### 62747 results for qubit oscillator frequency

Contributors: Leyton, V., Thorwart, M., Peano, V.

Date: 2011-09-26

**qubit** states, and (b) the corresponding detector response A as a function...**the** two **qubit** states....**oscillator** **frequency** Ω , where the coupling term is considered as a perturbation...purpose of a **qubit**-detector setup, **the** **qubit**-resonator coupling typically...**frequency** ω e x for the same parameters as in Fig. fig2. fig4...**the** **qubit** for **the** same parameters as in a). fig3...**frequencies** ω e x close to the fundamental **frequency** Ω . In order to see...**qubit**, which is based on resonant few-photon transitions in a driven nonlinear...**qubit** for the same parameters as in a). fig3...**quadratic** **qubit**-detector coupling induces a global frequency shift of ...**qubit** states, and (b) **the** corresponding detector response A as a function...**qubit** (black solid line). The blue dashed line indicates **the** response ...**frequency** ω e x . The parameters are the same as in Fig. fig2. fig5...**frequencies**. We show that this detection scheme offers the advantage of...**qubit** states is given by the **frequency** gap δ ω e x ≃ 2 g . Figure fig3...**Qubit** state detection using the quantum Duffing oscillator...**qubit** and is used as its detector. Close to the fundamental resonator **frequency**, the nonlinear resonator shows sharp resonant few-photon transitions...**qubit** coupled to an Ohmically damped harmonic **oscillator**. This model can...**qubit** inductively coupled to a driven SQUID detector in its nonlinear ...large **qubit** bias), this coincides with **the** shifted one....**qubit**-detector coupling induces a global **frequency** shift of the response...**qubit** state, these few-photon resonances are shifted to different driving...**qubit** prepared in its ground state | ↓ (orange solid line) and in its ...**qubit** and is used as its detector. Close to the fundamental resonator ... We introduce a detection scheme for the state of a **qubit**, which is based on resonant few-photon transitions in a driven nonlinear resonator. The latter is parametrically coupled to the **qubit** and is used as its detector. Close to the fundamental resonator **frequency**, the nonlinear resonator shows sharp resonant few-photon transitions. Depending on the **qubit** state, these few-photon resonances are shifted to different driving **frequencies**. We show that this detection scheme offers the advantage of small back action, a large discrimination power with an enhanced read-out fidelity, and a sufficiently large measurement efficiency. A realization of this scheme in the form of a persistent current **qubit** inductively coupled to a driven SQUID detector in its nonlinear regime is discussed.

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Contributors: Kofman, A. G., Zhang, Q., Martinis, J. M., Korotkov, A. N.

Date: 2006-06-02

frequency of the two-qubit imaginary-swap quantum gate....**qubits**. The damped **oscillations** of the superconducting phase after the...**oscillator** model, which is advantageous for design of **qubits** with weak...**qubit** as a harmonic **oscillator**. However, to analyze the measurement error...**qubits**. The damped oscillations of the superconducting phase after the...**oscillations** in the “right” well. This dissipative evolution leads to ...**qubit** is treated both classically and quantum-mechanically. The results...**oscillation** **frequency** is shown in Fig. f3 for C x = 0 (solid line) and...**frequency** of the two-**qubit** imaginary-swap quantum gate....= 25 ns....T...Th... model since **the **qubit excitation quickly moves **the **qubit frequency out...).]... **the **second-qubit energy,...**qubit** may be to a much lower energy than for the **oscillator**; (c) After...**qubit**, which is highly excited after the measurement, is described classically...two-**qubit** operations) for a given tolerable value of the measurement error...**the **resonance with **the **second qubit....respectively....**qubit** energy E 2 (in units of ℏ ω l 2 ) in the **oscillator** model as a function...first-**qubit** **oscillation** **frequency** f d as a function of time t (normalized...**frequencies**, with the difference **frequency** increasing in time, d t ~ 2...resonance with **the **second qubit....**frequency** for the second **qubit**: ω l 2 / 2 π = 10.2 GHz for N l 2 = 10 ...**frequency** of two-**qubit** operations) for a given tolerable value of the ...height N l 2 .....]...**qubit** may significantly excite the second **qubit**, leading to its measurement...2.1...**qubits** ... 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) for a given tolerable value of the measurement error probability.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-09-08

the **qubit**-oscillator system:...**qubit**-oscillator system. The same parameters as in Fig. Fig::Dynam1 are...**oscillator** modes in the spectrum, while the latter can bring the **qubit**'s...**qubit** energy splitting (extreme driving). Both **qubit**-oscillator coupling...**oscillation** **frequencies** are plotted against the dimensionless coupling...**oscillator** degrees of freedom from the density operator of the **qubit**-**oscillator**...**qubit**-**oscillator** system against the static bias ε for weak coupling g ...**qubit** tunneling matrix element of different nature: the former can be ...**oscillation** **frequencies** Ω K vanish. However, third-order corrections in...**qubit** energy splitting (extreme driving). Both **qubit**-**oscillator** coupling...driven **qubit** , might occur also for a **qubit**-oscillator system in the ultrastrong...**oscillator** **frequency** are commensurable, Ω / ω ex = j / N with integers...**oscillator** states are included. Numerical calculations are shown by red...**qubit** . Analogously, our analytical solution now predicts localization...**qubit**-oscillator system in the ultrastrong coupling regime, where the ...**qubit**-**oscillator** system in the ultrastrong coupling regime, where the ...**oscillator** **frequency** approaches unity or goes beyond, and simultaneously...**qubit** for ε = 0 , Δ / Ω = 0.4 , ω ex / Ω = 5.3 , A / Ω = 8.0 , and temperature...**qubit**-oscillator system in the ultrastrong coupling and extreme driving...**oscillations** overlaid. For long times this localization vanishes (see ...**qubit**-oscillator system against the static bias ε for weak coupling g ...the **qubit** for ε = 0 , Δ / Ω = 0.4 , ω ex / Ω = 5.3 , A / Ω = 8.0 , and...**qubit** , might occur also for a **qubit**-**oscillator** system in the ultrastrong...**Qubit**-oscillator system under ultrastrong coupling and extreme driving...**qubit** ( ε = 0 ). Further, Δ / Ω = 0.4 , ω ex / Ω = 5.3 and A / Ω = 8.0...**qubit**-**oscillator** system. The same parameters as in Fig. Fig::Dynam1 are...**qubit**'s dynamics to a standstill at short times (coherent destruction ... We introduce an approach to studying a driven **qubit**-**oscillator** system in the ultrastrong coupling regime, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity or goes beyond, and simultaneously for driving strengths much bigger than the **qubit** energy splitting (extreme driving). Both **qubit**-**oscillator** coupling and external driving lead to a dressing of the **qubit** tunneling matrix element of different nature: the former can be used to suppress selectively certain **oscillator** modes in the spectrum, while the latter can bring the **qubit**'s dynamics to a standstill at short times (coherent destruction of tunneling) even in the case of ultrastrong coupling.

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Contributors: Fedorov, A., Feofanov, A. K., Macha, P., Forn-Díaz, P., Harmans, C. J. P. M., Mooij, J. E.

Date: 2010-04-09

the bare **qubit**-oscillator coupling 2 g and corresponds to** the **resonance... the **qubit**. The gradiometer loop (emphasized by a dashed line) is used...**Qubit** at its Symmetry Point...**qubit**. (c) MW frequency vs f ϵ (controlled by** the **amplitude of** the **current...**oscillator** **frequency** ν o s c ....**Frequency** of the vacuum Rabi **oscillations** extracted from data (a) and ...**qubit** whose gap can be tuned fast and have coupled this **qubit** strongly...**oscillations** (a) and MW **frequency** (b) vs magnetic f α . In the experiment...**qubit** biased at its symmetry point shows a minimum in the energy splitting...**qubit**-**oscillator** system. The minimum of energy splitting of the **qubit** ...**qubit**-resonator coupling ($g/h\sim0.1\nu_{\rm osc}$). Here being at resonance...**qubit**-resonator system and generate vacuum Rabi oscillations. When the...**oscillator** to the **qubit**. (c) MW **frequency** vs f ϵ (controlled by the amplitude...**oscillations**. When the gap is made equal to the **oscillator** **frequency** $...**effective** **qubit**-oscillator coupling strength reduced by sin η .... the **qubit**-oscillator system. The minimum of energy splitting of the **qubit**...**oscillator**. We show full spectroscopy of the **qubit**-resonator system and ... A flux **qubit** biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a **qubit** whose gap can be tuned fast and have coupled this **qubit** strongly to an LC **oscillator**. We show full spectroscopy of the **qubit**-resonator system and generate vacuum Rabi **oscillations**. When the gap is made equal to the **oscillator** **frequency** $\nu_{osc}$ we find the strongest **qubit**-resonator coupling ($g/h\sim0.1\nu_{\rm osc}$). Here being at resonance coincides with the optimal coherence of the symmetry point. Significant further increase of the coupling is possible.

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Contributors: Xian-Ting Liang

Date: 2007-12-05

lower-**frequency** and high-**frequency** cut-off of the baths modes ω0=11Δ, ...**qubits** coupled to an Ohmic bath directly and via an intermediate harmonic...**qubit** **in** the **qubit**-**IHO**-bath model can be modulated through changing the...**in** the two models may have almost same decoherence and relaxation times...**qubits** in the two models may have almost same decoherence and relaxation...**qubit**-**IHO** and **IHO**-bath and the oscillation frequency of the **IHO**....**oscillator** (IHO). Here, we suppose the **oscillation** **frequencies** of the ...**qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO....**qubit** in the **qubit**-IHO-bath model can be modulated through changing the...**qubit** coupled to an Ohmic bath directly and via an intermediate harmonic ... Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** coupled to an Ohmic bath directly and via an intermediate harmonic **oscillator** (IHO). Here, we suppose the **oscillation** **frequencies** of the bath modes are higher than the IHO’s. When we choose suitable parameters the **qubits** in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the **qubit** in the **qubit**-IHO-bath model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO.

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Contributors: Altomare, Fabio, Cicak, Katarina, Sillanpää, Mika A., Allman, Michael S., Sirois, Adam J., Li, Dale, Park, Jae I., Strong, Joshua A., Teufel, John D., Whittaker, Jed D.

Date: 2010-02-02

**qubit** spectroscopy. The right ordinate displays the ratio between the ...**qubit** when its **frequency** is far from the cavity's resonant **frequency**. ...These correspond to the qubit states | 0 if the qubit did not tunnel and...**qubit** when its frequency is far from the cavity's resonant frequency. ...**qubits**. The left ordinate displays the **oscillation** **frequency** as determined...or frequency) values for qubit 1 (qubit 2). Notice that the crosstalk transferred to qubit 2 (qubit 1) is flux independent of qubit 1 (qubit...**qubit** and the resonant **frequency** in the left well ( N l ) as a function...**qubit**, (b) the CPW cavity, (c) the second **qubit**. (Red): ϕ 1 = 0.8949 ϕ...**qubit** behavior that agrees well with the experimental data. These results...**qubit** transfers part of its energy to the CPW cavity. The second **qubit**...**qubit** (classically) undergoes large **oscillations** in the deeper right well...values were determined for qubit 2 (qubit 1) by performing a Gaussian ...**qubit** is measured, the superconducting phase can undergo damped **oscillations**...**oscillation** is large, the **frequency** of the **oscillations** is lower than ...**qubits**. The left ordinate displays the resonant **frequency** as measured ...**qubit** 2. (b) Simulation: ratio between the maximum energy acquired by ...**frequency** of **oscillation** in the right well matches the CPW cavity resonant...**oscillation** in right well matches the CPW cavity resonant **frequency** and...**qubits** coupled by a resonant coplanar waveguide cavity. After the first...**qubit** 2, after **qubit** 1 has already tunneled as function of the (dimensionless...**qubit** **frequency**. As the system loses energy due to the damping, the **oscillation**...second qubit. In Fig. fig:experiment(b) we plot, for the second qubit...**qubits** coupled by a coplanar waveguide...**frequency** chirped noise signal whose **frequency** crosses that of the cavity...**qubits** can be reduced by use of linear or possibly nonlinear resonant ...**qubit** is measured, the superconducting phase can undergo damped oscillations...**oscillator**). C i is the total i - **qubit** (or CPW cavity) capacitance, L ... We analyze the measurement crosstalk between two flux-biased phase **qubits** coupled by a resonant coplanar waveguide cavity. After the first **qubit** is measured, the superconducting phase can undergo damped **oscillations** resulting in an a.c. voltage that produces a **frequency** chirped noise signal whose **frequency** crosses that of the cavity. We show experimentally that the coplanar waveguide cavity acts as a bandpass filter that can significantly reduce the crosstalk signal seen by the second **qubit** when its **frequency** is far from the cavity's resonant **frequency**. We present a simple classical description of the **qubit** behavior that agrees well with the experimental data. These results suggest that measurement crosstalk between superconducting phase **qubits** can be reduced by use of linear or possibly nonlinear resonant cavities as coupling elements.

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Contributors: Serban, I., Dykman, M. I., Wilhelm, F. K.

Date: 2009-07-29

**qubit** for the case when its detector, the Josephson bifurcation amplifier...**frequency**. This new **frequency** scale results from the interplay of the ...**qubit** relaxation rates are different in different states. They can display... in the **qubit** relaxation rates noted** in** Ref. ...**qubit** **frequency** and resonant enhancement, which is due to quasienergy ...**qubit** frequency and resonant enhancement, which is due to quasienergy ...**to** the **qubit**, Γ e ≪ κ , it can be satisfied even at resonance....**oscillator** approaches bifurcation points where the corresponding attractor...**qubit** **frequency** and twice the modulation **frequency**; Γ 0 = ℏ C Γ r a 2 ... the **qubit** Γ e ∝ R e ~ N + - ω q - 2 ω F sharply increases if the **qubit**...**qubit** measured by a driven Duffing oscillator...**where** the **qubit** is resonantly pumped; the corresponding condition is m...**qubit** states differs from the thermal Boltzmann distribution. If the **oscillator**-mediated...**qubit** frequency and twice the modulation frequency; Γ 0 = ℏ C Γ r a 2 ...scaled **qubit** temperature T e f f * = k B T e f f / ℏ ω q as function of...dominating **qubit** decay mechanism, the **qubit** distribution is determined...**oscillator** decay rate. The dependence of ν a on the control parameter ...**qubit** Γ e ∝ R e ~ N + - ω q - 2 ω F sharply increases if the **qubit** **frequency**...**qubit** temperature T e f f * = k B T e f f / ℏ ω q as function of the scaled...**frequencies** ν a / | δ ω | for the same κ / | δ ω . Curves 1 and 2 refer...**qubit**....**oscillator** changes the effective temperature of the **qubit**. ... We investigate the relaxation of a superconducting **qubit** for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The **qubit** relaxation rates are different in different states. They can display strong dependence on the **qubit** **frequency** and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven **oscillator** changes the effective temperature of the **qubit**.

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Contributors: Zorin, A. B., Chiarello, F.

Date: 2009-08-27

**qubit** which is insensitive to the charge variable, biased in the optimal...into the **qubit** loop. Capacitance C includes both the self-capacitance ...**qubit** **frequency** as a function of parameter β L for fixed L = 50 pH and...of the **qubit** coupled to a resonant circuit and (b) possible equivalent...**qubit** on the basis of the radio-**frequency** SQUID with the screening parameter...**qubit** coupled to a resonant circuit and (b) possible equivalent compound...**qubit** **frequency** within the range of sufficiently large anharmonicity (...potential **qubit** allowing manipulation within the two basis **qubit** states...**qubit** **frequency** ν 10 = Δ E 0 / h and the anharmonicity factor δ computed...**oscillator** type (left inset) to the set of the doublets (right inset),...the **qubit** energy dramatically decreases and the **qubit** states are nearly...**qubit** can be tuned within an appreciable range allowing variable **qubit**-**qubit**... **qubit** with the inductance value L = 50 pH and the set of capacitances...**frequency** in this **qubit** can be tuned within an appreciable range allowing...**qubit** on the basis of the radio-frequency SQUID with the screening parameter...**qubit** ....The **qubit** frequency as a function of parameter β L for fixed L = 50 pH...**qubit**-**qubit** coupling....**oscillator**-type states in two separate wells. The spectrum in the central...this **qubit** ....**qubit** allowing manipulation within the two basis **qubit** states | 0 and ...**qubit** based on the Josephson oscillator with strong anharmonicity...**frequency** shift in the circuit due to excitation of the **qubit** with the...**qubit** energy dramatically decreases and the **qubit** states are nearly the...**qubit** in the ground (solid lines) and excited (dashed lines) states calculated ... We propose a superconducting phase **qubit** on the basis of the radio-**frequency** SQUID with the screening parameter value $\beta_L = (2\pi/\Phi_0)LI_c \approx 1$, biased by a half flux quantum $\Phi_e=\Phi_0/2$. Significant anharmonicity ($> 30%$) can be achieved in this system due to the interplay of the cosine Josephson potential and the parabolic magnetic-energy potential that ultimately leads to the quartic polynomial shape of the well. The two lowest eigenstates in this global minimum perfectly suit for the **qubit** which is insensitive to the charge variable, biased in the optimal point and allows an efficient dispersive readout. Moreover, the transition **frequency** in this **qubit** can be tuned within an appreciable range allowing variable **qubit**-**qubit** coupling.

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Contributors: Thrailkill, Z. E., Lambert, J. G., Ramos, R. C.

Date: 2009-09-20

**qubits**. Second, small ripples, or **oscillations**, begin to appear. These...**oscillations** between the **qubits** and resonators....**qubit** (Q) coupled to an array of two resonators (R1, R2) via identical...**qubits** will require quantum information to be stored in and transferred...**qubit** from an array of resonators so that it can function within the same...**Qubits**...active** qubit** and Q2 is the control

**. In the simulation, the three...**

**qubit****frequencies**to couple

**qubits**. We find that an array of resonators with...

**frequencies**also cause slight non-uniformities in the high

**frequency**

**oscillations**...

**oscillate**into

**qubit**2, as shown in Fig. fig2 and fig3. As the detuning...

**qubits**maintain equal

**frequencies**as they are simultaneously detuned from...

**qubit**is characterized as having capacitance C J and critical current ...

**qubits**dispersively. We show that a control

**qubit**can be used to effectively...

**qubit**and the two resonators; since the two resonators are identical here... qubits....

**qubits**have been shown to be promising components for a future quantum...

**oscillations**of the excitation. The detuning of the control

**qubit**Q2 can...

**frequency**of R3 is a little closer to the

**frequency**of the

**qubits**. The...

**qubits**. We find that an array of resonators with different frequencies...

**frequency**range used by the resonators....

**qubit**-resonator coupling strength is 110 MHz. At zero detuning, the excitation...

**qubit**-

**qubit**and

**-resonator coupling strengths. At large detuning,...**

**qubit****oscillates**slightly faster than in (b) because the small offsets in

**frequency**...

**frequencies**can be individually addressed to store and retrieve information...control”

**qubit**placed between the resonator array and the active

**...control**

**qubit****qubit**(Q2) between the active

**qubit**(Q1) and the resonator array...

**qubit**can be effectively used to turn coupling on and off between a

**...**

**qubit****oscillates**between the two

**qubits**without significant interference from...

**qubits**from R2. In (b), the

**frequencies**of all three resonators are equal ... Josephson junction-based

**qubits**have been shown to be promising components for a future quantum computer. A network of these superconducting

**qubits**will require quantum information to be stored in and transferred among them. Resonators made of superconducting metal strips are useful elements for this purpose because they have long coherence times and can dispersively couple

**qubits**. We explore the use of multiple resonators with different resonant

**frequencies**to couple

**qubits**. We find that an array of resonators with different

**frequencies**can be individually addressed to store and retrieve information, while coupling

**qubits**dispersively. We show that a control

**qubit**can be used to effectively isolate an active

**qubit**from an array of resonators so that it can function within the same

**frequency**range used by the resonators.

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Contributors: Volkov, P. A., Fistul, M. V.

Date: 2013-05-31

**qubit** (solid green (thick) line) and tails on other **qubits** (solid red ...**qubits** display coherent quantum beatings with N different **frequencies**,...**frequencies** $\omega_1=\bar{\Delta}/\hbar$ and $\omega_2=\tilde{\omega}...th qubit (solid green (thick) line) and tails on other qubits (solid red...**qubits**. In the presence of such interaction we analyze quantum correlation...**qubits** $C_i(t)$ to obtain two collective quantum-mechanical coherent **oscillations**...**frequency** of the cavity renormalized by interaction. The amplitude of ...**qubits** are characterized by energy level differences $\Delta_i$ and we...**qubits** $C_i(t)$ to obtain two collective quantum-mechanical coherent oscillations...**qubits** display coherent quantum beatings with N different frequencies,...**qubits** (two-level systems) incorporated into a low-dissipation resonant...**qubits**...**oscillations** can be strongly enhanced in the resonant case when $\omega ... We report a theoretical study of coherent collective quantum dynamic effects in an array of N **qubits** (two-level systems) incorporated into a low-dissipation resonant cavity. Individual **qubits** are characterized by energy level differences $\Delta_i$ and we take into account a spread of parameters $\Delta_i$. Non-interacting **qubits** display coherent quantum beatings with N different **frequencies**, i.e. $\omega_i=\Delta_i/\hbar$ . Virtual emission and absorption of cavity photons provides a long-range interaction between **qubits**. In the presence of such interaction we analyze quantum correlation functions of individual **qubits** $C_i(t)$ to obtain two collective quantum-mechanical coherent **oscillations**, characterized by **frequencies** $\omega_1=\bar{\Delta}/\hbar$ and $\omega_2=\tilde{\omega}_R$, where $\tilde{\omega}_R$ is the resonant **frequency** of the cavity renormalized by interaction. The amplitude of these **oscillations** can be strongly enhanced in the resonant case when $\omega_1 \simeq \omega_2$.

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