Superconducting quantum computing is experiencing a tremendous growth. Although major milestones have already been achieved, useful quantum-computing applications are hindered by a variety of decoherence phenomena. Decoherence due to two-level systems (TLSs) hosted by amorphous dielectric materials is ubiquitous in planar superconducting devices. We use high-quality quasilumped element resonators as quantum sensors to investigate TLS-induced loss and noise. We perform two-tone experiments with a probe and pump electric field; the pump is applied at different power levels and detunings. We measure and analyze time series of the quality factor and resonance frequency for very long time periods, up to 1000 h. We additionally carry out simulations based on the TLS interacting model in presence of a pump field. We find that loss and noise are reduced at medium and high power, matching the simulations, but not at low power.
We study quantum information processing using superpositions of Fock states in superconducting resonators, as quantum $d$-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators coupled by superconducting circuits of Josephson juctions. These gates use experimentally demonstrated interactions, and provide an attractive route to quantum information processing using harmonic oscillator modes.
We present a theoretical analysis of methods to synthesize entangled states of two superconducting resonators. These methods use experimentally demonstrated interactions of resonators with artificial atoms, and offer efficient routes to generate nonclassical states. We analyze physical implementations, energy level structure, and the effects of decoherence through detailed dynamical simulations.
We study a superconducting circuit that can act as a toolbox to generate various Bogoliubov-linear and nonlinear quantum operations on the microwave photon modes of superconducting resonators within one single circuit. The quantum operations are generated by exploring dispersive four-wave mixing (FWM) processes involving the resonator modes. Different FWM geometries can be realized by adjusting the circuit parameters and by applying appropriate microwave drivings. We illustrate this scheme using a circuit made of two superconducting qubits that couple with each other. Each qubit couples with o…
We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together reveal different decay and decoherence mechanisms in a general microwave resonator. These results form a solid basis for understanding the scattering spectrums of networks of microwave resonators, and p…
Superconducting quantum computing architectures comprise resonators and qubits that experience energy loss due to two-level systems (TLS) in bulk and interfacial dielectrics. Understanding these losses is critical to improving performance in superconducting circuits. In this work, we present a method for quantifying the TLS losses of different bulk and interfacial dielectrics present in superconducting coplanar waveguide (CPW) resonators. By combining statistical characterization of sets of specifically designed CPW resonators on isotropically etched silicon substrates with detailed electromag…
We present a method to synthesize an arbitrary quantum state of two superconducting resonators. This state-synthesis algorithm utilizes a coherent interaction of each resonator with a tunable artificial atom to create entangled quantum superpositions of photon number (Fock) states in the resonators. We theoretically analyze this approach, showing that it can efficiently synthesize NOON states, with large photon numbers, using existing technology.
In this paper, we propose a scheme to realize three-qubit quantum phase gate of one qubit simultaneously controlling two target qubits using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The two lowest levels |0> and |1> of each SQUID are used to represent logical states while the higher energy levels |2> and |3> are utilized for gate realization. Our scheme does not require adiabatic passage, second order detuning, and the adjustment of the level spacing during gate operation which reduce the gate time significantly. The scheme is gen…
We present an experimental feasible scheme to synthesize two-mode continuous-variable entangled states of two superconducting resonators that are interconnected by two gap-tunable superconducting qubits. We show that, with each artificial atom suitably driven by a bichromatic microwave field to induce sidebands in the qubit-resonator coupling, the stationary state of the photon fields in the two resonators can be cooled and steered into a two-mode squeezed vacuum state via a dissipative quantum dynamical process, while the superconducting qubits remain in their ground states. In this scheme th…
We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the elect…
Superconducting resonators interfaced with paramagnetic spin ensembles are used to increase the sensitivity of electron spin resonance experiments and are key elements of microwave quantum memories. Certain spin systems that are promising for such quantum memories possess 'sweet spots' at particular combinations of magnetic fields and frequencies, where spin coherence times or linewidths become particularly favorable. In order to be able to couple high-Q superconducting resonators to such specific spin transitions, it is necessary to be able to tune the resonator frequency under a constant mag…
We report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are Nitrogen-Vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the NV center electron spin resonance.
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins magnetically coupled to a superconducting resonator. We report on a cavity QED experiment with magnetically anisotropic Er3+:Y2SiO5 crystals and demonstrate strong coupling of rare-earth spins to a lumped element resonator. In addition, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without a…
Vortices trapped in thin-film superconducting microwave resonators can have a significant influence on the resonator performance. Using a variable-linewidth geometry for a weakly coupled resonator we are able to observe the effects of a single vortex trapped in the resonator through field cooling. For resonant modes where the vortex is near a current antinode, the presence of even a single vortex leads to a measurable decrease in the quality factor and a dispersive shift of the resonant frequency. For modes with the vortex located at a current node, the presence of the vortex results in no det…
We investigate a network of coupled superconducting transmission line resonators, each of them made nonlinear with a capacitively shunted Josephson junction coupling to the odd flux modes of the resonator. The resulting eigenmode spectrum shows anticrossings between the plasma mode of the shunted junction and the odd resonator modes. Notably, we find that the combined device can inherit the complete nonlinearity of the junction, allowing for a description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID instead of a single junction, the nonlinearity can be tuned between 10 k…
We introduce a microwave circuit architecture for quantum signal processing combining design principles borrowed from high-Q 3D resonators in the quantum regime and from planar structures fabricated with standard lithography. The resulting '2.5D' whispering-gallery mode resonators store 98% of their energy in vacuum. We have measured internal quality factors above 3 million at the single photon level and have used the device as a materials characterization platform to place an upper bound on the surface resistance of thin film aluminum of less than 250nOhms.
The loss and noise mechanisms of superconducting resonators are useful tools for understanding decoherence in superconducting circuits. While the loss mechanisms have been heavily studied, noise in superconducting resonators has only recently been investigated. In particular, there is an absence of literature on noise in the single photon limit. Here, we measure the loss and noise of an aluminium on silicon quarter-wavelength ($λ/4$) resonator in the single photon regime.
We demonstrate experimentally the creation and measurement of an entangled state between a microscopic two level system and a macroscopic superconducting resonator where their indirect interaction is mediated by an artificial atom, a superconducting persistent current qubit (PCQB). We show that the microscopic two level system, formed by a defect in an oxide layer, exhibits an order of magnitude longer dephasing time than the PCQB, while the dephasing time of the entangled states between the microscopic two level system and macroscopic superconducting resonator is significantly longer than the…
We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a …
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…
Long-distance two-qubit coupling, mediated by a superconducting resonator, is a leading paradigm for performing entangling operations in a quantum computer based on spins in semiconducting materials. Here, we demonstrate a novel, controllable spin-photon coupling based on a longitudinal interaction between a spin qubit and a resonator. We show that coupling a singlet-triplet qubit to a high-impedance superconducting resonator can produce the desired longitudinal coupling when the qubit is driven near the resonator's frequency. We measure the energy splitting of the qubit as a function of the d…
We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field fluctuations. These are found to be in agreement with theoretical predictions; in particular we experimentally observe the phenomenon of quantum heating.
The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum non-demolition measurement of the number of photons in a given resonator mode. Quantum non-demolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response. We show that the sensitivity of such a detection scheme is directly related to the dephasing rate induced by such an intermode coupling. We show that high sensitivity is expected when the detector mode …
An all-resonant method is proposed to control the quantum state of superconducting resonators. This approach uses a tunable artificial atom linearly coupled to resonators, and allows for efficient routes to Fock state synthesis, qudit logic operations, and synthesis of NOON states. This resonant approach is theoretically analyzed, and found to perform signficantly better than existing proposals using the same technology.
A coupled system of a superconducting transmission line resonator with a semiconductor double quantum dot is analyzed. We simulate the phase shift of the microwave signal in the resonator, which is sensitive to the quantum dot qubit state and manipulation. The measurement quality is sufficiently high and the results demonstrate a solid-state quantum processor based on this type of circuit can be envisioned.
We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level. The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsi…
We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending …
Coupled superconducting transmission line resonators have applications in quantum information processing and fundamental quantum mechanics. A particular example is the realization of fast beam splitters, which however is hampered by two-mode squeezer terms. Here, we experimentally study superconducting microstrip resonators which are coupled over one third of their length. By varying the position of this coupling region we can tune the strength of the two-mode squeezer coupling from 2.4% to 12.9% of the resonance frequency of 5.44GHz. Nevertheless, the beam splitter coupling rate for maximally…
By simultaneously coupling multiple two-level artificial atoms to two superconducting resonators, we design a quantum switch that tunes the resonator-resonator coupling strength from zero to a large value proportional to the number of qubits. This process is implemented by engineering the qubits into different subradiant states, where the microwave photons decay from different qubits destructively interfere with each other such that the resonator-resonator coupling strength keeps stable in an open environment. Based on a three-step control scheme, we switch the coupling strength among differen…
A scheme is proposed for engineering two-mode squeezed states of two separated cold atomic clouds positioned near the surface of a superconducting stripline resonator. Based on the coherent magnetic coupling between the atomic spins and a stripline resonator mode, the desired two-mode squeezed state can be produced via precisely control on the dynamics of the system. This scheme may be used to realize scalable on-chip quantum networks with cold atoms coupling to stripline resonators.
We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantum interference device (SQUID) that terminates one of the resonators. This produces a nonlinear interaction on the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths t…
Interfacing superconducting quantum processors, working in the GHz frequency range, with optical quantum networks and atomic qubits is a challenging task for the implementation of distributed quantum information processing as well as for quantum communication. Using spin ensembles of rare earth ions provide an excellent opportunity to bridge microwave and optical domains at the quantum level. In this letter, we demonstrate magnetic coupling of Er$^{3+}$ spins doped in Y$_{2}$SiO$_{5}$ crystal to a high-Q coplanar superconducting resonator.
We analyze the current and zero-frequency current noise properties of a superconducting single electron resonator (SSET) coupled to a resonator, focusing on the regime where the SSET is operated in the vicinity of the Josephson quasiparticle resonance. We consider a range of coupling strengths and resonator frequencies to reflect the fact that in practice the system can be tuned to quite a high degree with the resonator formed either by a nanomechanical oscillator or a superconducting stripline fabricated in close proximity to the SSET. For very weak couplings the SSET acts on the resonator li…
We demonstrate the coupling of rare-earth ions locally implanted in a substrate (Gd$^{3+}$ in Al$_{2}$O$_{3}$) to a superconducting NbN lumped-element micro-resonator. The hybrid device is fabricated by a controlled ion implantation of rare-earth ions in well-defined micron-sized areas, aligned to lithographically defined micro-resonators. The technique does not degrade the internal quality factor of the resonators which remain above $10^{5}$. Using microwave absorption spectroscopy we observe electron-spin resonances in good agreement with numerical modelling and extract corresponding couplin…
We design and fabricate two types of superconducting niobium coplanar waveguide microwave resonators with different coupling capacitors on high purity Si substrates. Their microwave transmissions are measured at the temperatures of 20 mK. It is found that these two types of resonators possess significantly-different loaded quality factors; one is $5.6\times{10}^{3}$, and the other is $4.0\times{10}^{4}$. The measured data are fitted well by classical ABCD matrix approach. We found that the transmission peak deviates from the standard Lorentizian with a frequency broadening.
We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87 %; of the missing 13 %, only 3 % is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by t…
We propose a tunable nonlinear interaction for the implementation of quantum logic operations on pairs of superconducting resonators, where the two-resonator interaction is mediated by a transmon quantum bit (qubit). This interaction is characterized by a high on-to-off coupling ratio and allows for fast qubit-type and $d$-level system (qudit)-type operations for quantum information processing with multiphoton cavity states. We present analytical and numerical calculations showing that these operations can be performed with practically unit fidelity in absence of any dissipative phenomena, whe…
Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two …
We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor $Q_i$. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure $Q_i$ as function of frequency, power and temperature. We observe a linear increase of $Q_i$ with frequency, as predicted by …
We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations…
A system consisting of two qubits and a resonator is considered in the presence of different sources of noise, bringing to light the possibility for making the two qubits evolve in a synchronized way. A direct qubit-qubit interaction turns out to be a crucial ingredient as well as dissipation processes involving the resonator. The detrimental role of local dephasing of the qubits is also taken into account.
We present a theoretical analysis of different methods to synthesize entangled states of two superconducting resonators. These methods use experimentally demonstrated interactions of resonators with artificial atoms, and offer efficient routes to generate nonclassical states. We analyze the theoretical structure of these algorithms and their average performance for arbitrary states and for deterministically preparing NOON states. Using a new state synthesis algorithm, we show that NOON states can be prepared in a time linear in the desired photon number and without any state-selective interact…
We discuss the prospects of employing an NbN superconducting microwave stripline resonator for studying the dynamical Casimir effect experimentally. Preliminary experimental results, in which optical illumination is employed for modulating the resonance frequencies of the resonator, show that such a system is highly promising for this purpose. Moreover, we discuss the undesirable effect of heating which results from the optical illumination, and show that degradation in noise properties can be minimized by employing an appropriate design.
The addition of nonlinearity to an harmonic resonator provides a route to complex dynamical behaviour of resonant modes, including coupling between them. We present a superconducting device that makes use of the nonlinearity of Josephson junctions to introduce a controlled, tunable, nonlinear inductance to a thin film coplanar waveguide resonator. Considering the device as a potential quantum optical component in the microwave regime, we create a sensitive bifurcation amplifier and then demonstrate spectroscopy of other resonant modes via the intermode coupling. We find that the sensitivity of…
We propose a way for implementing quantum information transfer with two superconducting flux qubits, by coupling them to a resonator. This proposal does not require adjustment of the level spacings or uniformity in the device parameters. Moreover, neither adiabatic passage nor a second-order detuning is needed by this proposal, thus the operation can be performed much faster when compared with the previous proposals.
We propose a novel architecture for superconducting circuits to improve the efficiency of a quantum annealing system. To increase the capability of a circuit, it is desirable for a qubit to be coupled not only with adjacent qubits but also with other qubits located far away. We introduce a circuit that uses a lumped element resonator coupled each with one qubit. The resonator-qubit pairs are coupled by rf-superconducting quantum interference device (SQUID) based couplers. These pairs make a large quantum system for quantum annealer. This system could prepare the problem Hamiltonian and tune th…
We present a scheme for the deterministic generation of entangled photon pairs in a superconducting resonator array. The resonators form a Jaynes-Cummings lattice via the coupling to superconducting qubits, and the Kerr-like nonlinearity arises due to the coupling.We show that entangled photons can be generated on demand by applying spectroscopic techniques and exploiting the nonlinearity and symmetry in the resonators. The scheme is robust against small parameter spreads due to fabrication errors. Our findings can be used as a key element for quantum information processing in superconducting …
We propose an experimentally realizable hybrid quantum circuit for achieving a strong coupling between a spin ensemble and a transmission-line resonator via a superconducting flux qubit used as a data bus. The resulting coupling can be used to transfer quantum information between the spin ensemble and the resonator. In particular, in contrast to the direct coupling without a data bus, our approach requires far less spins to achieve a strong coupling between the spin ensemble and the resonator (e.g., three to four orders of magnitude less). This proposed hybrid quantum circuit could enable a lo…
We present a scalable quantum-bus-based device for generating the entanglement on microwave photons (MPs) in distant superconducting resonators (SRs). Different from the processors in previous works with some resonators coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs $r_j$ which are coupled to the quantum bus (another common resonator $R$) in its different positions simply, assisted by superconducting quantum interferometer devices. By using the technique for catching and releasing a MP state in a 1D SR, it can work as an entanglement generator or a node in quant…
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
We investigate the electromechanical coupling between a nanomechanical resonator and two parametrically coupled superconducting coplanar waveguide cavities that are driven by a two-mode squeezed microwave source. We show that, with the selective coupling of the resonator to the cavity Bogoliubov modes, the radiation-pressure type coupling can be greatly enhanced by several orders of magnitude, enabling the single photon strong coupling to be reached. This allows the investigation of a number of interesting phenomena such as photon blockade effects and the generation of nonclassical quantum sta…
Coupling a resonator to a superconducting qubit enables various operations on the qubit, including dispersive readout and unconditional reset. The speed of these operations is limited by the external decay rate of the resonator. However, increasing the decay rate also increases the rate of qubit decay via the resonator, limiting the qubit lifetime. Here, we demonstrate that the resonator-mediated qubit decay can be suppressed by utilizing the distributed-element, multi-mode nature of the resonator. We show that the suppression exceeds two orders of magnitude over a bandwidth of 600 MHz. We use…
We propose a quantum processor for the scalable quantum computation on microwave photons in distant one-dimensional superconducting resonators. It is composed of a common resonator R acting as a quantum bus and some distant resonators $r_j$ coupled to the bus in different positions assisted by superconducting quantum interferometer devices (SQUID), different from previous processors. R is coupled to one transmon qutrit, and the coupling strengths between $r_j$ and R can be fully tuned by the external flux through the SQUID. To show the processor can be used to achieve universal quantum computa…
We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e. quantum superpositions of pairs of distinguishable coherent states 180$^\circ$ out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented, and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement …
