.

Vacuum-field-induced THz transport gap in a carbon nanotube quantum dot.

The control of light-matter interaction at the most elementary level has become an important resource for quantum technologies. Implementing such interfaces in the THz range remains an outstanding problem. Here, we couple a single electron trapped in a carbon nanotube quantum dot to a THz resonator. The resulting light-matter interaction reaches the deep strong coupling regime that induces a THz energy gap in the carbon nanotube solely by the vacuum fluctuations of the THz resonator. This is directly confirmed by transport measurements. Such a phenomenon which is the exact counterpart of inhibition of spontaneous emission in atomic physics opens the path to the readout of non-classical states of light using electrical current. This would be a particularly useful resource and perspective for THz quantum optics.

Demonstration of an Effective Ultrastrong Coupling between Two Oscillators.

When the coupling rate between two quantum systems becomes as large as their characteristic frequencies, it induces dramatic effects on their dynamics and even on the nature of their ground state. The case of a qubit coupled to a harmonic oscillator in this ultrastrong coupling regime has been investigated theoretically and experimentally. Here, we explore the case of two harmonic oscillators in the ultrastrong coupling regime. Probing the properties of their ground state remains out of reach in natural implementations. Therefore, we have realized an analog quantum simulation of this coupled system by dual frequency pumping a nonlinear superconducting circuit. The pump amplitudes directly tune the effective coupling rate. We observe spectroscopic signature of a mode hybridization that is characteristic of the ultrastrong coupling. We experimentally demonstrate a key property of the ground state of this simulated ultrastrong coupling between modes by observing simultaneous single- and two-mode squeezing of the radiated field below vacuum fluctuations.

Author Correction: Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing.

The original version of this Article omitted the following from the Acknowledgements: Z. Leghtas' primary affiliation is Centre Automatique et Systèmes, Mines ParisTech. This has been corrected in both the PDF and HTML versions of the Article.

Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing.

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.

Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States.

Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying an active feedback condition 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.

Quantum engineering. Confining the state of light to a quantum manifold by engineered two-photon loss.

Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially engineered interaction with the environment can become a resource for the generation and protection of quantum states. This notion can be generalized to the confinement of a system into a manifold of quantum states, consisting of all coherent superpositions of multiple stable steady states. We have confined the state of a superconducting resonator to the quantum manifold spanned by two coherent states of opposite phases and have observed a Schrödinger cat state spontaneously squeeze out of vacuum before decaying into a classical mixture. This experiment points toward robustly encoding quantum information in multidimensional steady-state manifolds.

Tracking photon jumps with repeated quantum non-demolition parity measurements.

Quantum error correction is required for a practical quantum computer because of the fragile nature of quantum information. In quantum error correction, information is redundantly stored in a large quantum state 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-quantum-bit parities, must correspond to a special symmetry property inherent in the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition way (projecting without further perturbing the state) and more quickly than errors occur. Previously, quantum non-demolition measurements of quantum jumps between states of well-defined energy have been performed in systems such as trapped ions, electrons, cavity quantum electrodynamics, nitrogen-vacancy centres and superconducting quantum bits. So far, however, no fast and repeated monitoring of an error syndrome has been achieved. Here we track the quantum jumps of a possible error syndrome, namely the photon number parity of a microwave cavity, by mapping this property onto an ancilla quantum bit, whose only role is to facilitate quantum state manipulation and measurement. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schrödinger cat states (quantum superpositions of different coherent states of light) in a harmonic oscillator. We demonstrate the projective nature of this measurement onto a region of state space with well-defined parity by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared with the cavity lifetime, has a high single-shot fidelity and has a 99.8 per cent probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of quantum information in cat states realized earlier, the quantum non-demolition parity tracking that we demonstrate represents an important step towards implementing an active system that extends the lifetime of a quantum bit.

Autonomously stabilized entanglement between two superconducting quantum bits.

Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors, but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes. The 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 using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset, single-qubit state stabilization, and the creation and stabilization of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence, obviating the need for a complicated external feedback loop to correct errors. 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 for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits, will be an essential tool for the implementation of quantum error correction.

Demonstrating a driven reset protocol for a superconducting qubit.

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 appropriate 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 µs; faster times and higher fidelity are predicted upon parameter optimization.