Qubit Loop Research Articles

Superconducting flux qubit with ferromagnetic Josephson π-junction operating at zero magnetic field

Conventional superconducting flux qubits require the application of a precisely tuned magnetic field to set the operation point at half a flux quantum through the qubit loop, which complicates the on-chip integration of this type of device. It has been proposed that by inducing a π-phase shift in the superconducting order parameter using a precisely controlled nanoscale-thickness superconductor/ferromagnet/superconductor Josephson junction, commonly referred to as π-junction, it is possible to realize a flux qubit operating at zero magnetic flux. Here, we report the realization of a zero-flux-biased flux qubit based on three NbN/AlN/NbN Josephson junctions and a NbN/PdNi/NbN ferromagnetic π-junction. The qubit lifetime is in the microsecond range, which we argue is limited by quasiparticle excitations in the metallic ferromagnet layer. Our results pave the way for developing quantum coherent devices, including qubits and sensors, that utilize the interplay between ferromagnetism and superconductivity.

Tunable and switchable coupling between two superconducting resonators

We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit drive power and the dynamic range of the resonator input power.

Coherent Frequency Conversion in a Superconducting Artificial Atom with Two Internal Degrees of Freedom

By adding a large inductance in a dc-SQUID phase qubit loop, one decouples the junctions' dynamics and creates a superconducting artificial atom with two internal degrees of freedom. In addition to the usual symmetric plasma mode (s mode) which gives rise to the phase qubit, an antisymmetric mode (a mode) appears. These two modes can be described by two anharmonic oscillators with eigenstates |ns> and |na> for the s and a mode, respectively. We show that a strong nonlinear coupling between the modes leads to a large energy splitting between states |0s,1a> and |2s,0a>. Finally, coherent frequency conversion is observed via free oscillations between the states |0s,1a> and |2s,0a>.

Non-demolition Adiabatic Measurement of the Phase Qubit State

An adiabatic method for a single-shot non-demolition measurement of the phase qubit is suggested. The qubit is inductively coupled to a low-frequency resonator, which in turn is connected with a classical measurement device (phase meter). The resonator drives adiabatic oscillations of the supercurrent in the qubit loop. The back reaction of the qubit loop on the resonator depends on the qubit state. Measuring the phase shift of the resonator’s oscillations one can determine the state of the qubit. Numerical computations with available experimental parameters show that the phase difference between the two qubit states increases at a rate of 0.0044 rad/ns with the fidelity of about 0.9989 and the measurement time of about 100 ns. The fidelity of the measurement is estimated taking into consideration possible quantum transitions inside and outside the qubit manifold. An increase of the phase difference is possible but it is linked to a reduction of the fidelity. The requirements for the reproducibility of the qubit and resonator parameters are formulated.

Strong Coupling of a Cavity QED Architecture for a Current-biased Flux Qubit

We propose a scheme for a cavity quantum electrodynamics (QED) architecture for a current-biased superconducting flux qubit with three Josephson junctions. The qubit operation is performed by using a bias current coming from the current mode of the circuit resonator. If the phase differences of junctions are to be coupled with the bias current, the Josephson junctions should be arranged in an asymmetric way in the qubit loop. Our QED scheme provides a strong coupling between the flux qubit and the transmission line resonator of the circuit.

Remote sensing and control of phase qubits

We demonstrate a remote sensing design of phase qubits by separating the control and readout circuits from the qubit loop. This design improves measurement reliability because the control readout chip can be fabricated using more robust materials and can be reused to test different qubit chips. Typical qubit measurements such as Rabi oscillations, spectroscopy, and excited-state energy relaxation are presented.

Quantum loop programs

Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops and describe its computational process. The function computed by a quantum loop is defined, and a denotational semantics and a weakest precondition semantics of a quantum loop are given. The notions of termination and almost termination are proposed for quantum loops. This paper only consider the case of finite-dimensional state spaces. Necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented. A quantum loop is said to be (almost) terminating if it (almost) terminates on any input state. We show that a quantum loop is almost terminating if and only if it is uniformly almost terminating. It is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop (almost) terminating, provided that some dimension restriction is satisfied. Moreover, a representation of the function computed by a quantum loop is given in terms of finite summations of matrices. To illustrate the notions and results obtained in this paper, two simple classes of quantum loop programs, one qubit quantum loops, and two qubit quantum loops defined by controlled gates, are carefully examined, and to show their expressive power, quantum loops are applied in describing quantum walks.

Macroscopic many-qubit interactions in superconducting flux 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 artificial-spin systems to study many-body systems that cannot be found naturally.

Rf-SQUID qubit readout using a fast flux pulse

We report on development of a set-up for measuring intrawell dynamics in a Nb-basedrf-SQUID qubit described by a double well potential, by rapidly tilting the potential,allowing escape to the adjacent well with high probability for an excited state but lowprobability for the ground state. The rapid tilt of the double well potential is accomplishedvia a readout flux pulse inductively coupled to the qubit from a microstrip transmissionline on a separate chip suspended above the qubit chip. The readout pulse is analogous tothe current bias pulse used to readout phase qubits and hysteretic dc-SQUIDmagnetometers.The coupling between the transmission line and the qubit is carefully controlled via a windowin the ground plane between the signal conductor of the microstrip and the qubit loop. Sincethe high frequency transmission lines are on a separate chip, they can be independentlycharacterized and reused for different qubit samples. Clean flux pulses as short as 5 ns withrise times of 0.5 ns have been coupled to the qubit to measure escape rates higher than108 s−1, the lifetime of the excited state, and coherent oscillations between the ground and excitedstates within the same well.

Controllable Coupling of Superconducting Flux Qubits

We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.

Controllable Coupling between Flux Qubits

We propose an experimentally realizable method to control the coupling between two flux qubits. In our proposal, the bias fluxes are always fixed for these two inductively coupled qubits. The detuning of these two qubits can be initially chosen to be sufficiently large, so that their initial interbit coupling is almost negligible. When a variable frequency or time-dependent magnetic flux (TDMF) is applied to one of the qubits, a well-chosen frequency of the TDMF can be used to compensate the initial detuning and to couple two qubits. This proposed method avoids fast changes of either qubit frequencies or the amplitudes of the bias magnetic fluxes through the qubit loops, and also offers a remarkable way to implement any logic gate, as well as tomographically measure flux qubit states.

Superconducting qubit network with controllable nearest-neighbour coupling

We investigate the design and functionality of a network of loop-shaped charge qubits with switchable nearest-neighbour coupling. The qubit coupling is achieved by placing large Josephson junctions (JJs) at the intersections of the qubit loops and selectively applying bias currents. The network is scalable and makes it possible to perform a universal set of quantum gates. The coupling scheme allows gate operation at the charge degeneracy point of each qubit, and also applies to charge-phase qubits. Additional JJs included in the qubit loops for qubit readout can also be employed for qubit coupling.

Direct Josephson coupling between superconducting flux qubits

We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed.

Josephson junction qubit network with current-controlled interaction

We design and evaluate a scalable charge qubit chain network with controllable current-current coupling of neighbouring qubit loops via local dc-current gates. The network allows construction of general N-qubit gates. The proposed design is in line with current main stream experiments.

Method for direct observation of coherent quantum oscillations in a superconducting phase qubit: Computer simulations

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high quality resonant tank circuit, inductively coupled to the phase qubit. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase qubit). We explicitly account for the back action of a tank circuit and for the unpredictable nature of outcome of a single measurement. According to the results of our simulations the Rabi oscillations in MHz range can be detected using conventional NMR pulse Fourier technique.

Theory of weak continuous measurements in a strongly driven quantum bit

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector---namely, a spectrum of voltage fluctuations and an impedance---are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating-wave approximations. Back-action effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about the frequency and decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behavior as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.

Method for direct observation of coherent quantum oscillations in a superconducting phase qubit

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems were so far restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a new method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high quality resonant tank circuit, inductively coupled to the phase qubit. Detailed calculation for zero and non-zero temperature are made for the case of persistent current qubit. According to the estimates for dephasing and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in MHz range.