### 62755 results for qubit oscillator frequency

Contributors: Poletto, S., Chiarello, F., Castellano, M. G., Lisenfeld, J., Lukashenko, A., Cosmelli, C., Torrioli, G., Carelli, P., Ustinov, A. V.

Date: 2008-09-08

**oscillation** **frequency** ω 0 depends on the amplitude of the manipulation...flux **qubit** circuit. (b) The control **flux **Φ c changes the potential barrier...**The** **qubit** is manipulated by changing two magnetic fluxes Φ x and Φ c ,... for **qubit** initialization in **the** left or right well, and Φ x 1 equal to...**the** **qubit** . **The** circuit was manufactured by Hypres using standard Nb/...**the** **qubit** flux is performed by measuring **the** switching current of an unshunted...coherent evolution of **the** **qubit**....**qubits**. An other advantage of this type of **qubit** is its insensitivity ...**oscillation** **frequencies** for the corresponding pulse amplitudes....for **qubit** manipulation at which the **qubit** potential has a shape as indicated...**oscillation** **frequency** could be tuned between 6 and 21 GHz by changing ...**oscillation** **frequencies** for different values of Φ c (open circles). Excellent...**oscillation** **frequency** as shown in Fig. fig:4(a). In Fig. fig:5, we plot...**oscillation** **frequency**, and (b) for different potential symmetry by detuning...**oscillations** of a tunable superconducting flux **qubit** by manipulating its...**qubit** by manipulating its energy potential with a nanosecond-long pulse...**qubit** manipulation at which the **qubit** potential has a shape as indicated...**qubit** circuit. (b) The control flux Φ c changes the potential barrier ...**oscillate** at a **frequency** ranging from 6 GHz to 21 GHz, tunable via the...**qubit** initially prepared in the state, and for (a) different pulse amplitudes...**oscillation** **frequency**, as shown in Fig. fig:4(b), is consistent with ...**qubit** manipulated without microwaves ... We experimentally demonstrate the coherent **oscillations** of a tunable superconducting flux **qubit** by manipulating its energy potential with a nanosecond-long pulse of magnetic flux. The occupation probabilities of two persistent current states **oscillate** at a **frequency** ranging from 6 GHz to 21 GHz, tunable via the amplitude of the flux pulse. The demonstrated operation mode allows to realize quantum gates which take less than 100 ps time and are thus much faster compared to other superconducting **qubits**. An other advantage of this type of **qubit** is its insensitivity to both thermal and magnetic field fluctuations.

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Contributors: Makhlin, Yuriy, Shnirman, Alexander

Date: 2003-12-22

**oscillations** of the solid lines are compensated by the dashed line from...low-**frequency**, e.g. 1/f noise, motivated by recent experiments with superconducting...Josephson charge qubit. The simplest Josephson charge qubit is the Cooper-pair...**oscillations** of the solid lines in the diagrams and assuming very slow... ≫ E J for the qubit in Fig. F:qb at the degeneracy point, where the charge...**qubit**. The simplest Josephson charge **qubit** is the Cooper-pair box shown...the qubit’s 2 × 2 density matrix ρ ̂ , exp - i L 0 t θ t , where L 0 is...low-**frequency** noise is equivalent to that of quadratic longitudinal coupling...**frequencies**, we find:...**oscillations** under the influence of both low- and high-**frequency** fluctuations...high-**frequency** dashed line. The relaxation process in e also contributes...**qubit**...the qubit’s density matrix). The term in Fig. F:2ordera gives...**qubits** by transverse low-frequency noise... charge qubit ... We analyze the dissipative dynamics of a two-level quantum system subject to low-**frequency**, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-**frequency** noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent **oscillations** under the influence of both low- and high-**frequency** fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing.

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Contributors: Bertet, P., Chiorescu, I., Semba, K., Harmans, C. J. P. M, Mooij, J. E.

Date: 2004-05-03

**frequency** f 2 at the value f 2 * and measured Rabi **oscillations** (black...**oscillations** with high visibility (65%)....**oscillations**....**frequency** to the **qubit** resonance and measured the switching probability...**qubit** by resonant activation...**frequency** of the **qubit** and (insert) persistent-current versus external...**qubit** and (insert) persistent-current versus external flux. The squares...**qubit** damping time T 1 , to prevent loss of excited state population. ...**qubit** state, which we detect by resonant activation. With a measurement...**frequency**. fig4...**oscillations** at a Larmor **frequency** f q = 7.15 ~ G H z (b) Switching probability...high-**frequency** side of the peak. Thus the plasma **oscillator** non-linearity...**qubit** loop (the scale bar indicates 1 ~ μ m ). Two layers of Aluminium...**frequency** on the **qubit** state, which we detect by resonant activation. ...between the **qubit** states in a time shorter than the **qubit**’s energy relaxation...**oscillation** measured by DC current pulse (grey line, amplitude A = 40 ...**qubit**. It relies on the dependency of the measuring Superconducting Quantum...**qubit** to be in 0 would result into broadening of the curve P s w π ), ...**SQUID** and the **qubit** by fitting the **qubit** “step" appearing in the **SQUID** ... We present the implementation of a new scheme to detect the quantum state of a persistent-current **qubit**. It relies on the dependency of the measuring Superconducting Quantum Interference Device (SQUID) plasma **frequency** on the **qubit** state, which we detect by resonant activation. With a measurement pulse of only 5ns, we observed Rabi **oscillations** with high visibility (65%).

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Contributors: Hua, Ming, Deng, Fu-Guo

Date: 2013-09-30

**qubit**-state-dependent resonator transition, which means the **frequency** ... qubit-state-dependent resonator transition, which means the frequency...**qubits** assisted by a resonator in the quasi-dispersive regime with a new...three-qubit gate, such as a Fredkin gate on a three-qubit system can also... qubit. (b) The number-state-dependent qubit transition, which means the...**frequency** of two **qubits** between and are chosen as ω 0 , 1 ; 1 / 2 π = ...**oscillations** in our cc-phase gate on a three-charge-**qubit** system. Here...**qubits** can play an important role in shortening largely the operation ... qubits, and q 3 is** the **target** qubit**. The initial state of this system...the** qubit** q in** the **transition between** the **energy levels | i q and | j ...**frequency** shift δ q takes place on the **qubit** due to the photon number ...**qubits**.... the** qubit** q in** the **transition between** the **energy levels | i q and | j...**frequencies** of the **qubits**....**oscillation** (ROT) ROT 0 : | 0 1 | 1 2 | 0 a ↔ | 0 1 | 0 2 | 1 a , while...**qubits**. **Qubits** are placed around the maxima of the electrical field amplitude...**oscillation**, respectively. The MAEV s vary with the transition **frequency**...**frequency** of q 2 (which equals to the transition **frequency** of R a when...**oscillation** varying with the coupling strength g 2 and the **frequency** of...**Qubits** in Circuit QED...**qubit**-state-dependent resonator transition frequency and the tunable period...**qubits**. More interesting, the non-computational third excitation states...**qubits** than previous proposals....second qubit ω 2 . (a) The outcomes for ROT 0 : | 0 1 | 1 2 | 0 a ↔ | ...**oscillation** and an unwanted one. This operation does not require any kind...**qubit**-state-dependent resonator transition **frequency** and the tunable period... qubit and q 2 is** the **target** qubit**. The initial state of** the **system composed...**frequency** on R a becomes ... We present a fast quantum entangling operation on superconducting **qubits** assisted by a resonator in the quasi-dispersive regime with a new effect --- the selective resonance coming from the amplified **qubit**-state-dependent resonator transition **frequency** and the tunable period relation between a wanted quantum Rabi **oscillation** and an unwanted one. This operation does not require any kind of drive fields and the interaction between **qubits**. More interesting, the non-computational third excitation states of the charge **qubits** can play an important role in shortening largely the operation time of the entangling gates. All those features provide an effective way to realize much faster quantum entangling gates on superconducting **qubits** than previous proposals.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-07-30

**oscillator** **frequency** approaches unity and goes beyond. In this regime ...**oscillator** **frequency** Ω , ε = l Ω . In this case we found that the levels...**qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore...**frequency** peaks coming from the two dressed **oscillation** **frequencies** Ω ...**Qubit**-oscillator system: An analytical treatment of the ultra-strong coupling...**qubit** for an **oscillator** at low temperature. We consider the coupling strength...**oscillations** **frequency** Ω j l . For l being not an integer those doublets...**qubit**-oscillator detuning. Furthermore, the dynamics is not governed anymore...**qubit** for an oscillator at low temperature. We consider the coupling strength...**qubit** ( ε / Ω = 0.5 ) at resonance with the oscillator Δ b = Ω in the ...**frequencies** through a variation of the coupling....**qubit** ( ε / Ω = 0.5 ) at resonance with the **oscillator** Δ b = Ω in the ...**frequency** range. The lowest **frequency** peaks originate from transitions...**qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime...**oscillations**. With increasing time small differences between numerical...**oscillation** **frequency** Ω j 0 . Numerical calculations and VVP predict group...**oscillation** **frequencies** Ω j 1 and Ω j 2 influence the longtime dynamics...**qubit** ( ε / Ω = 0.5 ) being at resonance with the **oscillator** ( Δ b = Ω ... We examine a two-level system coupled to a quantum **oscillator**, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the **qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including in particular also the finite bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the **qubit** for an **oscillator** at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many **frequencies** are contributing to the dynamics. They are gathered into groups whose spacing depends on the **qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a non-trivial dressing of the tunneling matrix element, which can be used to suppress specific **frequencies** through a variation of the coupling.

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Contributors: Greenberg, Ya. S., Izmalkov, A., Grajcar, M., Il'ichev, E., Krech, W., Meyer, H. -G.

Date: 2002-08-07

**oscillations** in a phase **qubit**. The external source, typically in GHz range...**qubit** levels. The resulting Rabi oscillations of supercurrent in the **qubit**...**qubit**. According to the estimates for dephasing and relaxation times, ...**qubit**. The external source, typically in GHz range, induces transitions...**frequency** in MHz range....three-**junction** **qubit** in classical regime, when the hysteretic dependence...**qubit** in classical regime, when the hysteretic dependence of ground-state...**qubit**...**qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit**...**qubit**. Detailed calculation for zero and non-zero temperature are made...**qubit** coupled to a tank circuit....**oscillations** between quantum states in mesoscopic superconducting systems ... 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.

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Contributors: Chen, Yu, Sank, D., O'Malley, P., White, T., Barends, R., Chiaro, B., Kelly, J., Lucero, E., Mariantoni, M., Megrant, A.

Date: 2012-09-09

**qubits** can be read out simultaneously using **frequency** multiplexing on ...four-**qubit** sample. F B 1 - 4 are control lines for each **qubit** and R R ...**qubit**, lowering the barrier between the metastable computational energy...**qubits** used in Ref. 6. In this experiment, we drove Rabi **oscillations** ...**qubit** flux bias, with no averaging. See text for details. fig.phase...**qubit** to a separate lumped-element superconducting readout resonator, ...**oscillations** for **qubits** Q 1 - Q 4 respectively, with the **qubits** driven...**qubits** can be read out simultaneously using frequency multiplexing on ... **qubit**’s | g ↔ | e transition and read out the** qubit** states simultaneously... qubits Q 1 to Q 4 . We then drove each

**separately using an on-resonance...**

**qubit****oscillations**in panels (a)-(d) compared to the multiplexed readout in ...

**frequency**for maximum visibility. (b) Reflected phase as a function of...

**qubits**Q 1 - Q 4 respectively, with the

**qubits**driven with 1, 2/3, 1/2...

**frequency**f n encodes the state of

**qubit**n . The phases φ n , n = 1 - ...

**qubit**, we demonstrated the

**frequency**-multiplexed readout by performing...

**frequency**-multiplexed readout. Multiplexed readout signals I p and Q p...

**qubits**, a significant advantage for scaling up to larger numbers of

**qubits**...

**qubits**. Using a quantum circuit with four phase

**qubits**, we couple each...

**qubit**was projected onto the | g or the | e state....

**qubit**in the left ( L , blue) and right ( R , red) wells. Dashed line ...

**qubit**projective measurement, where a current pulse allows a

**qubit**in ...

**frequency**(averaged 900 times), for the

**qubit**in the left ( L , blue) ...

**frequency**-multiplexed readout scheme for superconducting phase

**qubits**....

**qubits**, we couple each

**qubit**to a separate lumped-element superconducting...the

**Josephson junction. Each**

**qubit****is coupled to its readout resonator...**

**qubit****oscillations**measured simultaneously for all the

**qubits**, using the same...

**frequency**, with the

**qubit**prepared first in the left and then in the right...

**qubits**... 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 scaling up to larger numbers of

**qubits**.

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Contributors: Shevchenko, S. N., Omelyanchouk, A. N., Zagoskin, A. M., Savel'ev, S., Nori, F.

Date: 2007-12-12

**frequency** dependent on the perturbation amplitude. These serve as one ...**oscillations** from their classical Doppelganger.... of the qubit in state | 1 . Alternatively, instead of an RF readout pulse...**qubit** in Fig. 4 of Ref. [...**qubit** states....**qubits** (current-biased Josephson junctions) this effect can be mimicked...Phase qubit (a) and its Josephson energy (b). The metastable states and...**frequency**. The parameters used here are: η = 0.95 , E J / ℏ ω p = 300 ...**oscillations** in current-biased Josephson junctions: (a) and (b) show the...**qubits** provide a clear demonstration of quantum coherent behaviour in ...**frequency** in the classical case, in contrast to the positive Bloch-Siegert...a phase qubit is a current-biased Josephson junction (see Fig. scheme(...**qubit** in state | 1 . Alternatively, instead of an RF readout pulse one...**oscillations** can be produced by the subharmonics of the resonant **frequency**...as qubit states....flux qubit in Fig. 4 of Ref. [...**qubit** (a) and its Josephson energy (b). The metastable states and can ...**frequency** and the amplitude of the **oscillations** respectively for ϵ = 2...**qubit** is a current-biased Josephson junction (see Fig. scheme(a)), and...**qubit**...**frequency** for relatively weak (a) and strong (b) driving. Different values...Superconducting phase qubits provide a clear demonstration of quantum ... Rabi **oscillations** are coherent transitions in a quantum two-level system under the influence of a resonant perturbation, with a much lower **frequency** dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently [N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. 95, 067001 (2005)] that in phase **qubits** (current-biased Josephson junctions) this effect can be mimicked by classical **oscillations** arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between the classical and quantum effect. First, while the quantum Rabi **oscillations** can be produced by the subharmonics of the resonant **frequency** (multiphoton processes), the classical effect also exists when the system is excited at the overtones. Second, the shape of the resonance is, in the classical case, characteristically asymmetric; while quantum resonances are described by symmetric Lorentzians. Third, the anharmonicity of the potential results in the negative shift of the resonant **frequency** in the classical case, in contrast to the positive Bloch-Siegert shift in the quantum case. We show that in the relevant range of parameters these features allow to confidently distinguish the bona fide Rabi **oscillations** from their classical Doppelganger.

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### Temperature square dependence of the low **frequency** 1/f charge noise in the Josephson junction **qubits**

Contributors: Astafiev, O., Pashkin, Yu. A., Nakamura, Y., Yamamoto, T., Tsai, J. S.

Date: 2006-04-04

**qubits**, we study temperature dependence of the 1/f noise and decay of ...of qubit dephasing during coherent oscillations. The coherent oscillations...**oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated...**oscillations** decay as exp - t 2 / 2 T 2 * 2 with...**frequency** 1/f noise and the quantum f noise recently measured in the Josephson...**qubits** off the electrostatic energy degeneracy point is consistently explained...**frequency** independent in the measured **frequency** range (and usually do ...**qubit** as an SET and measure the low **frequency** charge noise, which causes...**oscillations** measured at T = 50 mK and the dashed envelope exemplifies...**qubit** as an SET and measure the low frequency charge noise, which causes...**frequency** 1/f noise that is observed in the transport measurements....**oscillation** as a function of t away from the degeneracy point ( θ ≠ π ...**qubits**...**qubit** dephasing during coherent **oscillations**. The coherent **oscillations** ... To verify the hypothesis about the common origin of the low **frequency** 1/f noise and the quantum f noise recently measured in the Josephson charge **qubits**, we study temperature dependence of the 1/f noise and decay of coherent **oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge **qubits** off the electrostatic energy degeneracy point is consistently explained by the same low **frequency** 1/f noise that is observed in the transport measurements.

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Contributors: Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Majer, J., Girvin, S. M., Schoelkopf, R. J.

Date: 2005-02-27

**qubit** population P vs. pulse separation Δ t using the pulse sequence shown... to determine **the** **qubit** transition frequency ω a = ω s + 2 π ν R a m s...applying to **the** **qubit** microwave pulses of frequency ω s , which are resonant...**oscillating** at the detuning **frequency** Δ a , s = ω a - ω s ∼ 6 M H z decay...**oscillations** in the **qubit** population P vs. Rabi pulse length Δ t (blue...**qubit** population P vs. pulse separation Δ t using** the **pulse sequence shown...**oscillation** experiment with a superconducting **qubit** we show that a visibility...**qubit** we show that a visibility in the **qubit** excited state population ...**oscillations** in the **qubit** at a **frequency** of ν R a b i = n s g / π , where... φ will be reduced in any **qubit** read-out for which **the** timescale of **the**...**qubit**. In the 2D density plot Fig. fig:2DRabi, Rabi **oscillations** are ...**oscillation** **frequency** ν R a b i with the pulse amplitude ϵ s ∝ n s , see...**qubit** excited state population of more than 90 % can be attained. We perform...**qubit** population P is plotted versus Δ** t** in Fig. fig:rabioscillationsa...**Qubit** with Dispersive Readout...**qubit** state by coupling the **qubit** non-resonantly to a transmission line...**superconducting** **qubit**, a visibility in **the** population of **the** **qubit** excited...**qubit**. In each panel the dashed lines correspond to the expected measurement...**to **the **qubit**. In each panel** the **dashed lines correspond **to **the expected...**oscillations** with Rabi pulse length Δ t , pulse **frequency** ω s and amplitude...**oscillations** in a superconducting **qubit**, a visibility in the population... the **qubit** population P vs. Rabi pulse length Δ t (blue dots) and fit ...**qubit** coherence time is determined to be larger than 500 ns in a measurement...**oscillator** at **frequency** ω L O . The Cooper pair box level separation is ... 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.

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