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.
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…
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…
From a physicist's standpoint, the most interesting part of quantum computing research may well be the possibility to probe the boundary between the quantum and the classical worlds. The more macroscopic are the structures involved, the better. So far, the most "macroscopic" qubit prototypes that have been studied in the laboratory are certain kinds of superconducting qubits. To get a feeling for how macroscopic these systems can be, the states of flux qubits which are brought in a quantum superposition corresponds to currents composed of as much as 10^5-10^6 electrons flowing in opposite dire…
A general method for directly measuring the low-frequency flux noise (below 10 Hz) in compound Josephson junction superconducting flux qubits has been used to study a series of 85 devices of varying design. The variation in flux noise across sets of qubits with identical designs was observed to be small. However, the levels of flux noise systematically varied between qubit designs with strong dependence upon qubit wiring length and wiring width. Furthermore, qubits fabricated above a superconducting ground plane yielded lower noise than qubits without such a layer. These results support the hy…
We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes even dominant over the single-qubit tunneling process in the states of two qubits. It is shown that due to the two-qubit tunneling processes both the ground state and excited state of the coupled flux qubits can be…
We consider a superconducting persistent-current qubit consisting of a three-junction superconducting loop in an applied magnetic field. We show that by choosing the field, Josephson couplings, and offset charges suitably, we can perfectly suppress the tunneling between two oppositely directed states of circulating current, leading to a vanishing of the splitting between the two qubit states. The suppression arises for interference between tunneling along different paths, and is analogous to that predicted previously for magnetic particles with half-integer spin.
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing. However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome. We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic pi junction which has a metallic contact and a normal Josephson junction with an insulating barrier. Thus, a quantum coherent two-level state is formed without an external magnetic field. This feature …
For successful realization of a quantum computer, its building blocks (qubits) should be simultaneously scalable and sufficiently protected from environmental noise. Recently, a novel approach to the protection of superconducting qubits has been proposed. The idea is to prevent errors at the "hardware" level, by building a fault-free (topologically protected) logical qubit from "faulty" physical qubits with properly engineered interactions between them. It has been predicted that the decoupling of a protected logical qubit from local noises would grow exponentially with the number of physical …
We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization of the superconducting flux and charge qubits. Then, by making use of a dressed state approach we describe the qubits' spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a DC SQUID in the inductive mode.
Entangled multi-qubit states may be generated through a dispersive collective QND measurement of superconducting qubits coupled to a microwave transmission line resonator. Using the quantum trajectory approach, we analyze the stochastic measurement traces that would be observed in experiments. We illustrate the synthesis of three-qubit W- and GHZ-states, and we analyze how the fidelity and the entanglement evolve in time during the measurement. We discuss the influence of decoherence and relaxation, as well as of imperfect control over experimental parameters. We show that the desired states c…
We study theoretically how decoherence affects superposition states composed of entangled states in inductively coupled two superconducting flux-qubits. We discover that the quantum fluctuation of an observable in a coupled flux-qubit system plays a crucial role in decoherence when the expectation value of the observable is zero. This examplifies that decoherence can be also induced through a quantum mechanically higher-order effect. We also find that there exists a decoherence free subspace for the environment coupled via a charge degree of freedom of the qubit system.
We present a hybrid semiconductor-based superconducting qubit device which remains coherent at magnetic fields up to 1 T. The qubit transition frequency exhibits periodic oscillations with magnetic field, consistent with interference effects due to the magnetic flux threading the cross section of the proximitized semiconductor nanowire junction. As induced superconductivity revives, additional coherent modes emerge at high magnetic fields, which we attribute to the interaction of the qubit and low-energy Andreev states.
We propose a scheme to couple two superconducting charge or flux qubits biased at their symmetry points with unequal energy splittings. Modulating the coupling constant between two qubits at the sum or difference of their two frequencies allows to bring them into resonance in the rotating frame. Switching on and off the modulation amounts to switching on and off the coupling which can be realized at nanosecond speed. We discuss various physical implementations of this idea, and find that our scheme can lead to rapid operation of a two-qubit gate.
We study fundamental limitations on the energy relaxation rate of a superconducting charge qubit with a large-gap Cooper-pair box, $Δ_b > Δ_r$. At a sufficiently large mismatch between the gap energies in the box $Δ_b$ and in the reservoir $Δ_r$,"quasiparticle poisoning" becomes ineffective even in the presence of nonequilibrium quasiparticles in the reservoir. The qubit relaxation still may occur due to higher-order (Andreev) processes. In this paper we evaluate the qubit energy relaxation rate due to Andreev processes.
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…
We propose to use an ancilla fluxonium qubit to interact with a Majorana qubit hosted by a topological one-dimensional wire. The coupling is obtained using the Majorana qubit-controlled 4 pi Josephson effect to flux bias the fluxonium qubit. We demonstrate how this coupling can be used to sensitively identify the topological superconductivity, to measure the state of the Majorana qubit, to construct 2-qubit operations, and to implement quantum memories with the topological protection.
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 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 analyze the crosstalk error mechanism in measurement of two capacitively coupled superconducting flux-biased phase qubits. The damped oscillations of the superconducting phase after the measurement of the first qubit may significantly excite the second qubit, leading to its measurement error. The first qubit, which is highly excited after the measurement, is described classically. The second qubit is treated both classically and quantum-mechanically. The results of the analysis are used to find the upper limit for the coupling capacitance (thus limiting the frequency of two-qubit operations…
Solid state qubits realized in superconducting circuits are potentially extremely scalable. However, strong decoherence may be transferred to the qubits by various elements of the circuits that couple individual qubits, particularly when coupling is implemented over long distances. We propose here an encoding that provides full protection against errors originating from these coupling elements, for a chain of superconducting qubits with a nearest neighbor anisotropic XY-interaction. The encoding is also seen to provide partial protection against errors deriving from general electronic noise.
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 present a new readout method for a superconducting flux qubit, based on the measurement of the Josephson inductance of a superconducting quantum interference device that is inductively coupled to the qubit. The intrinsic flux detection efficiency and back-action are suitable for a fast and nondestructive determination of the quantum state of the qubit, as needed for readout of multiple qubits in a quantum computer. We performed spectroscopy of a flux qubit and we measured relaxation times of the order of 80 $μs$.
We introduce a frequency-multiplexed readout scheme for superconducting phase qubits. Using a quantum circuit with four phase qubits, we couple each qubit to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four qubits can be read out simultaneously using frequency multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple qubits, a significant advantage for scali…
We propose an experimental scheme to simulate the dynamical quantum Hall effect and the related interaction-induced topological transition with a superconducting-qubit array. We show that a one-dimensional Heisenberg model with tunable parameters can be realized in an array of superconducting qubits. The quantized plateaus, which is a feature of the dynamical quantum Hall effect, will emerge in the Berry curvature of the superconducting qubits as a function of the coupling strength between nearest neighbor qubits. We numerically calculate the Berry curvatures of two-, four- and six-qubit array…
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 present a method for measuring the internal state of a superconducting qubit inside an on-chip microwave resonator. We show that one qubit state can be associated with the generation of an increasingly large cavity coherent field, while the other remains associated with the vacuum. By measuring the outgoing resonator field with conventional devices, an efficient single-shot QND-like qubit readout can be achieved, enabling a high-fidelity measurement in the spirit of the electron-shelving technique for trapped ions. We expect that the proposed ideas can be adapted to different superconductin…
We study a voltage-controlled version of the superconducting flux qubit [Chiorescu et al., Science 299, 1869 (2003)] and show that full control of qubit rotations on the entire Bloch sphere can be achieved. Circuit graph theory is used to study a setup where voltage sources are attached to the two superconducting islands formed between the three Josephson junctions in the flux qubit. Applying a voltage allows qubit rotations about the y axis, in addition to pure x and z rotations obtained in the absence of applied voltages. The orientation and magnitude of the rotation axis on the Bloch sphere…
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled DC superconducting quantum interference device (DC-SQUID). We determine the response function of the DC-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral d…
We design theoretically a new device to realize the general quantum storage based on dcSQUID charge qubits. The distinct advantages of our scheme are analyzed in comparison with existing storage scenarios. More arrestingly, the controllable XY-model spin interaction has been realized for the first time in superconducting qubits, which may have more potential applications besides those in quantum information processing. The experimental feasibility is also elaborated.
We present a robust method, based only on measurements, to produce superconducting cluster states. The measurement of the current of a few parallel Josephson-junction qubits realizes a novel type of quantum-state selector. Using this selector, one can produce various quantum entangled states and also realize a controlled-NOT gate without requiring an exact control of the interqubit interactions. In particular, cluster states for quantum computation could be produced with only single-qubit measurements.
We study the response of a magnetic-field-driven superconducting qubit strongly coupled to a superconducting coplanar waveguide resonator. We observed a strong amplification/damping of a probing signal at different resonance points corresponding to a one and two-photon emission/absorption. The sign of the detuning between the qubit frequency and the probe determines whether amplification or damping is observed. The larger blue detuned driving leads to two-photon lasing while the larger red detuning cools the resonator. Our experimental results are in good agreement with the theoretical model o…
Extending the qubit coherence times is a crucial task in building quantum information processing devices. In the three-dimensional cavity implementations of circuit QED, the coherence of superconducting qubits was improved dramatically due to cutting the losses associated with the photon emission. Next frontier in improving the coherence includes the mitigation of the adverse effects of superconducting quasiparticles. In these lectures, we review the basics of the quasiparticles dynamics, their interaction with the qubit degree of freedom, their contribution to the qubit relaxation rates, and …
We combine the ideas of qubit encoding and dispersive dynamics to enable robust and easy quantum information processing (QIP) on paired superconducting charge boxes sharing a common bias lead. We establish a decoherence free subspace on these and introduce universal gates by dispersive interaction with a LC resonator and inductive couplings between the encoded qubits. These gates preserve the code space and only require the established local symmetry and the control of the voltage bias.
Significant improvements in superconducting qubit coherence times have been achieved recently with three-dimensional microwave waveguide cavities coupled to transmon qubits. While many of the measurements in this direction have utilized superconducting aluminum cavities, other recent work has involved qubits coupled to copper cavities with coherence times approaching 0.1 ms. The copper provides a good path for thermalizing the cavity walls and qubit chip, although the substantial cavity loss makes conventional dispersive qubit measurements challenging. We are exploring various approaches for 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 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.
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.
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 evaluate the rates of energy and phase relaxation of a superconducting qubit caused by stray photons with energy exceeding the threshold for breaking a Cooper pair. All channels of relaxation within this mechanism are associated with the change in the charge parity of the qubit, enabling the separation of the photon-assisted processes from other contributions to the relaxation rates. Among the signatures of the new mechanism is the same order of rates of the transitions in which a qubit looses or gains energy.
This paper gives an introduction to the physics and principles of operation of quantized superconducting electrical circuits for quantum information processing.
We analyze the dynamics of a superconducting qubit and the phenomenon of multiorder Rabi oscillations in the presence of a time-modulated external field. Such a field is also presented as a bichromatic field consisting of two spectral components, which are symmetrically detuned from the qubit resonance frequency. This approach leads to obtaining qualitative quantum effects beyond those for the case of monochromatic excitation of qubits. We calculate Floquet states and quasienergies of the composite system "superconducting qubit plus time-modulated field" for various resonant regimes. We analyz…
We demonstrate the ability of an epitaxial semiconductor-superconductor nanowire to serve as a field-effect switch to tune a superconducting cavity. Two superconducting gatemon qubits are coupled to the cavity, which acts as a quantum bus. Using a gate voltage to control the superconducting switch yields up to a factor of 8 change in qubit-qubit coupling between the on and off states without detrimental effect on qubit coherence. High-bandwidth operation of the coupling switch on nanosecond timescales degrades qubit coherence.
In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 90 % can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The qubit coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.
We propose a realization of flux qubit based on the hybrid ferromagnetic-superconducting device where the flux bias is induced purely by vector potential of the vanishing magnetic field. We support our conclusions with theoretical analysis and self-consistent three-dimensional simulations for material specific parameters.
The quantum states of flux qubit is suggested to observe with the help of a new device, the superconducting differential double contour interferometer (DDCI). The flux qubit and the superconducting quantum interference device (DC-SQUID) are connected in the DDCI through the phase of the wave function rather than through magnetic flux. The critical current of DC-SQUID should change to the maximum value at the change of the flux qubit state thanks to this phase coupling. A large jump in the critical current and voltage enables to observe continuously the change in time the state of the flux qubi…
We show that an LC parametric transducer can be effectively used to monitor an adiabatic evolution of the superconducting flux qubit. We propose a new scheme to measure the qubit's state, which is a quantum nondemolition measurement. The scheme can be easily extended to a three-qubit system, and allows the reading out of the qubits' states while the system remains in the ground state. An implementation of the adiabatic quantum algorithm MAXCUT for three superconducting flux qubits is discussed.
Exploiting the intrinsic nonlinearity of superconducting Josephson junctions, we propose a scalable circuit with superconducting qubits (SCQs) which is very similar to the successful one now being used for trapped ions. The SCQs are coupled to the "vibrational" mode provided by a superconducting LC circuit or its equivalent (e.g., a SQUID). Both single-qubit rotations and qubit-LC-circuit couplings/decouplings can be controlled by the frequencies of the time-dependent magnetic fluxes. The circuit is scalable since the qubit-qubit interactions, mediated by the LC circuit, can be selectively per…
Single-shot readout experiments were performed on the two lowest-energy states of a superconducting qubit with three Josephson junctions embedded in a superconducting loop. We measured the qubit state via switching current Isw of a current-biased dc-SQUID, a quantum detector surrounding the qubit loop. The qubit signals were measured in a small Isw regime of the SQUID, typically less than 100 nA, where the Isw distribution is particularly narrow. The obtained single-shot data indicate that the qubit state is readout, through the flux generated by the qubit persistent-current, as energy eigenst…
We propose a method for switchable coupling between superconducting qubits using double resonance. The inter-qubit coupling is achieved by applying near-resonant oscillating fields to the two qubits. The deviation from resonance relaxes the criterion of strong driving fields while still allowing for a fully entangling two-qubit gate. This method avoids some of the shortcomings of previous proposals for switchable coupling. We discuss the possible application of our proposal to a pair of inductively coupled flux qubits, and we consider the extension to phase qubits.
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…
Detailed schemes are investigated for experimental verification of Quantum Zeno effect with a superconducting qubit. A superconducting qubit is affected by a dephasing noise whose spectrum is 1/f, and so the decay process of a superconducting qubit shows a naturally non-exponential behavior due to an infinite correlation time of 1/f noise. Since projective measurements can easily influence the decay dynamics having such non-exponential feature, a superconducting qubit is a promising system to observe Quantum Zeno effect. We have studied how a sequence of projective measurements can change the …
We use a scanning superconducting quantum interference device (SQUID) to image the magnetic flux produced by a superconducting device designed for quantum computing. The nanometer-scale SQUID-on-tip probe reveals the flow of superconducting current through the circuit as well as the locations of trapped magnetic flux. In particular, maps of current flowing out of a flux-control line in the vicinity of a qubit show how these elements are coupled, providing insight on how to optimize qubit control.
We propose a qubit-qubit coupling scheme for superconducting flux quantum bits (qubits), where a quantized Josephson junction resonator and microwave irradiation are utilized. The junction is used as a tunable inductance controlled by changing the bias current flowing through the junction, and thus the circuit works as a tunable resonator. This enables us to make any qubits interact with the resonator. Entanglement between two of many qubits whose level splittings satisfy some conditions, is formed by microwave irradiation causing a two-photon Rabi oscillation. Since the size of the resonator …
We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum non-demolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model to characterize the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly …
We show how the dynamical modulation of the qubit-field coupling strength in a circuit quantum electrodynamics architecture mimics the motion of the qubit at relativistic speeds. This allows us to propose a realistic experiment to detect microwave photons coming from simulated acceleration radiation. Moreover, by combining this technique with the dynamical Casimir physics, we enhance the toolbox for studying relativistic phenomena in quantum field theory with superconducting circuits.
We present a way to realize a 3-qubit quantum controlled-phase gate with superconducting qubit systems coupled to a cavity. This proposal does not require adjustment of the qubit level spacings or identical qubit-cavity coupling constants. Moreover, since only a resonant interaction is applied, the gate can be performed fast, within $\sim $ 10 nanosecond. This proposal is quite general, which can be applied to various types of superconducting qubits, atoms trapped in a cavity, or quantum dots coupled to a resonator.
An interaction-free measurement protocol is described for a quantum circuit consisting of a superconducting qubit and a read-out Josephson junction. By measuring the state of the qubit one can ascertain the presence of a current pulse through the circuit at a previous time without any energy exchange between the qubit and the pulse.
In order to integrate superconducting qubits with rapid-single-flux-quantum (RSFQ) control circuitry, it is necessary to develop a fabrication process that fulfills at the same time the requirements of both elements: low critical current density, very low operating temperature (tens of milliKelvin) and reduced dissipation on the qubit side; high operation frequency, large stability margins, low dissipated power on the RSFQ side. For this purpose, VTT has developed a fabrication process based on Nb trilayer technology, which allows the on-chip integration of superconducting qubits and RSFQ circ…
