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.

Quantum error correction of a qubit encoded in grid states of an oscillator.

The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. One method to achieve this is quantum error correction (QEC), which prevents noise in the underlying system from causing logical errors. This approach derives from the reasonable assumption that noise is local, that is, it does not act in a coordinated way on different parts of the physical system. Therefore, if a logical qubit is encoded non-locally, we can-for a limited time-detect and correct noise-induced evolution before it corrupts the encoded information1. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a non-local qubit: a superposition of position eigenstates that forms grid states of a single oscillator2. However, the implementation of measurements that reveal this noise-induced evolution of the oscillator while preserving the encoded information3-7 has proved to be experimentally challenging, and the only realization reported so far relied on post-selection8,9, which is incompatible with QEC. Here we experimentally prepare square and hexagonal GKP code states through a feedback protocol that incorporates non-destructive measurements that are implemented with a superconducting microwave cavity having the role of the oscillator. We demonstrate QEC of an encoded qubit with suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous-variable systems and, in contrast to previous implementations of QEC10-14, can mitigate all logical errors generated by a wide variety of noise processes and facilitate fault-tolerant quantum computation.

Deterministic Remote Entanglement of Superconducting Circuits through Microwave Two-Photon Transitions.

Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wave packet. We achieve a Bell state fidelity of 73%, well explained by losses in the transmission line and decoherence of each qubit.

Using Spontaneous Emission of a Qubit as a Resource for Feedback Control.

Persistent control of a transmon qubit is performed by a feedback protocol based on continuous heterodyne measurement of its fluorescence. By driving the qubit and cavity with microwave signals whose amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we show that it is possible to stabilize permanently the qubit in any targeted state. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency η=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output analog Markovian feedback in the quantum regime.

Quantum optics. Quantum dynamics of an electromagnetic mode that cannot contain N photons.

Electromagnetic modes are instrumental in building quantum machines. In this experiment, we introduce a method to manipulate these modes by effectively controlling their phase space. Preventing access to a single energy level, corresponding to a number of photons N, confined the dynamics of the field to levels 0 to N - 1. Under a resonant drive, the level occupation was found to oscillate in time, similarly to an N-level system. Performing a direct Wigner tomography of the field revealed its nonclassical features, including a Schrödinger cat-like state at half period in the evolution. This fine control of the field in its phase space may enable applications in quantum information and metrology.

Observing interferences between past and future quantum states in resonance fluorescence.

The fluorescence of a resonantly driven superconducting qubit is measured in the time domain, providing a weak probe of the qubit dynamics. Prior preparation and final, single-shot measurement of the qubit allows us to average fluorescence records conditionally on past and future knowledge. The resulting interferences reveal purely quantum features characteristic of weak values. We demonstrate conditional averages that go beyond classical boundaries and probe directly the jump operator associated with relaxation. The experimental results are remarkably captured by a recent theory, which generalizes quantum mechanics to open quantum systems whose past and future are known.

Widely tunable, nondegenerate three-wave mixing microwave device operating near the quantum limit.

We present the first experimental realization of a widely frequency tunable, nondegenerate three-wave mixing device for quantum signals at gigahertz frequency. It is based on a new superconducting building block consisting of a ring of four Josephson junctions shunted by a cross of four linear inductances. The phase configuration of the ring remains unique over a wide range of magnetic fluxes threading the loop. It is thus possible to vary the inductance of the ring with flux while retaining a strong, dissipation-free, and noiseless nonlinearity. The device has been operated in amplifier mode, and its noise performance has been evaluated by using the noise spectrum emitted by a voltage-biased tunnel junction at finite frequency as a test signal. The unprecedented accuracy with which the crossover between zero-point fluctuations and shot noise has been measured provides an upper bound for the noise and dissipation intrinsic to the device.