Kitaev’s 0-π qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherencetimes of a realistic 0-π device can surpass that of today’s best superconducting qubits [Groszkowski et al., New Journal of Physics 20 043053 (2018)]. Here we address controllability of the 0-π qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity single-qubit gate that can interpolate smoothly between logical X and Z. We characterize the action of this gate using a multi-level treatment of the device, and analyze the impact of circuit element disorder and deviations in control and circuit parameters from their optimal values. Furthermore, we propose a cooling scheme to decrease the photon shot-noise dephasing rate, which we previously found to limit the coherence times of 0-π devices within reach of current experiments. Using this approach, we predict coherence time enhancements between one and three orders of magnitude, depending on parameter regime.
Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating photon interactions. Despitecontinuing efforts in designing anharmonic Josephson circuits with improved coherence times, the best photon lifetimes have been demonstrated in microwave cavities. Nevertheless, architectures based on quantum memories need a qubit element for addressing these harmonic modules at the cost of introducing additional loss channels and limiting process fidelities. This work focuses on tailoring the oscillator Hilbert space to enable a direct Rabi drive on individual energy levels. For this purpose we implement a flux-tunable inductive coupling between two linear resonators using a superconducting quantum interference device. We dynamically activate a three-wave mixing process through parametric flux modulation in order to selectively address the lowest eigenstates as an isolated two-level system. Measuring the Wigner function confirms we can prepare arbitrary states confined in the single photon manifold, with measured coherence times limited by the oscillator intrinsic quality factor. This architectural shift in engineering oscillators with stimulated nonlinearity can be exploited for designing long-lived quantum modules and offers flexibility in studying non-equilibrium physics with photons in a field-programmable simulator.
We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally. Our scheme utilizedred and blue sideband transitions in a system composed of a fluxonium qubit, a low-Q LC-oscillator, and a coupler enabling us to tune the interaction between them. Under parametric modulations of the coupling strength, the qubit can be steered into any desired pure or mixed single-qubit state. For realistic circuit parameters, we predict that stabilization can be achieved within 100 ns. By varying the ratio between the oscillator’s damping rate and the effective qubit-oscillator coupling strength, we can switch between under-damped, critically-damped, and over-damped stabilization and find optimal working points. We further analyze the effect of thermal fluctuations and show that the stabilization scheme remains robust for realistic temperatures.
Superconducting circuits rank among the most interesting architectures for the implementation of quantum information processing devices. The recently proposed 0-π qubit [Brooks etal., Phys. Rev. A 87, 52306 (2013)] promises increased protection from spontaneous relaxation and dephasing. In practice, this ideal behavior is only realized if the parameter dispersion among nominally identical circuit elements vanishes. In this paper we present a theoretical study of the more realistic scenario of slight variations in circuit elements. We discuss how the coupling to a spurious, low-energy mode affects the coherence properties of the 0-π device, investigate the relevant decoherence channels, and present estimates for achievable coherence times in multiple parameter regimes.
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achievedwith a tunable coupler design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasi-static tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single photon exchange in 6 ns. Qubit coherence times exceeding 20 μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon non-conserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80 %.
We realize a Λ system in a superconducting circuit, with metastable states exhibiting lifetimes up to 7ms. We exponentially suppress the tunneling matrix elements involved in spontaneousenergy relaxation by creating a „heavy“ fluxonium, realized by adding a capacitive shunt to the original circuit design. The device allows for both cavity-assisted and direct fluorescent readout, as well as state preparation schemes akin to optical pumping. Since direct transitions between the metastable states are strongly suppressed, we utilize Raman transitions for coherent manipulation of the states.
Qubit connectivity is an important property of a quantum processor, with an ideal processor having random access — the ability of arbitrary qubit pairs to interact directly. Here,we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-bit quantum memory, with a single transmon serving as the central processor. The quantum memory uses the eigenmodes of a linear array of coupled superconducting resonators. The memory bits are superpositions of vacuum and single-photon states, controlled by a single superconducting transmon coupled to the edge of the array. We selectively stimulate single-photon vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency, producing sidebands resonant with the modes. Utilizing these oscillations for state transfer, we perform a universal set of single- and two-qubit gates between arbitrary pairs of modes, using only the charge and flux bias of the transmon. Further, we prepare multimode entangled Bell and GHZ states of arbitrary modes. The fast and flexible control, achieved with efficient use of cryogenic resources and control electronics, in a scalable architecture compatible with state-of-the-art quantum memories is promising for quantum computation and simulation.
Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetryand topology. However, nonequilibrium phase transitions have remained a challenge, in part due to their complexity in theoretical descriptions and the additional experimental difficulties in systematically controlling systems out of equilibrium. Here, we study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state. We find experimental evidence for a dissipative phase transition in the system in which the steady state changes dramatically as the mean photon number is increased. Near the boundary between the two observed phases, the system demonstrates bistability, with characteristic switching times as long as 60 ms — far longer than any of the intrinsic rates known for the system. This experiment demonstrates the power of circuit QED systems for studying nonequilibrium condensed matter physics and paves the way for future experiments exploring nonequilbrium physics with many-body quantum optics.
Microwave photons inside lattices of coupled resonators and superconducting qubits can exhibit surprising matter-like behavior. Realizing such open-system quantum simulators presentsan experimental challenge and requires new tools and measurement techniques. Here, we introduce Scanning Defect Microscopy as one such tool and illustrate its use in mapping the normal-mode structure of microwave photons inside a 49-site Kagome lattice of coplanar waveguide resonators. Scanning is accomplished by moving a probe equipped with a sapphire tip across the lattice. This locally perturbs resonator frequencies and induces shifts of the lattice resonance frequencies which we determine by measuring the transmission spectrum. From the magnitude of mode shifts we can reconstruct photon field amplitudes at each lattice site and thus create spatial images of the photon-lattice normal modes.
In charge-coupled circuit QED systems, transition amplitudes and dispersive shifts are governed by the matrix elements of the charge operator. For the fluxonium circuit, these matrixelements are not limited to nearest-neighbor energy levels and are conveniently tunable by magnetic flux. Previously, their values were largely obtained numerically. Here, we present analytical expressions for the fluxonium charge matrix elements. We show that new selection rules emerge in the asymptotic limit of large Josephson energy and small inductive energy. We illustrate the usefulness of our expressions for the qualitative understanding of charge matrix elements in the parameter regime probed by previous experiments.