### 23045 results for qubit oscillator frequency

Contributors: Griffith, E. J., Ralph, J. F., Greentree, Andrew D., Clark, T. D.

Date: 2005-10-04

**qubit** PSD. Likewise the **qubit** Rabi frequency is found to be stronger in...**frequency** **oscillator** ( f o s c = 3.06 GHz) near the **qubit** and microwave...**qubit** PSD. Likewise the **qubit** Rabi **frequency** is found to be stronger in...**oscillator** as a probe through the backreaction effect of the **qubit** on ...**oscillator** **frequency**....**qubit** (Cooper-pair box coupled) to an RLC oscillator model is performed...**qubit** on the oscillator circuit, we extract frequency splitting features...**oscillator** cycles. Then the **oscillator** and **qubit** charge expec...**oscillator** circuit, we extract **frequency** splitting features analogous ...**qubit**. In addition, **qubit** is constantly driven by a microwave field at...**qubit** PSD. However it is important to note that the **qubit** dynamics such...**qubit** (Cooper-pair box coupled) to an RLC **oscillator** model is performed...**qubit** transition frequency ( f q u b i t ≈ 3.49GHz) and the diagonally...**qubit**, characterisation, **frequency** spectrum...**qubit** geometry is transformed to a classical electrical circuit model ...**frequency**. Therefore, it is possible to probe the **qubit** energy level structure...**qubit** characterization and coupling schemes. In addition we find this ...**oscillator** **frequencies**, (1.36GHz and 3.06GHz)....**oscillator** energies. Firstly, the **oscillator** resonant **frequency** is set...**frequency** **oscillator** of 3.06GHz which can excite this **qubit**. In addition...**qubit** is driven at f m w = 5.00 GHz. An increase in bias noise power (...**qubit** energy level structure by using the power increase in the oscillator...**oscillator** spectrum. We also observe a **frequency** splitting when the **qubit**...**qubit**, characterisation, frequency spectrum...**qubit** capacitances C J and C g , (the Josephson junction capacitance and ... A theoretical spectroscopic analysis of a microwave driven superconducting charge **qubit** (Cooper-pair box coupled) to an RLC **oscillator** model is performed. By treating the **oscillator** as a probe through the backreaction effect of the **qubit** on the **oscillator** circuit, we extract **frequency** splitting features analogous to the Autler-Townes effect from quantum optics, thereby extending the analogies between superconducting and quantum optical phenomenology. These features are found in a **frequency** band that avoids the need for high **frequency** measurement systems and therefore may be of use in **qubit** characterization and coupling schemes. In addition we find this **frequency** band can be adjusted to suit an experimental **frequency** regime by changing the **oscillator** **frequency**.

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

Date: 2006-06-02

two-**qubit** crosstalk....**qubits**. The damped **oscillations** of the superconducting phase after the...**qubit** as a harmonic **oscillator**. However, to analyze the measurement error...**qubits**. The damped oscillations of the superconducting phase after the...second-**qubit** energy E 2 t in the classical model taking into account energy...**qubit** (Fig. f9) shortens significantly the time interval during which...**oscillations** in the “right” well. This dissipative evolution leads to ...**qubit** is treated both classically and quantum-mechanically. The results...**qubit** potential is used; energy relaxation in the second **qubit** is neglected...two-**qubit** imaginary-swap quantum gate....**frequency** of the two-**qubit** imaginary-swap quantum gate....**qubits**....**qubit** may be to a much lower energy than for the **oscillator**; (c) After...**frequency** f d increase, while it starts to decrease at t > 0.52 T 1 (after...**qubit**, which is highly excited after the measurement, is described classically...two-**qubit** operations) for a given tolerable value of the measurement error...**qubit** excitation (though still almost without switching) between 3 ns ...**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...**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 ...**qubit** energy in the ground state ≈ ℏ ω l 2 / 2 . Even though the mean ...**frequency** f d of the driving force (Fig. f3) which passes through the...**qubit** may significantly excite the second **qubit**, leading to its measurement...**qubit**. The dashed line in Fig. f8 shows C x , T T 1 dependence in the...**qubits**...**qubit** energy for the same parameters (Fig. f7'), we see that the two ... 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: Chirolli, Luca, Burkard, Guido

Date: 2009-06-04

**qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied...**qubit** in the state "0" vs driving time τ 1 and τ 2 , at Rabi **frequency**...**qubit** surrounded by a SQUID. b) Measurement scheme: b1) two short pulses...**qubit** state is extracted from the **oscillator** measurement outcomes, and...**qubit**-shifted **frequencies**, Δ ω ≈ ± g . For weak driving amplitude f , ...**oscillator** driving amplitude is f / 2 π = 20 ~ G H z and a damping rate...**qubit** QND measurement is studied in the regime of strong projective **qubit**...**qubit** current states is made small compared to the **qubit** gap E = ϵ 2 +...**qubit** is coupled to a harmonic oscillator which undergoes a projective...**oscillator** at resonance with the bare harmonic **frequency**, Δ ω = 0 . The...**qubit**-dependent "position" x s are shown in the top panel. Fig2...**qubit**-split **frequencies**, that is enhanced when the driving strength f ...**qubit** in a generic state. Here, ϵ and Δ represent the energy difference...**frequency** ϵ 2 + Δ 2 , before and between two measurements prepare the ...**qubit**-shifted **frequency**....**qubit** state is extracted from the oscillator measurement outcomes, and...**qubit** measurement. Two mechanisms lead to deviations from a perfect QND...**oscillator** to a **qubit**-dependent state. c) Perfect QND: conditional probability...**qubit** turns out to be quadratic. The **qubit** Hamiltonian is H S = ϵ σ Z ...**qubit** is coupled to a harmonic **oscillator** which undergoes a projective...**oscillator** is driven at resonance with the bare harmonic **frequency** and...**qubit** relaxation time T 1 = 10 ~ n s is assumed. Fig1...**qubit**) and quantify the degree to which such a **qubit** measurement has a...**qubit**-shifted **frequencies**, the probability has a two-peak structure whose...**qubits** coupled to a circuit **oscillator**....**qubit** state and measurement outcomes and a weak **qubit** measurement....**oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ ...**qubit**-dependent....**qubit** driving time τ 1 and τ 2 starting with the **qubit** in the state | ...**qubit** coupled to a harmonic oscillator ... We theoretically describe the weak measurement of a two-level system (**qubit**) and quantify the degree to which such a **qubit** measurement has a quantum non-demolition (QND) character. The **qubit** is coupled to a harmonic **oscillator** which undergoes a projective measurement. Information on the **qubit** state is extracted from the **oscillator** measurement outcomes, and the QND character of the measurement is inferred by the result of subsequent measurements of the **oscillator**. We use the positive operator valued measure (POVM) formalism to describe the **qubit** measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the **oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied to QND measurements performed on superconducting **qubits** coupled to a circuit **oscillator**.

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Contributors: Serban, I., Solano, E., Wilhelm, F. K.

Date: 2007-02-28

**qubit** initially in the state 1 / 2 | ↑ + | ↓ the probability distribution...**qubit**. The dephasing rate is also expected to diverge. The peaks at Ω ...**qubit** split already during the transient motion of p ̂ t , much faster...**qubit** has been lost....**qubit** and **oscillator** or between **oscillator** and bath, corrections of the...**qubit** and the oscillator by means of their full Floquet state master equations...**qubit** and **oscillator**. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and ℏ ν / k...**qubit** quadratically coupled to its detector, a damped harmonic **oscillator**...**qubit** and oscillator. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and ℏ ν / k...**qubit** and **oscillator**. We also show that the pointer becomes measurable...**qubit** drawn in the single junction version, the surrounding SQUID loop...**qubit** quadratically coupled to its detector, a damped harmonic oscillator...**qubit** with one Josephson junction (phase γ , capacitance C q and inductance...**qubit** and the **oscillator** by means of their full Floquet state master equations...**frequency** is at resonance with the harmonic **oscillator** — we have a continuum...**qubit** loop is Φ q and through the SQUID is Φ S ....**qubit** and oscillator. We also show that the pointer becomes measurable...**qubit** and the **oscillator** become entangled. The dephasing rate drops again...**frequencies** to the value obtained in the case without driving....**frequency** ν for different vales of κ ( Δ / Ω = 0.5 ). Here ℏ Ω / k B T...**qubit** states (c). Here ℏ Ω / k B T = 2 , Δ / Ω = 0.45 , κ / Ω = 0.025 ...**qubit** and explore several measurement protocols, which include a long-term...**qubit** as a two-level system. The **qubit** used in the actual experiment contains...**qubits**...**oscillator** has the **frequency** Ω because it has not yet "seen" the **qubit** ... Motivated by recent experiments, we study the dynamics of a **qubit** quadratically coupled to its detector, a damped harmonic **oscillator**. We use a complex-environment approach, explicitly describing the dynamics of the **qubit** and the **oscillator** by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured **qubit** and explore several measurement protocols, which include a long-term full read-out cycle as well as schemes based on short time transfer of information between **qubit** and **oscillator**. We also show that the pointer becomes measurable before all information in the **qubit** has been lost.

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Contributors: Beaudoin, Félix, da Silva, Marcus P., Dutton, Zachary, Blais, Alexandre

Date: 2012-08-09

**qubits** have **frequencies** separated enough that they do not overlap during...**qubit**-resonator or **qubit**-**qubit** spectrum. They are typically ver...**frequency** associated to the operating point φ i . This **frequency** is illustrated...two-**qubit** operations in circuit QED. ϵ is the strength of the drive used...**qubit**. The fidelity is extracted by injecting these unitaries in Eq. (...**qubit**-**qubit** entangled states. The parameters of every pulses entering ...**qubit** relaxation and dephasing is similar....**qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how...**qubit** (see Section sec:SB)....**qubits** and microwave resonators. Up to now, these transitions have been...**qubit** or the resonator, with the significant disadvantage that such implementations...**qubit** frequency using a flux-bias line. Not only can first-order transitions...**oscillations** have been seen to be especially large for big relevant ε ...**oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can...**oscillator** with **frequency** ω r = 7.8 GHz. As explained in Section sec:...**qubit** at the red sideband **frequency** assuming the second **qubit** is in its...**oscillations** in the Rabi **oscillations** that reduce the fidelity. These ...**qubit** transition **frequencies** in and out of resonance without crossing ...**qubit** frequency modulation...**oscillators** (see Section sec:Duffing) with E J 1 = 25 GHz, E J 2 = 35...**qubit** at the red sideband frequency assuming the second **qubit** is in its...**qubit** is excited. Blue dashed line: population transfer error 1 - P t ...**qubits** have frequencies separated enough that they do not overlap during...**qubit** splitting is modulated at a **frequency** that lies exactly between ... Sideband transitions have been shown to generate controllable interaction between superconducting **qubits** and microwave resonators. Up to now, these transitions have been implemented with voltage drives on the **qubit** or the resonator, with the significant disadvantage that such implementations only lead to second-order sideband transitions. Here we propose an approach to achieve first-order sideband transitions by relying on controlled **oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can first-order transitions be significantly faster, but the same technique can be employed to implement other tunable **qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how such first-order sideband transitions can be used to implement a high fidelity controlled-NOT operation between two transmons coupled to the same resonator.

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Contributors: Yoshihara, Fumiki, Nakamura, Yasunobu, Yan, Fei, Gustavsson, Simon, Bylander, Jonas, Oliver, William D., Tsai, Jaw-Shen

Date: 2014-02-06

**oscillation**, $1/f$ noise...**oscillation** curves with different Rabi **frequencies** Ω R measured at different...** qubit’s** energy eigenbasis; this component is not averaged out when Ω R...

**frequency**δ ω (black open circles) and the Bloch–Siegert shift δ ω B S...

**qubit**'s level splitting of 4.8 GHz, a regime where the rotating-wave approximation...

**oscillations**due to quasistatic flux noise. “Optimal" in the last column...

**qubit**’s energy eigenbasis; this component is not averaged out when Ω R...

**oscillation**measurements, a microwave pulse is applied to the

**qubit**followed...

**oscillation**decay at ε = 0 , where the quasistatic noise contribution ...

**qubit**noise spectroscopy using Rabi oscillations under strong driving ...

**qubit**and its strong inductive coupling to a microwave line enabled high-amplitude...

**frequency**of ω m w / 2 π = 6.1 GHz, has a minimum of approximately ω ...

**frequency**range decreases with increasing

**frequency**up to 300 MHz, where...

**qubit**followed by a readout pulse, and P s w as a function of the microwave...

**frequencies**up to 1.7 GHz were achieved, approaching the

**qubit**'s level...

**frequency**Ω R 0 at the shifted resonance decreases as ε increases, while...

**qubit**by studying the decay of Rabi oscillations under strong driving ...

**frequency**, and cal: Γ R s t δ ω m w stands for the calculation to study...

**oscillations**under strong driving conditions. The large anharmonicity ...high-

**frequency**flux noise spectrum in a superconducting flux

**qubit**by ...

**qubit**by a mutual inductance of 1.2 pH and nominally cooled to 35 mK. ... We infer the high-

**frequency**flux noise spectrum in a superconducting flux

**qubit**by studying the decay of Rabi

**oscillations**under strong driving conditions. The large anharmonicity of the

**qubit**and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi

**frequencies**up to 1.7 GHz were achieved, approaching the

**qubit**'s level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide

**frequency**range decreases with increasing

**frequency**up to 300 MHz, where the spectral density is not very far from the extrapolation of the 1/f spectrum obtained from the free-induction-decay measurements. We discuss a possible origin of the flux noise due to surface electron spins.

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Contributors: Ginossar, Eran, Bishop, Lev S., Girvin, S. M.

Date: 2012-07-19

**qubit**, see Fig. gino:fig:return. Such an asymmetric **qubit** dependent response...**qubit** state measurement in circuit quantum electrodynamics...**qubit** and cavity are on resonance or far off-resonance (dispersive)....**oscillator** with its set of transition **frequencies** depending on the state...**qubit** and cavity are strongly coupled. We focus on the parameter ranges...**qubit** is detuned from the cavity ( ω q - ω c / 2 π ≈ 2 g ). It is followed...**qubit** frequency. (c) Wave packet snapshots at selected times (indicated...**qubit** quantum state discrimination and we present initial results for ...**qubit** state and it is realized where the cavity and **qubit** are strongly...**frequency**)....**oscillator**...**qubits** in the circuit quantum electrodynamics architecture, where the ...**qubit**. (d) The temporal evolution of the reduced density matrix | ρ m ...**qubit**, it is necessary to solve the coherent control problem...**oscillator** and we analyze the quantum and semi-classical dynamics. One...**oscillator** (Duffing **oscillator**) Duffing **oscillator**, constructed by making...**frequency**. For (b), if the state of one (‘spectator’) **qubit** is held constant...**frequency** response bifurcates, and the JC **oscillator** enters a region of...**frequency** and amplitude. Despite the presence of 4 **qubits** in the device...**qubit**; (c) for the model extended to one transmon **qubit** koch charge-insensitive...**qubit** **frequency**. (c) Wave packet snapshots at selected times (indicated...**qubit** being detuned. Due to the interaction with the **qubit**, the cavity...**qubits**...**frequency** of panel (b) conditioned on the initial state of the **qubit**. ...**qubit** decay times ( T 1 ), including a very long T 1 = 15 μ s indicating ... In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the **qubit** and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon **qubits** in the circuit quantum electrodynamics architecture, where the system behaves essentially as a nonlinear quantum **oscillator** and we analyze the quantum and semi-classical dynamics. One of the central motivations is that under strong excitation tones, the nonlinear response can lead to **qubit** quantum state discrimination and we present initial results for the cases when the **qubit** and cavity are on resonance or far off-resonance (dispersive).

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Contributors: Whittaker, J. D., da Silva, F. C. S., Allman, M. S., Lecocq, F., Cicak, K., Sirois, A. J., Teufel, J. D., Aumentado, J., Simmonds, R. W.

Date: 2014-08-08

**qubit** lifetimes are relatively large across the full **qubit** spectrum with...**Qubits**...**oscillations** for **frequencies** near f 01 = 7.38 GHz. (b) Line-cut on-resonance...**qubit** anharmonicity, **qubit**-cavity coupling and detuning. A tunable cavity...**qubit** inductively coupled to a single-mode, resonant cavity with a tunable...**qubit** anharmonicity α r versus **qubit** **frequency** ω 01 / 2 π (design A )....**qubit** flux bias is swept. Two different data sets (with the **qubit** reset...**qubit** far detuned, biased at its maximum **frequency**. The solid line is ...**qubit** and cavity **frequencies** and the dashed lines show the new coupled...**qubits**....**qubit** **frequency**, at f 01 = 7.98 GHz, Ramsey **oscillations** gave T 2 * = ...**qubit**-cavity system, we show that dynamic control over the cavity **frequency**...**qubit** anharmonicity as shown later in Fig. Fig9....**qubit** **frequencies**. In order to capture the maximum dispersive **frequency**...**qubit**, and residual bus coupling for a system with multiple **qubits**. With...**qubit** anharmonicity α r versus **qubit** frequency ω 01 / 2 π (design A )....**qubit** evolutions and optimize state readout during **qubit** measurements....**oscillation** decay time of T ' = 409 ns. (c) Ramsey **oscillations** versus...**qubit** is ...**qubit**) (see text)....**qubit** **frequenc**...**qubit** spectrum....**oscillations** gave T ' = 727 ns, a separate measurement of **qubit** energy...**frequency**, f c min ≈ 4.8 GHz. Notice in Fig. Fig6(a) that Rabi **oscillations**...**frequency** provides a way to strongly vary both the **qubit**-cavity detuning...**frequency** that allows for both microwave readout of tunneling and dispersive...**qubit** for various frequencies in order to excite the **qubit** transitions...**qubit** frequency change both Δ 01 and the **qubit**’s anharmonicity α . In ...**qubit** flux detuning near f 01 = 7.38 GHz. (d) Line-cut along the dashed ... We describe a tunable-cavity QED architecture with an rf SQUID phase **qubit** inductively coupled to a single-mode, resonant cavity with a tunable **frequency** that allows for both microwave readout of tunneling and dispersive measurements of the **qubit**. Dispersive measurement is well characterized by a three-level model, strongly dependent on **qubit** anharmonicity, **qubit**-cavity coupling and detuning. A tunable cavity **frequency** provides a way to strongly vary both the **qubit**-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the **qubit**, and residual bus coupling for a system with multiple **qubits**. With our **qubit**-cavity system, we show that dynamic control over the cavity **frequency** enables one to avoid Purcell losses during coherent **qubit** evolutions and optimize state readout during **qubit** measurements. The maximum **qubit** decay time $T_1$ = 1.5 $\mu$s is found to be limited by surface dielectric losses from a design geometry similar to planar transmon **qubits**.

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Contributors: Wei, L. F., Liu, Yu-xi, Nori, Franco

Date: 2004-02-27

**qubits** without direct interaction can be effectively coupled by sequentially...**oscillator** with adjustable **frequency**. The coupling between any **qubit** and...**qubits**, located on the left of the dashed line, coupled to a large CBJJ...**qubit**-bus system. Here, C g k and 2 ε J k are the gate capacitance and...**qubit** and the bus can be controlled by modulating the magnetic flux applied...**qubits** and the bus. The dashed line only indicates a separation between...**qubit**. ζ k is the maximum strength of the coupling between the k th **qubit**...**qubits** via a current-biased information bus...**frequency** ω b . The detuning between the **qubit** and the bus energies is...**qubit** and the bus energies is ℏ Δ k = ε k - ℏ ω b . n = 0 , 1 is occupation...**qubit**. This tunable and selective coupling provides two-**qubit** entangled ... Josephson **qubits** without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an **oscillator** with adjustable **frequency**. The coupling between any **qubit** and the bus can be controlled by modulating the magnetic flux applied to that **qubit**. This tunable and selective coupling provides two-**qubit** entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality.

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Contributors: Zorin, A. B.

Date: 2003-12-09

**frequency** ω r f ≈ ω 0 , the resonant **frequency** of the uncoupled tank circuit...**qubit** by Duty et al. . Their Al Cooper pair box had E c ≈ 0.8 Δ s c and...**frequency** ω 0 = 2 π × 100 MHz, L T / C T 1 / 2 = 100 Ω , k 2 Q β L = ...**qubit** state with the rf **oscillation** span ± π / 2 is preferable in either...**qubit** based on a superconducting single charge transistor inserted in ...radio-**frequency** readout of the **qubit**. (a) The resonance curves of the ...**qubit** whose value, as well as the produced **frequency** shift δ ω 0 , is ...**qubit** operation. In this basis, the Hamiltonian ( H0) is diagonal,...**oscillations** induced in the **qubit**. Recently, we proposed a transistor ...**qubit**. Another useful quantity is the Josephson inductance of the double...**frequency** of these **oscillations** is sufficiently low, ω r f ≪ Ω , they ...**qubit** dephasing and relaxation due to electric and magnetic control lines...**qubit** states by measuring the effective Josephson inductance of the transistor...**qubit**. Recently, we proposed a transistor configuration of the Cooper ...**qubit** in magic points producing minimum decoherence are given....**qubit** parameters are the same as in Fig. 2....**qubit** inductively coupled to a tank circuit by mutual inductance M . The...radio-**frequency** driven tank circuit enabling the readout of the **qubit** ...**qubit** calculated for the mean Josephson coupling E J 0 ≡ 1 2 E J 1 + E...**qubit** parameters (see caption of Fig. 2)....**frequency** Ω . Increase in amplitude of steady **oscillations** up to φ a ≈...**qubit** parameters (see caption of Fig. 2)....**qubit**....**oscillations** and has a small effect on the rise time of the response signal...**qubit** with radio frequency readout: coupling and decoherence ... The charge-phase Josephson **qubit** based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-**frequency** driven tank circuit enabling the readout of the **qubit** states by measuring the effective Josephson inductance of the transistor. The effect of **qubit** dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the **qubit** in magic points producing minimum decoherence are given.

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