We investigate the quantum dynamics of a system of two coupled superconducting qubits under microwave irradiation. We find that, with the qubits operated at the charge co-degeneracy point, the quantum evolution of the system can be described by a new effective Hamiltonian which has the form of two coupled qubits with tunable coupling between them. This Hamiltonian can be used for experimental tests on macroscopic entanglement and for implementing quantum gates.
We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multi-photon processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.
We demonstrate Josephson junction based double-balanced mixer and phase shifter circuits operating at 6-10 GHz, and integrate these components to implement both a monolithic amplitude/phase vector modulator and a quadrature mixer. The devices are actuated by flux signals, dissipate no power on chip, exhibit input saturation powers in excess of 1 nW, and provide cryogenic microwave modulation solutions for integrated control of superconducting qubits.
Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot (DQD) charge qubit strongly coupled to a high-impedance SQUID array resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation and Hahn-echo measurements …
We introduce a new entangling gate between two fixed-frequency qubits statically coupled via a microwave resonator bus which combines the following desirable qualities: all-microwave control, appreciable qubit separation for reduction of crosstalk and leakage errors, and the ability to function as a two-qubit conditional-phase gate. A fixed, always-on interaction is explicitly designed between higher energy (non-computational) states of two transmon qubits, and then a conditional-phase gate is `activated' on the otherwise unperturbed qubit subspace via a microwave drive. We implement this micr…
High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this work, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a $π$-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the …
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.
Although single and two-qubit gates are sufficient for universal quantum computation, single-shot three-qubit gates greatly simplify quantum error correction schemes and algorithms. We design fast, high-fidelity three-qubit entangling gates based on microwave pulses for transmon qubits coupled through a superconducting resonator. We show that when interqubit frequency differences are comparable to single-qubit anharmonicities, errors occur primarily through a single unwanted transition. This feature enables the design of fast three-qubit gates based on simple analytical pulse shapes that are e…
We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88 and quantum process tomography reveals a gate fidelity of 81%.
We present an analytical and comprehensive description of the quantum dynamics of a microwave resonantly driven superconducting phase qubit coupled to a microscopic two-level system (TLS), covering a wide range of the external microwave field strength. Our model predicts several interesting phenomena in such an ac driven four-level bipartite system including anomalous Rabi oscillations, high-contrast beatings of Rabi oscillations, and extraordinary two-photon transitions. Our experimental results in a coupled qubit-TLS system agree quantitatively very well with the predictions of the theoretic…
We propose a procedure for transferring the state a microwave qubit via a transmission line from one resonator to another resonator, with a theoretical efficiency arbitrarily close to 100%. The emission and capture of the microwave energy is performed using tunable couplers, whose transmission coefficients vary in time. Using the superconducting phase qubit technology and tunable couplers with maximum coupling of 100 MHz, the procedure with theoretical efficiency $η=0.999$ requires a duration of about 400 ns (excluding propagation time) and an ON/OFF ratio of 45. The procedure may also be used…
We study the quantum operation of coupled superconducting flux qubits under a microwave irradiation. The flux qubits can be described as magnetic dipole moments in the limit of weak microwave field amplitude consistent with usual experimental situations. With the Hamiltonian for coupled qubits under a microwave field, we show that a strong coupling enables to realize the high performance controlled-NOT gate operation. For practical quantum computing we analyze the effect of microwave on switching function of phase-coupled qubits.
We analyze the dynamics of a continuously observed, damped, microwave driven solid state charge qubit. The qubit consists of a single electron in a double well potential, coupled to an oscillating electric field, and which is continuously observed by a nearby point contact electrometer. The microwave field induces transitions between the qubit eigenstates, which have a profound effect on the detector output current. We show that useful information about the qubit dynamics, such as dephasing and relaxation rates, and the Rabi frequency, can be extracted from the DC detector conductance and the …
Superconducting circuits and microwave signals are good candidates to realize quantum networks, which are the backbone of quantum computers. We have realized a quantum node based on a 3D microwave superconducting cavity parametrically coupled to a transmission line by a Josephson ring modulator. We first demonstrate the time-controlled capture, storage and retrieval of an optimally shaped propagating microwave field, with an efficiency as high as 80%. We then demonstrate a second essential ability, which is the timed-controlled generation of an entangled state distributed between the node and …
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.
The quantum state of a flux qubit was successfully pulse-controlled by using a resonant microwave. We observed Ramsey fringes by applying a pair of phase-shifted pi/2 microwave pulses without introducing detuning. With this method, the qubit state can be rotated on an arbitrary axis in the x-y plane of the Bloch sphere in a rotating frame. We obtained a qubit signal from a coherent oscillation with an angular velocity of up to 2pi*11.4 Grad/s. In combination with Rabi pulses, this method enables us to achieve full control of single qubit operation. It also offers the possibility of orders of m…
The dynamics of a superconducting quantum point contact biased at subgap voltages is shown to be strongly affected by a microwave electromagnetic field. Interference among a sequence of temporally localized, microwave-induced Landau-Zener transitions between current carrying Andreev levels results in energy absorption and in an increase of the subgap current by several orders of magnitude. The contact is an interferometer in the sense that the current is an oscillatory function of the inverse bias voltage. Possible applications to Andreev-level spectroscopy and microwave detection are discusse…
Superconducting circuits offer a scalable platform for the construction of large-scale quantum networks where information can be encoded in multiple temporal modes of propagating microwaves. Characterization of such microwave signals with a method extendable to an arbitrary number of temporal modes with a single detector and demonstration of their phase-robust nature are of great interest. Here we show the on-demand generation and Wigner tomography of a microwave time-bin qubit with superconducting circuit quantum electrodynamics architecture. We perform the tomography with a single heterodyne…
We present the first observation of Landau-Zener-Stückelberg (LZS) interference of the dressed states arising from an artificial atom, a superconducting phase qubit, interacting with a microwave field. The dependence of LZS interference fringes on various external parameters and the initial state of the qubit agrees quantitatively very well with the theoretical prediction. Such LZS interferometry between the dressed states enables us to control the quantum states of a tetrapartite solid-state system with ease, demonstrating the feasibility of implementing efficient multipartite quantum logic g…
A localized qubit entangled with a propagating quantum field is well suited to study non-local aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero, one and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entang…
Large-scale quantum computers must be built upon quantum bits that are both highly coherent and locally controllable. We demonstrate the quantum control of the electron and the nuclear spin of a single 31P atom in silicon, using a continuous microwave magnetic field together with nanoscale electrostatic gates. The qubits are tuned into resonance with the microwave field by a local change in electric field, which induces a Stark shift of the qubit energies. This method, known as A-gate control, preserves the excellent coherence times and gate fidelities of isolated spins, and can be extended to…
A challenge in building large-scale superconducting quantum processors is to find the right balance between coherence, qubit addressability, qubit-qubit coupling strength, circuit complexity and the number of required control lines. Leading all-microwave approaches for coupling two qubits require comparatively few control lines and benefit from high coherence but suffer from frequency crowding and limited addressability in multi-qubit settings. Here, we overcome these limitations by realizing an all-microwave controlled-phase gate between two transversely coupled transmon qubits which are far …
Carbon nanotube quantum dots allow accurate control of electron charge, spin and valley degrees of freedom in a material which is atomically perfect and can be grown isotopically pure. These properties underlie the unique potential of carbon nanotubes for quantum information processing, but developing nanotube charge, spin, or spin-valley qubits requires efficient readout techniques as well as understanding and extending quantum coherence in these devices. Here, we report on microwave spectroscopy of a carbon nanotube charge qubit in which quantum information is encoded in the spatial position…
Superconducting flux qubits are considered to investigate macroscopic many-qubit interactions. Many-qubit states based on current states can be manipulated through the current-phase relation in each superconducting loop. For flux qubit systems comprised of $N$ qubit loops, a general expression of low energy Hamiltonian is presented in terms of low energy levels of qubits and macroscopic quantum tunnelings between the many-qubit states. Many-qubit interactions classified by {\em Ising type- or tunnel-}exchange interactions can be observable experimentally. Flux qubit systems can provide various…
Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Our results provide evidence that this entanglement transfer by dissipation is feasible yielding to a steady-state amount of entanglement in the bipartite quantum syste…
The superconducting fluxonium circuit is an artificial atom with a strongly anharmonic spectrum: when biased at a half flux quantum, the lowest qubit transition is an order of magnitude smaller in frequency than those to higher levels. Similar to conventional atomic systems, such a frequency separation between the computational and noncomputational subspaces allows independent optimizations of the qubit coherence and two-qubit interactions. Here we describe a controlled-Z gate for two fluxoniums connected either capacitively or inductively, with qubit transitions fixed near 500 MHz. The gate i…
We investigate the propagation of microwave photons in a one-dimensional open waveguide interacting with a number of artificial atoms (qubits). Within the formalism of projection operators and non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme for the calculation of the transmission and reflection factors of the microwave signal in a waveguide which contains an arbitrary number \emph{N} of non-interacting qubits. We considered in detail the resonances and photon mediated entanglement for two and three qubits in a chain. We showed that in non Markovian case the reso…
We describe and characterize a microwave setup to probe the Andreev levels of a superconducting atomic contact. The contact is part of a superconducting loop inductively coupled to a superconducting coplanar resonator. By monitoring the resonator reflection coefficient close to its resonance frequency as a function of both flux through the loop and frequency of a second tone we perform spectroscopy of the transition between two Andreev levels of highly transmitting channels of the contact. The results indicate how to perform coherent manipulation of these states.
We propose and analyze an interface between a topological qubit and a superconducting flux qubit. In our scheme, the interaction between Majorana fermions in a topological insulator is coherently controlled by a superconducting phase that depends on the quantum state of the flux qubit. A controlled phase gate, achieved by pulsing this interaction on and off, can transfer quantum information between the topological qubit and the superconducting qubit.
Parametric control of a superconducting flux qubit has been achieved by using two-frequency microwave pulses. We have observed Rabi oscillations stemming from parametric transitions between the qubit states when the sum of the two microwave frequencies or the difference between them matches the qubit Larmor frequency. We have also observed multi-photon Rabi oscillations corresponding to one- to four-photon resonances by applying single-frequency microwave pulses. The parametric control demonstrated in this work widens the frequency range of microwaves for controlling the qubit and offers a hig…
Superconducting spin qubits, also known as Andreev spin qubits, promise to combine the benefits of superconducting qubits and spin qubits defined in quantum dots. While most approaches to control these qubits rely on controlling the spin degree of freedom via the supercurrent, superconducting spin qubits can also be coupled to each other via the superconductor to implement two-qubit quantum gates. We theoretically investigate the interaction between superconducting spin qubits in the weak tunneling regime and concentrate on the effect of spin-orbit interaction (SOI), which can be large in semi…
The study of quantum heat transport in superconducting circuits is significant for further understanding the connection between quantum mechanics and thermodynamics, and for possible applications for quantum information. The first experimental realisations of devices demonstrating photonic heat transport mediated by a qubit have already been designed and measured. Motivated by the analysis of such experimental results, and for future experimental designs, we numerically evaluate the photonic heat transport of qubit-resonator devices in the linear circuit regime through electromagnetic simulati…
Silicon-Germanium (SiGe) is a material that possesses a multitude of applications ranging from transistors to eletro-optical modulators and quantum dots. The diverse properties of SiGe also make it attractive to implementations involving superconducting quantum computing. Here we demonstrate the fabrication of transmon quantum bits on SiGe layers and investigate the microwave loss properties of SiGe at cryogenic temperatures and single photon microwave powers. We find relaxation times of up to 100 $μ$s, corresponding to a quality factor Q above 4 M for large pad transmons. The high Q values ob…
In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in…
We propose a superconducting qubit design, based on a tunable RF-SQUID and nanowire kinetic inductors, which has a dramatically reduced transverse electromagnetic coupling to its environment, so that its excited state should be metastable. If electromagnetic interactions are in fact responsible for the current excited-state decay rates of superconducting qubits, this design should result in a qubit lifetime orders of magnitude longer than currently possible. Furthermore, since accurate manipulation and readout of superconducting qubits is currently limited by spontaneous decay, much higher fid…
Superconducting microwave circuits based on coplanar waveguides (CPW) are susceptible to parasitic slotline modes which can lead to loss and decoherence. We motivate the use of superconducting airbridges as a reliable method for preventing the propagation of these modes. We describe the fabrication of these airbridges on superconducting resonators, which we use to measure the loss due to placing airbridges over CPW lines. We find that the additional loss at single photon levels is small, and decreases at higher drive powers.
We describe a scheme for the efficient generation of microwave photon pairs by parametric downconversion in a superconducting transmission line resonator coupled to a Cooper pair box serving as an artificial atom. By properly tuning the first three levels with respect to the cavity modes, the down-conversion probability may become higher than in the most efficient schemes for optical photons. We show this by numerically simulating the dissipative quantum dynamics of the coupled cavity-box system and discuss the effects of dephasing and relaxation. The setup analyzed here might form the basis f…
We report on radio-frequency measurements of the charge-phase qubit being under continuous microwave irradiation in the state of weak coupling to a radio-frequency tank circuit. We studied the rf impedance dependence on the two important parameters such as power of microwave irradiation whose frequency is close to the gap between the two lowest qubit energy levels, and temperature of the internal heat bath. We have found that backaction effects of the qubit on the rf tank, and vice versa, tank on the qubit, lead to a negative as well as a positive real part of the qubit impedance Re$Z(ω)$ seen…
We present a practical design and implementation of a broadband sample holder suitable for microwave experiments with superconducting integrated circuits at millikelvin temperatures. Proposed design can be easily integrated in standard dilution cryostats, has flat pass band response in a frequency range from 0 to 32 GHz, allowing the RF testing of the samples with substrate size up to 4x4 mm. The parasitic higher modes interference in the holder structure is analyzed and prevented via design considerations. The developed setup can be used for characterization of superconducting parametric ampl…
The quantum degeneracy point approach [D. Vion et al., Science 296, 886 (2002)] effectively protects superconducting qubits from low-frequency noise that couples with the qubits as transverse noise. However, low-frequency noise in superconducting qubits can originate from various mechanisms and can couple with the qubits either as transverse or as longitudinal noise. Here, we present a quantum circuit containing a universal quantum degeneracy point that protects an encoded qubit from arbitrary low-frequency noise. We further show that universal quantum logic gates can be performed on the encod…
A normal metal - superconductor hybrid single-electron trap with tunable barrier is utilized as a tool for spectrum analysis at the extremely low signal levels, using only well filtered cryogenic microwave background as a photon source in the frequency range from about 50 to 210 GHz. We probe millimeter wave propagation in two superconducting systems: a Josephson junction array around its plasma frequency, and a superconducting titanium film in the limit when the photon energies are larger than the superconducting energy gap. This regime is relevant for improving the performance of cryogenic q…
The statistics photons in the resonance fluorescence of a qubit excited by microwave and radio-frequency (RF) fields have been studied. It has been established that the coherent dissipative dynamics of the qubit with allowance for multiphoton emission and absorption of RF photons in each act of emission and absorption of a microwave photon results in periodic alternation of photon bunching and antibunching. It has been shown that periodically varying statistics photons can be smoothly transformed to the purely sub-Poisson statistics by varying the parameters of the RF field. The conditions for…
We present an approach to achieve efficient single-photon frequency conversion in the microwave domain based on coherent control in superconducting quantum circuits, which consist of a driven artificial atom coupled to a semi-infinite transmission line. Using the full quantum-mechanical method, we analyze the single-photon scattering process in this system and find that single-photon frequency up- or down-conversion with efficiency close to unity can be achieved by adjusting the parameters of the control field applied to the artificial atom. We further show that our approach is experimentally …
Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters .
Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasi-probability distr…
We present a theoretical scheme that allows to perform a universal set of holonomic gates on a two qubit register, formed by a $^{13}$C nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of $^{13}$C atoms allows to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.
Low-frequency noise can induce serious decoherence in superconducting qubits. Due to its diverse physical origin, such noise can couple with the qubits either as transverse or as longitudinal noise. Here, we present a universal quantum degeneracy point approach that can protect an encoded qubit from arbitrary low-frequency noise. We further show that universal quantum logic gates can be performed on the encoded qubits with high fidelity. The proposed scheme can be readily implemented with superconducting flux qubits or with a qubit coupling with a superconducting resonator. Meanwhile, the sche…
We theoretically study a circuit quantum electrodynamics (QED) architecture with superconducting flux qubits. The qubit is coupled to the transmission line resonator by an ac current originating from the current mode of the resonator. Ultrastrong coupling can be obtained by varying the capacitance between the qubit and the resonator. We propose a scalable design where the two-qubit coupling can be achieved.
Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). They constitute a promising approach to quantum information processing [1, 2], complementary to superconducting qubits [3]. Typically, semiconductor qubit-qubit coupling is short range [1, 2, 4, 5], effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle, which represents a significant constraint towards scaling to reach dense 1D or 2D arrays of QD qubits. Following the success of circuit quantum eletrodynamics [6], …
Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional single-qubit gate. Supplemented with one braiding operation, this gate allows to perform arbitrary single-qubit operations.
We have studied interactions between two capacitively coupled GaAs/AlGaAs few-electron double quantum dots. Each double quantum dot defines a tunable two-level system, or qubit, in which a single excess electron occupies either the ground state of one dot or the other. Applying microwave radiation we resonantly drive transitions between states and non-invasively measure occupancy changes using proximal quantum point contact charge detectors. The level structure of the interacting two-qubit system is probed by driving it at a fixed microwave frequency whilst varying the energy detuning of both …
We study quantum critical phenomena in the microwave scattering of the subohmic spin-boson system, which exhibits a quantum phase transition at a critical system-reservoir coupling. By relating the reflection coefficient of a microwave with the dynamic susceptibility of the subohmic spin-boson system, we clarify the appearance of quantum critical phenomena in microwave scattering. Further, we propose experimental setups to realize the subohmic spin-boson system in a superconducting circuit composed of a charge qubit and a dissipative transmission line.
We consider the influence of nonradiative damping of qubits on the microwave transport of photons, propagating in an open one-dimensional microstrip line. Within the framework of the formalism of a non-Hermitian Hamiltonian we obtained the expressions for the transmission and reflection coefficients for two qubits which explicitly account for the indirect interaction between qubits due to nonradiative decay into common bath. It is shown that this interaction leads to the results that are significantly different from those already known
We propose a platform for universal quantum computation that uses conventional $s$-wave superconducting leads to address a topological qubit stored in spatially separated Majorana bound states in a multi-terminal topological superconductor island. Both the manipulation and read-out of this "Majorana superconducting qubit" are realized by tunnel couplings between Majorana bound states and the superconducting leads. The ability of turning on and off tunnel couplings on-demand by local gates enables individual qubit addressability while avoiding cross-talk errors. By combining the scalability of …
We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectrosc…
