We have studied the impact of low-frequency magnetic flux noise upon superconducting transmon qubits with various levels of tunability. We find that qubits with weaker tunability exhibit dephasing that is less sensitive to flux noise. This insight was used to fabricate qubits where dephasing due to flux noise was suppressed below other dephasing sources, leading to flux-independent dephasing times T2* ~ 15 us over a tunable range of ~340 MHz. Such tunable qubits have the potential to create high-fidelity, fault-tolerant qubit gates and fundamentally improve scalability for a quantum processor.
Recent progress in superconducting qubits has demonstrated the potential of these devices for the future of quantum information processing. One desirable feature for quantum computing is independent control of qubit interactions as well as qubit energies. We demonstrate a new type of superconducting charge qubit that has a V-shaped energy spectrum and uses quantum interference to provide independent control over the qubit energy and dipole coupling to a superconducting cavity. We demonstrate dynamic access to the strong coupling regime by tuning the coupling strength from less than 200 kHz to …
A quantum-mechanical model for the interaction of Josephson vortices (fluxons) embedded in superconducting transmission line is presented. The vortices interact through emission and absorption of linear waves (electromagnetic cavity modes). We show that in a classical regime this peculiar type of interaction is determined by the product of instantaneous velocities of fluxons. In a quantum regime, this property provides tunable coupling between vortices which can be used for entanglement of vortex qubits. The physical mechanism of the vortex interaction is similar to that proposed for qubits ba…
We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe $T_1$ and $T_2$ times of 1.6 and 1.9 $μ$s, respectively. This work demonstrates how…
We study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits [Y. Chen et al., arXiv:1402.7367]. The coupler circuit uses a single flux-biased Josephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse XX coupling from that obtained in the harmonic approximati…
Flux-tunable qubits are a useful resource for superconducting quantum processors. They can be used to perform cPhase gates, facilitate fast reset protocols, avoid qubit-frequency collisions in large processors, and enable certain fast readout schemes. However, flux-tunable qubits suffer from a trade-off between their tunability range and sensitivity to flux noise. Optimizing this trade-off is particularly important for enabling fast, high-fidelity, all-microwave cross-resonance gates in large, high-coherence processors. This is mainly because cross-resonance gates set stringent conditions on t…
In this work we show that a tunable coupling between microwave resonators can be engineered by means of simple Josephson junctions circuits, such as dc- and rf-SQUIDs. We show that by controlling the time dependence of the coupling it is possible to switch on and off and modulate the cross-talk, boost the interaction towards the ultrastrong regime, as well as to engineer red and blue sideband couplings, nonlinear photon hopping and classical gauge fields. We discuss how these dynamically tunable superconducting circuits enable key applications in the fields of all optical quantum computing, co…
We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, $\sqrt{\rm SWAP}$, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.
Digital Predistortion for Flux Control of Tunable Superconducting Qubits
Quantum Engineering Solutions (QES), Keysight Technologies Inc.（Keysight Technologies Inc.）；Abdus Salam Centre for Theoretical Physics, Imperial College London（伦敦帝国理工学院阿卜杜斯·萨拉姆理论物理中心）；Division of Physics and Applied Physics, Nanyang Technological University（南洋理工大学物理与应用物理系）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
We study an LC-circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge--phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.
We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable coupling strength g. We show that this coupling strength can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0 the qubit is in a decoherence free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore we show that in the decoherence free subspace the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.
We experimentally confirm the functionality of a coupling element for flux-based superconducting qubits, with a coupling strength $J$ whose sign and magnitude can be tuned {\it in situ}. To measure the effective $J$, the groundstate of a coupled two-qubit system has been mapped as a function of the local magnetic fields applied to each qubit. The state of the system is determined by directly reading out the individual qubits while tunneling is suppressed. These measurements demonstrate that $J$ can be tuned from antiferromagnetic through zero to ferromagnetic.
We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device (SQUID). We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 μs when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on res…
We develop a theory for non-degenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a strong nonlinear regime at the parametric instability threshold, and calculate maximum gain values. Above the threshold, in the parametric oscillator regime the linear cavity response diverges at the oscillator frequency at all pump strengths. We show that this divergence is related to the continuous degeneracy of the free oscillator state with respect to t…
We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Non-reciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to i…
We propose to implement tunable interaction of superconducting flux qubits with cavity-assisted interaction and strong driving. The qubits have a three-level Lambda configuration, and the decay of the excited state will be greatly suppressed due to the effective large detuning. The implemented interaction is insensitive to the cavity field state and can be controlled by modulating the phase difference of the driving fields of the qubits. In particular, our scheme is based on the typical circuit QED setup and thus will provide a simple method towards the tunable interaction of superconducting q…
We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstrate that this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamic coupling by implementing a novel adiabatic controlled-Z gate, at a spe…
We propose a tunable on-chip micromaser using a superconducting quantum circuit (SQC). By taking advantage of externally controllable state transitions, a state population inversion can be achieved and preserved for the two working levels of the SQC and, when needed, the SQC can generate a single photon. We can regularly repeat these processes in each cycle when the previously generated photon in the cavity is decaying, so that a periodic sequence of single photons can be produced persistently. This provides a controllable way for implementing a persistent single-photon source on a microelectr…
Fabrication of sub-micron Josephson junctions is demonstrated using standard processing techniques for high-coherence, superconducting qubits. These junctions are made in two separate lithography steps with normal-angle evaporation. Most significantly, this work demonstrates that it is possible to achieve high coherence with junctions formed on aluminum surfaces cleaned in situ with Ar milling before the junction oxidation. This method eliminates the angle-dependent shadow masks typically used for small junctions. Therefore, this is conducive to the implementation of typical methods for improv…
We measure the coherence of a new superconducting qubit, the {\em low-impedance flux qubit}, finding $T_2^* \sim T_1 \sim 1.5μ$s. It is a three-junction flux qubit, but the ratio of junction critical currents is chosen to make the qubit's potential have a single well form. The low impedance of its large shunting capacitance protects it from decoherence. This qubit has a moderate anharmonicity, whose sign is reversed compared with all other popular qubit designs. The qubit is capacitively coupled to a high-Q resonator in a $λ/2$ configuration, which permits the qubit's state to be read out disp…
We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit driv…
We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is scalable, and allows to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analy…
We report on highly tunable radio frequency (rf) characteristics of a low-loss and compact three dimensional (3D) metamaterial made of superconducting thin film spiral resonators. The rf transmission spectrum of a single element of the metamaterial shows a fundamental resonance peak at $\sim$24.95 MHz that shifts to a 25$\%$ smaller frequency and becomes degenerate when a 3D array of such elements is created. The metamaterial shows an $\emph{in-situ}$ tunable narrow frequency band in which the real part of the effective permeability is negative over a wide range of temperature, which reverts t…
We describe a simple and efficient scheme for the readout of a tunable flux qubit, and present preliminary experimental tests for the preparation, manipulation and final readout of the qubit state, performed in incoherent regime at liquid Helium temperature. The tunable flux qubit is realized by a double SQUID with an extra Josephson junction inserted in the large superconducting loop, and the readout is performed by applying a current ramp to the junction and recording the value for which there is a voltage response, depending on the qubit state. This preliminary work indicates the feasibilit…
We have designed, fabricated and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC current through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor $Q_i> 180,000$. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurem…
Within the kinetic energy driven superconducting mechanism, we study the interplay between superconductivity and the nodal and antinodal superconducting quasiparticle coherences in cuprate superconductors, and find the s-wave superconducting transition temperature is heavily suppressed by the antinodal superconducting quasiparticle coherence, while the d-wave superconducting transition temperature is enhanced, therefore the antinodal superconducting quasiparticle coherence plays a more crucial role in superconductivity of cuprate superconductors.
We report on experiments with superconducting metamaterials containing Josephson junctions. In these structures, split-ring resonators used in conventional metamaterials are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split-ring resonators, these elements can be seen as LC-resonators that couple to the magnetic field. The advantage of superconducting thin-film metamaterials is that, due to the tunable intrinsic inductance of the Josephson junction, the resonance frequency of the rf-SQUID can be changed by applying an external dc …
We report on the superconducting properties of amorphous NbxSi1-x thin films. The normal-state resistance and critical temperatures can be separately adjusted to suit the desired application. Notably, the relatively low electron-phonon coupling of these films makes them good candidates for an "all electron bolometer" for Cosmological Microwave Background radiation detection. Moreover, this device can be made to suit both high and low impedance readouts.
We experimentally demonstrate the coherent oscillations of a tunable superconducting flux qubit by manipulating its energy potential with a nanosecond-long pulse of magnetic flux. The occupation probabilities of two persistent current states oscillate at a frequency ranging from 6 GHz to 21 GHz, tunable via the amplitude of the flux pulse. The demonstrated operation mode allows to realize quantum gates which take less than 100 ps time and are thus much faster compared to other superconducting qubits. An other advantage of this type of qubit is its insensitivity to both thermal and magnetic fie…
We demonstrate a low-dissipation dielectric metamaterial with tunable properties based on the Josephson effect. Superconducting wires loaded with regularly spaced Josephson junctions ($I_c \approx 0.25$ $μ$A) spanning a K-band waveguide and aligned with the microwave electric fields create a superconducting dielectric metamaterial. Applied dc current tunes the cutoff frequency and effective permittivity of this unique electric metamaterial. The results are in agreement with an analytical model for microwave transmission through the artificial dielectric medium.
We report on the fabrication and electrical transport properties of gate-tunable superconducting quantum interference devices (SQUIDs), made of semiconducting PbS nanowire contacted with PbIn superconducting electrodes. Applied with a magnetic field perpendicular to the plane of the nano-hybrid SQUID, periodic oscillations of the critical current due to the flux quantization in SQUID are observed up to T = 4.0 K. Nonsinusoidal current-phase relationship is obtained as a function of temperature and gate voltage, which is consistent with a short and diffusive junction model.
We present a dual cut-off, dc-tunable low-pass microwave filter on a superconducting Nb microstrip with uniaxial asymmetric nanogrooves. The frequency response of the device was measured in the range $300$\,KHz to $14$\,GHz at different temperatures, magnetic fields, and dc current values. The microwave loss is most effectively reduced when the Abrikosov vortex lattice spatially matches the underlying washboard pinning landscape. The forward transmission coefficient $S_{21}(f)$ of the microstrip has a dc-tunable cut-off frequency $f_d$ which notably changes under dc bias reversal, due to the t…
We study the flux pinning properties of superconductor/magnetic micro-rings lattice hybrid structures. The used open triangular micromagnets represent an eight-fold degree of freedom system, with six polarized and two flux-closure possible states. By conveniently choosing the magnetic state of the underlying rings it is possible to induce different pinning potentials. We show that the magnetic vortex state with minimum stray field produces a weaker pinning in comparison with the polarized states.
We discuss experimental results obtained using a tunable cylindrical coaxial cavity constituted by an outer Cu cylinder and an inner Pb-BSCCO wire. We have used this device for investigating the microwave response of the superconducting wire, both in the linear and nonlinear regimes. In particular, by tuning the different modes of the cavity to make them resonant at exactly harmonic frequencies, we have detected the power emitted by the superconducting inner wire at the second- and third-harmonic frequency of the driving field. The results obtained in the nonlinear regime, whether for the micr…
Hybrid superconducting--spin systems offer the potential to combine highly coherent atomic quantum systems with the scalability of superconducting circuits. To fully exploit this potential requires a high quality-factor microwave resonator, tunable in frequency and able to operate at magnetic fields optimal for the spin system. Such magnetic fields typically rule out conventional Al-based Josephson junction devices that have previously been used for tunable high-$Q$ microwave resonators. The larger critical field of niobium (Nb) allows microwave resonators with large field resilience to be fab…
Over the last decade it has been shown that magnetic non-collinearity at a s-wave superconductor/ferromagnet interface is a key ingredient for spin-singlet to spin-triplet pair conversion. This has been verified in several synthetic non-collinear magnetic structures. A magnetically soft and hard ferromagnetic layer combination in a bi-layer structure can function as a field tunable non-collinear magnetic structure which may offer magnetic-field tuneability of singlet-to-triplet pair conversion. From magnetization measurements of Nb/Co/Py/Nb multilayers we demonstrate a reversible enhancement o…
A superconducting double spin valve device is proposed. Its operation takes advantage of the interplay between the spin-filtering effect of ferromagnetic insulators and superconductivity-induced out-of-equilibrium transport. Depending on the degree of nonequilibrium, extraordinary large tunnel magnetoresistance as large as 10^2...10^6% can be obtained for realistic material parameters, and it can be tuned over several orders of magnitude under proper voltage biasing and temperature. The relevance of this setup for low-temperature applications is further discussed.
It is shown that transition from the mixed state without the phase coherence to the mixed state with the long-range phase coherence (i.e. to the Abrikosov state) of superconductors without disorder must be first order phase transition. The phase coherence appearance in thin superconducting film with strong disorder is considered. The observed smooth transition is explained by increasing of the effective fluctuation dimensionality (from zero to one) in superconductors with strong disorder. Mendelssohn model is used for the explanation of the resistive properties of film with strong disorder.
We study a superconducting single-charge transistor, where the coherence of Cooper pair tunneling is destroyed by the coupling to a tunable dissipative environment. Sequential tunneling and cotunneling processes are analyzed to construct the shape of the conductance peaks and their dependence on the dissipation and temperature. Unexpected features are found due to a cross-over between two distinct regimes, one `environment-assisted' the other `environment-dominated'. Several of the predictions have been confirmed by recent experiments. The model and results apply also to the dynamics of Joseph…
We have developed a novel system consisting of a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG), for which the dissipation can be tuned in the immediate vicinity of the S-SET. Within linear response, the S-SET conductance varies nonmonotonically with increasing 2DEG impedance. We find good agreement between our experimental results and a model incorporating electromagnetic fluctuations in both the S-SET leads and the 2DEG, as well as low-frequency switching of the S-SET offset charge.
Increasing the degree of control over physical qubits is a crucial component of quantum computing research. We report a superconducting qubit of fluxonium type with the Ramsey coherence time reaching $T_2^*= 1.48 \pm 0.13 \mathrm{~ms}$, which exceeds the state of the art value by an order of magnitude. As a result, the average single-qubit gate fidelity grew above $0.9999$, surpassing, to our knowledge, any other solid-state quantum system. Furthermore, by measuring energy relaxation of the parity-forbidden transition to second excited state, we exclude the effect of out-of-equilibrium quasipa…
We have fabricated 5 nm ultra-thin NbN nanowires that form a dense and regular array in the linear channels of mesoporous SBA-15 silica substrates. Bulk NbN is a well-known classical superconductor with Tc of 16 K. We show that, by being incorporated into this nanostructure, the composite material exhibits typical quasi-one-dimensional characteristics. We compare the superconducting properties with those of superconducting Pb nanowires of same dimensionality in identical configuration within the linear SBA-15 pores. While Pb nanowire arrays show a pronounced crossover from 1D superconductivity…
We study the problem of phase coherence in doped striped cuprates. We assume the stripes to form a network of one-dimensional Luttinger liquids which are dominated by superconducting fluctuations and pinned by impurities. The problem of phase coherence is discussed. We study the dynamics of the superconducting phase using a model of resistively shunted junctions which leads to a Kosterlitz-Thouless transition. We show that our results are consistent with recent experiments in Zn-doped cuprates. We also explain the scaling of the superconducting critical temperature $T_c$ with the incommensurab…
Broadly Tunable Sub-terahertz Emission from Internal Branches of the Current-voltage Characteristics of Superconducting Bi2Sr2CaCu2O8+d Single Crystals
Japan Society for the Promotion of Science（日本学术振兴会）；Quantum Beam Science Directorate, Japan Atomic Energy Agency（日本原子力机构量子束科学部）；Graduate School of Pure & Applied Sciences, University of Tsukuba（筑波大学纯科学与应用科学学院）
In the present work, we report the new findings on the doping level dependence of the phase coherence between superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) grains. The experimental results from the strongly underdoped and overdoped regimes deviated from the expectation based on the doping level dependence of the superfluid density at $T$ = 0 K. These findings appear to be governed by interplay between competing orders inside the superconducting dome of cuprate superconductors. Two quantum critical points are likely to exist at the underdoped and overdoped regimes beneath the supercon…
The global phase coherence in doubly-connected superconductors leads to fluxoid quantization, allowing the superfluid velocity vs to be controlled by an applied magnetic flux. In ultrasmall samples this quantization requirement leads, surprisingly, to the destruction of the phase coherence itself around half-integer flux quanta, because of the sample-size-induced growth in vs, as predicted by de Gennes. We report observations of the predicted phenomenon in ultrathin Al and Au0.7In0.3 cylinders, and the corresponding phase diagram for ultrathin superconducting cylinders. The new phase diagram f…
The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we discover the tunable universality class of superconductor-metal transition by changing the di…
In this paper we analyze, using scanning tunneling spectroscopy (STS), the local density of electronic states (LDOS) in nearly optimally doped BSCCO in zero field. We see both dispersive and non-dispersive spatial LDOS modulations as a function of energy in our samples. Moreover, a spatial map of the superconducting coherence peak heights shows the same structure as the low energy LDOS. This suggests that these non-dispersive LDOS modulations originate from an underlying charge-density modulation which interacts with superconductivity.
