Contributors: Gustavsson, Simon, Bylander, Jonas, Yan, Fei, Forn-Díaz, Pol, Bolkhovsky, Vlad, Braje, Danielle, Fitch, George, Harrabi, Khalil, Lennon, Donna, Miloshi, Jovi

Date: 2012-01-30

qubit tunnel coupling is Δ = 5.4 . (b) Rabi frequency vs bias current ...qubit Rabi frequency. This opens an additional noise channel, and we find...qubit, to first order, is insensitive to flux noise . The qubit-resonator...qubit that is tunably coupled to a microwave resonator. We find that the...qubit Rabi frequency. This opens an additional noise channel, and we find...the qubit energy detuning ε , the first-order qubit-resonator coupling...qubit experiences an oscillating field mediated by off-resonant driving...by qubit energy relaxation. The dotted line marks the position for the...qubit tunably coupled to a harmonic oscillator...the qubit flux detuning defined as = Φ + Φ 0 / 2 and Φ 0 = h / 2 e . The qub... the qubit and the oscillator. The qubit state is encoded in currents ...qubit experiences an oscillating field mediated by off-resonant driving...the qubit, appearing already at moderate qubit-resonator coupling g 1 ...qubit loop (blue arrow), while the mode of the harmonic oscillator is ...low-frequency noise in the coupling parameter causes a reduction of the...of qubit A, measured vs at = 0 . The driving field seen by the qubit contains...qubit loop). The resonator frequency is around 2.3 and depends only weakly...qubit and the oscillator. The qubit state is encoded in currents circulating...qubit and the harmonic oscillator. In addition, the two-photon qubit (... the qubit and the harmonic oscillator. In addition, the two-photon qubit...qubit tunnel coupling is Δ = 5.4 . (b) Rabi frequency vs bias current ...qubit at large frequency detuning from the resonator while still staying...driving the qubit, appearing already at moderate qubit-resonator coupling...qubit frequency [see...frequency of qubit A, measured vs at = 0 . The driving field seen by the...frequencies corresponding to the sum of the qubit and resonator frequencies...oscillations to decaying sinusoids, a few examples of Rabi traces for ... We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.

Contributors: Korotkov, Alexander N.

Date: 2010-04-01

oscillations via low-frequency noise correlation. The idea is to measure...oscillations....frequency Ω coinciding with the Rabi frequency Ω R ....qubit Rabi oscillations are known to be non-decaying (though with a fluctuating...zero-frequency detector noise S a a 0 and cross-noise S a b 0 on the phase...qubit Rabi oscillations are known to be non-decaying (though with a fluctuating...qubits....qubit by two detectors, biased stroboscopically at the Rabi frequency....qubit is continuously monitored in the weak-coupling regime. In this paper...low-frequency noise depends on the relative phase between the two combs...qubit measured by two QPC detectors, which are biased by combs of short...qubit by two detectors, biased stroboscopically at the Rabi frequency. ... The qubit Rabi oscillations are known to be non-decaying (though with a fluctuating phase) if the qubit is continuously monitored in the weak-coupling regime. In this paper we propose an experiment to demonstrate these persistent Rabi oscillations via low-frequency noise correlation. The idea is to measure a qubit by two detectors, biased stroboscopically at the Rabi frequency. The low-frequency noise depends on the relative phase between the two combs of biasing pulses, with a strong increase of telegraph noise in both detectors for the in-phase or anti-phase combs. This happens because of self-synchronization between the persistent Rabi oscillations and measurement pulses. Almost perfect correlation of the noise in the two detectors for the in-phase regime and almost perfect anticorrelation for the anti-phase regime indicates a presence of synchronized persistent Rabi oscillations. The experiment can be realized with semiconductor or superconductor qubits.

Contributors: Strand, J. D., Ware, Matthew, Beaudoin, Félix, Ohki, T. A., Johnson, B. R., Blais, Alexandre, Plourde, B. L. T.

Date: 2013-01-03

qubit. The qubit contains a substantial asymmetry between its Josephson...combined qubit-resonator system, showing first-order red sideband transition...qubits. The terminations of the flux-bias lines for both qubits are visible...qubit and resonator.... of the qubit and cavity and roughly corresponds to κ + γ 1 / 2 , where...the qubits. The terminations of the flux-bias lines for both qubits are... qubits from the flux-bias lines....frequency. The sideband transitions are driven with a magnetic flux signal...oscillations can be explained by the separately measured loss of the qubit...frequency-modulated transmon qubit. The qubit contains a substantial asymmetry...qubit. This modulates the qubit splitting at a frequency near the detuning... qubit energy levels with negligible Joule heating of the refrigerator...qubit. This modulates the qubit splitting at a frequency near the detuning...qubit and resonator frequencies, leading to rates up to 85 MHz for exchanging...oscillations as a function of pulse duration vs. flux-drive frequency....of qubit-cavity layout and signal paths.... Qubit-state measurements were performed in the high-power limit . The qubits, labeled Q1 and Q2, were designed to be identical, with mutual...oscillation frequency Ω / 2 π extracted from the experimental linecuts...oscillation frequency from Eq. ( eq:H:t)....oscillations vs. drive frequency. Vertical white lines running through...qubits...oscillation frequency vs. flux drive amplitude (lower horizontal axis)...qubit and resonator frequencies, leading to rates up to 85 MHz for exchanging ... We demonstrate rapid, first-order sideband transitions between a superconducting resonator and a frequency-modulated transmon qubit. The qubit contains a substantial asymmetry between its Josephson junctions leading to a linear portion of the energy band near the resonator frequency. The sideband transitions are driven with a magnetic flux signal of a few hundred MHz coupled to the qubit. This modulates the qubit splitting at a frequency near the detuning between the dressed qubit and resonator frequencies, leading to rates up to 85 MHz for exchanging quanta between the qubit and resonator.

Contributors: Averin, Dmitri V., Rabenstein, Kristian, Semenov, Vasili K.

Date: 2005-10-27

qubit density matrix is nearly diagonal in the σ z basis, and the measurement...qubit which suppresses the effect of back-action dephasing on the qubit...qubit. The fluxons are periodically injected into the JTL by the generator...oscillations. The fluxon injection frequency f is matched to the qubit...oscillation frequency Δ : f ≃ Δ / π , so that the individual acts of measurement...Qubits...qubit oscillation frequency Δ : f ≃ Δ / π , so that the individual acts...measured qubit. The fluxons are periodically injected into the JTL by ...oscillation dynamics. ... We suggest a new type of the magnetic flux detector which can be optimized with respect to the measurement back-action, e.g. for the situation of quantum measurements. The detector is based on manipulation of ballistic motion of individual fluxons in a Josephson transmission line (JTL), with the output information contained in either probabilities of fluxon transmission/reflection, or time delay associated with the fluxon propagation through the JTL. We calculate the detector characteristics of the JTL and derive equations for conditional evolution of the measured system both in the transmission/reflection and the time-delay regimes. Combination of the quantum-limited detection with control over individual fluxons should make the JTL detector suitable for implementation of non-trivial quantum measurement strategies, including conditional measurements and feedback control schemes.

Contributors: Jerger, Markus, Poletto, Stefano, Macha, Pascal, Hübner, Uwe, Il'ichev, Evgeni, Ustinov, Alexey V.

Date: 2012-05-29

of the qubit and resonator. We demonstrate FDM by measuring the maximum...and qubit, ω q and ω r are the angular resonance frequencies of the qubit...oscillations ...qubit, ω q and ω r are the angular resonance frequencies of the qubit ...Qubits...qubits using a frequency division multiplexing technique is demonstrated...qubits. Consequently, scaling up superconducting qubit circuits is no ...qubits far detuned from the resonances. (b) FDM readout of six flux qubits... qubits....qubits involved in the measurement. Here, we present a readout scheme ...three qubits. Left plots: Rabi oscillations at several powers; traces ...frequencies. The local oscillator inputs of both mixers are fed from the...qubits....oscillation frequency versus power of the excitation tone; the error bars...frequency matches the transition between their ground and excited states...of qubits #2, 3 and 5. The qubit manipulation microwave excites qubits... qubit manipulation signal is generated by a single microwave source for...qubits on a chip....qubits taken into account. The readout frequency of device #3 is shown...qubits using a frequency division multiplexing technique is demonstrated...anti-crossings between the qubit and the corresponding resonator. There...long as the qubit remains far detuned from the resonator. The amplitude...qubit, qubit register, dispersive readout, frequency division multiplexing...three qubits. Here, we used individual microwave excitations for every qub...qubits. We discuss how this technique can be scaled up to read out hundreds...oscillations at three different powers for all qubits. The measured linear...qubit, qubit register, dispersive readout, frequency division multiplexing...qubit, the instantaneous dispersive shift of the center frequency of the...qubits #2, 3 and 5. The qubit manipulation microwave excites qubits when...qubits. Left plots: Rabi oscillations at several powers; traces are vertically ... An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of qubits involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple qubits. Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits. We discuss how this technique can be scaled up to read out hundreds of qubits on a chip.

Contributors: Rabenstein, K., Sverdlov, V. A., Averin, D. V.

Date: 2004-01-26

oscillations in an unbiased qubit dephased by the non-Gaussian noise with...qubit dynamics with noise which agree with the analytical results and ...qubit dynamics. Note different scales for γ in parts (a) and (b). Inset...qubit dynamics with noise. Solid line is the exponential fit of the oscillation...qubit decoherence at long times t ≫ τ for ε = 0 and (a) Gaussian and (...of qubit dynamics with noise. Solid line is the exponential fit of the...qubit basis states fluctuating under the influence of noise v t ....frequency while the noise correlation time $\tau$ determines the time ...diagram of qubit basis states fluctuating under the influence of noise...simulations of qubit dynamics. Note different scales for γ in parts (a...oscillations in a qubit by low-frequency noise. Decoherence strength is...unbiased qubit dephased by the non-Gaussian noise with characteristic ...qubit by low-frequency noise. Decoherence strength is controlled by the...Qubit decoherence by low-frequency noise ... We have derived explicit non-perturbative expression for decoherence of quantum oscillations in a qubit by low-frequency noise. Decoherence strength is controlled by the noise spectral density at zero frequency while the noise correlation time $\tau$ determines the time $t$ of crossover from the $1/\sqrt{t}$ to the exponential suppression of coherence. We also performed Monte Carlo simulations of qubit dynamics with noise which agree with the analytical results and show that most of the conclusions are valid for both Gaussian and non-Gaussian noise.

Contributors: Reuther, Georg M., Zueco, David, Hänggi, Peter, Kohler, Sigmund

Date: 2011-05-05

qubit (blue) coupled to a dc-SQUID. The interaction is characterised ...qubit oscillations. This corroborates the underlying measurement relation...oscillator frequency Ω < 10 ω q b , for which the adiabatic approximation...coherent qubit oscillations at the degeneracy point ϵ = 0 . The full qubit-oscillator...qubit dynamics is obtained by recording the oscillator response to resonant...the qubit’s time evolution is rather coherent (see section  sec:sn on q...qubit-osc-phase-spectrum(b). It reflects the qubit dynamics in terms of...from the qubit dynamics are visible at frequencies Ω ± ω q b . In order...fig:qubit-osc-phase-spectrum....qubit oscillations. This corroborates the underlying measurement relation...oscillator frequency Ω = 10 ω q b , which obviously represents a good ...frequency shift of the resulting harmonic oscillator (green) can be probed...qubit readout which provides the time evolution of a flux qubit observable...qubit to a harmonic oscillator with high frequency, representing a dc-SQUID...qubit dynamics is obtained by recording the oscillator response to resonant...qubit readout via nonlinear Josephson inductance...of a qubit with finite coupling to the oscillator and a reference qubit...low-frequency qubit dynamics. Finally, we centre the clipped spectrum ...frequency window of size 2 Δ Ω centred at the oscillator frequency Ω ,...qubit with finite coupling to the oscillator and a reference qubit without...qubit oscillations at the degeneracy point ϵ = 0 . The full qubit-oscillator...qubit-osc-phase-spectrum....oscillations with (angular) frequency ω q b . (b) Power spectrum ξ o u...  fig:qubit-osc-phase-spectrum(b). It reflects the qubit dynamics in terms...oscillator (blue solid line). The sidebands stemming from the qubit dynamics...qubit with finite coupling to the oscillator and a reference qubit without...qubit to a harmonic oscillator with high frequency, representing a dc-SQUID ... We propose a generalisation of dispersive qubit readout which provides the time evolution of a flux qubit observable. Our proposal relies on the non-linear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc-SQUID. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.

Contributors: Xian-Ting Liang

Date: 2008-09-03

qubits in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO...frequencies. However, the qubits in the two models have different decoherence...frequency ω of the bath modes, where Δ=5×109Hz,λκ=1,ξ=0.01,Ω0=10Δ,T=0.01K...qubit-IHO and IHO-bath and the oscillation frequency of the IHO....frequencies for the two cases are taken according to Fig. 2. ...low-frequency bath. The parameters are the same as in Fig. 1. ...qubit in SIB model can be modulated through changing the coupling coefficients...qubits in the two models have different decoherence and relaxation as ...high-frequency baths. ...qubits in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO...qubits coupled to low- and medium-frequency Ohmic baths directly and via...frequencies are investigated. It is shown that the qubits in SB and SIB...frequencies. The decoherence and relaxation of the qubit in SIB model ...frequencies and effective bath in (b) low and (d) medium frequencies. ...qubit-IHO and IHO-bath and the oscillation frequency of the IHO....qubits in SB and SIB models have the same decoherence and relaxation as ... Using the numerical path integral method we investigate the decoherence and relaxation of qubits in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO)-bath (SIB) models. The cases that the environment baths with low and medium frequencies are investigated. It is shown that the qubits in SB and SIB models have the same decoherence and relaxation as the baths with low frequencies. However, the qubits in the two models have different decoherence and relaxation as the baths with medium frequencies. The decoherence and relaxation of the qubit in SIB model can be modulated through changing the coupling coefficients of the qubit-IHO and IHO-bath and the oscillation frequency of the IHO.

Contributors: Johansson, J., Saito, S., Meno, T., Nakano, H., Ueda, M., Semba, K., Takayanagi, H.

Date: 2005-10-17

qubit. The SQUID functions as a detector for the qubit state: the switching...qubit and then brought the qubit and the oscillator into resonance where...and qubit experiments: qubit dephasing rate Γ φ = 0.1  GHz, qubit relaxation...qubit LC oscillator system...qubit and oscillator manifests itself as the vacuum Rabi oscillation |...frequency components a 0 , , a 3 obtained from the fit as a function of...oscillations when a 2 ns long pulse with frequency ν e x = 4.35 GHz and...weak qubit signal in this region. After the MW pulses the qubit state ...frequency Ω R until the shift pulse ends and the system returns to the...qubit–oscillator system showing the LC oscillator at ν r = 4.35  GHz and...qubit and a superconducting LC circuit acting as a quantum harmonic oscillator...oscillations: the qubit is oscillating between the excited state and the...qubit and the detector SQUID enclosing it are the small square loops in...qubit. The qubit is also enclosed by a larger loop containing on–chip ...oscillator between the vacuum state and the first excited state. We have...qubit and LC oscillator parameters (obtained from spectroscopy and qubit...qubit is oscillating between the excited state and the ground state and...oscillator [see Fig.  fig1(b)] with resonance frequency ω r = 2 π ν r ...qubit loop and two in the SQUID. The LC mode is indicated by the dashed...qubit and the SQUID. The qubit dimension is 10.2 × 10.4   μ m 2 . (c) ...oscillation frequency when the LC circuit was not initially in the vacuum...oscillation frequency is determined only by the system‘s intrinsic parameters...qubit LC oscillator mutual inductance to be M = 5.7  pH. The current and...qubit is spatially separated from the rest of the circuitry. The qubit...qubit LC oscillator mutual inductance to be M = 5.7  pH. The current and...qubit and a superconducting LC circuit acting as a quantum harmonic oscillator...the qubit and then brought the qubit and the oscillator into resonance ... We have observed the coherent exchange of a single energy quantum between a flux qubit and a superconducting LC circuit acting as a quantum harmonic oscillator. The exchange of an energy quantum is known as the vacuum Rabi oscillations: the qubit is oscillating between the excited state and the ground state and the oscillator between the vacuum state and the first excited state. We have also obtained evidence of level quantization of the LC circuit by observing the change in the oscillation frequency when the LC circuit was not initially in the vacuum state.

Contributors: Bennett, Douglas A., Longobardi, Luigi, Patel, Vijay, Chen, Wei, Averin, Dmitri V., Lukens, James E.

Date: 2008-11-14

qubit using pulsed microwaves and rapid flux pulses. The modified rf SQUID...oscillation's waveform is compared to analytical results obtained for ...frequencies of the Rabi oscillations that correspond to these microwave... rf SQUID qubit and the readout magnetometer, (c) a cross section of the...our qubit is large enough to cause a measurable effect. If the flux noise...Qubits...frequency flux noise....frequency); 0 V ’s (no detuning), 0.1 V ∘ ’s (0.21 n s -1 ), 0.45 V ’s...in our qubit is large enough to cause a measurable effect. If the flux...investigating superconducting phase qubits . In general these gaps do ...Qubits \and Flux Qubit \and SQUIDs...oscillations for detunings going from top to bottom of 0.094, 0.211, 0.328...oscillations. The line is a fit to Eq. fin for δ = 0 averaged over quasi-static...it appears that the qubit is coupled strongly to a two level fluctuator...decoherence in the qubit, one would expect a resonance in the microwave...qubit and the readout magnetometer, (c) a cross section of the wafer around...frequency flux noise and is consistent with independent measurement of...oscillations is dominated by the lifetime of the excited state and low...oscillates in time, demonstrating the phenomenon of Rabi oscillations,...oscillations when δ = 0 and the microwave frequency, f x r f = 17.9 G ...qubit in terms of Ω ....qubits . Ω ,  the frequency of the oscillations for δ = 0 , is ideally...frequency ... We report measurements of coherence times of an rf SQUID qubit using pulsed microwaves and rapid flux pulses. The modified rf SQUID, described by an double-well potential, has independent, in situ, controls for the tilt and barrier height of the potential. The decay of coherent oscillations is dominated by the lifetime of the excited state and low frequency flux noise and is consistent with independent measurement of these quantities obtained by microwave spectroscopy, resonant tunneling between fluxoid wells and decay of the excited state. The oscillation's waveform is compared to analytical results obtained for finite decay rates and detuning and averaged over low frequency flux noise.