### 23555 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...**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** circuit, we extract **frequency** splitting features analogous ...**qubit** (Cooper-pair box coupled) to an RLC **oscillator** model is performed... **qubit**. In addition, **qubit** is constantly driven by a microwave field at...The... / C q ....**qubit**, characterisation, **frequency** spectrum...weakly in the **qubit** PSD. Likewise the **qubit** Rabi frequency is found to...**frequency**. Therefore, it is possible to probe the **qubit** energy level structure...but only weakly in the qubit PSD. Likewise the qubit Rabi frequency is...**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 coupled to a many level harmonic oscillator, investigated for... the qubit PSD. Likewise the qubit Rabi frequency is found to be stronger...**oscillator** cycles. Then the **oscillator** and **qubit** charge expectation values.......stronger in the **qubit** PSD. However it is important to note** that** the **qubit**...**frequency** (3.06GHz) bias **oscillator**. This higher **frequency** bias field ...**qubit**, characterisation, frequency spectrum...**frequency** bias **oscillator** of 3.06GHz.... the qubit PSD. However **it **is important to note that the qubit dynamics...**qubit** energy levels, with one and two photon transitions (3.49GHz and ...**oscillator** period, note that γ differs for the two bias **oscillator** **frequencies** ... 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

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: Chirolli, Luca, Burkard, Guido

Date: 2009-06-04

**qubit** in the state "0" vs driving time τ 1 and τ 2 , at Rabi **frequency**...**qubit** states $|0>$ and $|1>$ during measurements. Our theory can be applied...**qubit** state is extracted from the **oscillator** measurement outcomes, and...**qubit**-shifted **frequencies**, Δ ω ≈ ± g . For weak driving amplitude f , ...**oscillator** **frequency** ω h o , the state of the **qubit** is encoded in the ...**oscillator** driving amplitude is f / 2 π = 20 ~ G H z and a damping rate...**qubit** in the state | 0 0 | . Correction in Δ t are up to second order....**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...**qubit** states | 0 and | 1 , are represented for illustrative purposes by...**qubit**-dependent "position" x s are shown in the top panel. Fig2... the **qubit** QND measurement is studied in** the **regime of strong projective ...**qubit**-split **frequencies**, that is enhanced when the driving strength f ...**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...two **qubit** states produce opposite magnetic field that translate into **a qub**...**qubit**-shifted **frequencies**, the probability has a two-peak structure whose...**qubits** coupled to a circuit **oscillator**....**oscillator**, and (ii) quantum tunneling between the **qubit** states $|0>$ ...**qubit** driving time τ 1 and τ 2 starting with the **qubit** in the state | ...**qubit** coupled to a harmonic oscillator...the effect of **qubit** relaxation and **qubit** tunneling on** the **conditional ... 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: 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

i n ≈ 4 , qubit lifetimes are relatively large across** the **full qubit ...**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...a) Relative **qubit** anharmonicity** α r **versus **qubit** frequency ω 01 / 2 π ...is** the **qubit junction critical current, with** the **phase difference across the...**qubit** anharmonicity α r versus **qubit** **frequency** ω 01 / 2 π (design A )....**qubit** inductively coupled to a single-mode, resonant cavity with a tunable...minima....QB...**qubit** **frequency** change both Δ 01 and the ** qubit’s** anharmonicity α . In ...

**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**...measure of the

**qubit**anharmonicity as shown later in Fig. Fig9....

**phase**

**qubit**(design A ) remains stable enough for operation (see text)...

**qubit**

**frequencies**. In order to capture the maximum dispersive

**frequency**...

**qubit**, and residual bus coupling for a system with multiple

**qubits**. With...

**qubit**evolutions and optimize state readout during

**qubit**measurements....

**frequency**of f c m a x = 7.07 GHz while sweeping the

**qubit**flux bias ...

**oscillation**decay time of T ' = 409 ns. (c) Ramsey

**oscillations**versus...

**oscillations**gave T ' = 727 ns, a separate measurement of

**qubit**energy...the

**qubit**flux bias is swept. Two different data sets (with the

**qubit**... GHz while sweeping

**the**qubit flux bias φ q . In

**both**cases, when the ...

**frequency**provides a way to strongly vary both the

**qubit**-cavity detuning...cavity (

**qubit**) (see text)....

**frequency**that allows for both microwave readout of tunneling and dispersive...resultant flux coupling of

**the**qubit bias coil, M q

**B**= 10.9 pH. The ... 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: Serban, I., Solano, E., Wilhelm, F. K.

Date: 2007-02-28

between qubit and oscillator. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and... seen by the qubit. The dephasing rate is also expected to diverge. The...**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...through the qubit loop is Φ q and through the SQUID is Φ S .... of a qubit with one Josephson junction (phase γ , capacitance C q and...**qubit** quadratically coupled to its detector, a damped harmonic **oscillator**...effect after the qubit and the oscillator become entangled. The dephasing...**qubit** and **oscillator**. We also show that the pointer becomes measurable...states of the qubit split already during the transient motion of p ̂ t...**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...different qubit states (c). Here ℏ Ω / k B T = 2 , Δ / Ω = 0.45 , κ / ... we later approximate the qubit as a two-level system. The qubit used ...**qubits**...**oscillator** has the **frequency** Ω because it has not yet "seen" the **qubit**...about the qubit state, and has the advantage of avoiding decoeherence ... 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: Ginossar, Eran, Bishop, Lev S., Girvin, S. M.

Date: 2012-07-19

**qubit** state measurement in circuit quantum electrodynamics...**qubit** and cavity are on resonance or far off-resonance (dispersive)....superconducting transmon qubits...**frequency** and amplitude. The region of bifurcation...**oscillator** with its set of transition **frequencies** depending on the state...**qubit** and cavity are strongly coupled. We focus on the parameter ranges...**qubit** decay** . **T 1** . **has** . **distinct influence on** the **lifetime of** the **QCS...**qubit** quantum state discrimination and we present initial results for ...**frequency**).... 4 transmon qubits transmonat 7.0** . **7.5** . **8.0** . **12.3** . **H z** . **All qubits...**oscillator**...**qubits** in the circuit quantum electrodynamics architecture, where the ...**oscillator** and we analyze the quantum and semi-classical dynamics. One...**oscillator** (Duffing **oscillator**) Duffing **oscillator**, constructed by making... the **qubit** is detuned from** the **cavity** . **ω q** . **ω c** . **2 π** . **2 g ). It is...disruptive to the **qubit** state and it is realized where** the **cavity and ... **qubit** (Fig. gino:chirp_figure). This selective dynamical mapping of** th**...**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...one **qubit**, see Fig. gino:fig:return. Such an asymmetric **qubit** dependent...**qubit** **frequency**. (c) Wave packet snapshots at selected times (indicated...anharmonic transmon....the **qubit** being detuned. Due to the interaction with the **qubit**, the cavity...**frequency** of panel (b) conditioned on the initial state of the **qubit**. ...**qubit** state q : (a) for the JC model, parameters as in Figs. gino:fig ... 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: Yoshihara, Fumiki, Nakamura, Yasunobu, Yan, Fei, Gustavsson, Simon, Bylander, Jonas, Oliver, William D., Tsai, Jaw-Shen

Date: 2014-02-06

**oscillation**, $1/f$ noise...parallel to the qubit’s energy eigenbasis; this component is not averaged...**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...

**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...

**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...

**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 ...

**qubit**by studying the decay of Rabi oscillations under strong driving ...the qubit followed by a readout pulse, and P s w as a function of the ...to the qubit followed by a readout pulse, and P s w as a function of the... qubit by a mutual inductance of 1.2 pH and nominally cooled to 35 mK....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: 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...**the** **second** **qubit**. The fidelity is extracted by injecting these unitaries...two-**qubit** operations in circuit QED. ϵ is the strength of the drive used...**qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how...anticrossings in the qubit-resonator or qubit-qubit spectrum. They are...**qubit** or the resonator, with the significant disadvantage that such implementations...of the fidelity on qubit relaxation and dephasing is similar....**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...two-**qubit** operations in circuit QED. ϵ is **the** strength of **the** drive used...**qubit** frequency modulation...**oscillators** (see Section sec:Duffing) with E J 1 = 25 GHz, E J 2 = 35...**qubit** splitting is modulated at a **frequency** that lies exactly between ...**frequency** associated to the operating point φ i . This **frequency** is illustrated...coming from the spectator qubit (see Section sec:SB)....prepare qubit-qubit entangled states. The parameters of every pulses entering...**qubits** and microwave resonators. Up to now, these transitions have been...**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 ...**eqn**:trace). The qubits are taken to be transmons, which are modelled as...**oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can...**oscillations** in the Rabi **oscillations** that reduce the fidelity. These ...**qubit** transition **frequencies** in and out of resonance without crossing ...**second** **qubit** is excited. Blue dashed line: population transfer error 1...**qubit** at **the** red sideband frequency assuming **the** **second** **qubit** is in its ... 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: Zorin, A. B.

Date: 2003-12-09

**qubit** state with the rf oscillation span ± π / 2 is preferable in either...**frequency** ω r f ≈ ω 0 , the resonant **frequency** of the uncoupled tank circuit...**frequency** ω 0 = 2 π × 100 MHz, L T / C T 1 / 2 = 100 Ω , k 2 Q β L = ...lines). The **qubit** parameters are the same as in Fig. 2....**qubit** state with the rf **oscillation** span ± π / 2 is preferable in either...radio-**frequency** readout of the **qubit**. (a) The resonance curves of the ...**qubit** based on a superconducting single charge transistor inserted in ...states of the **qubit**....**given** **qubit** parameters (see caption of Fig. 2)....**qubit** whose value, as well as the produced **frequency** shift δ ω 0 , is ...The **qubit** is controlled by charge Q 0 generated by the gate and flux Φ...charge-flux **qubit** are characterized by self-capacitances C 1 and C 2 and...**oscillations** induced in the **qubit**. Recently, we proposed a transistor ...**frequency** of these **oscillations** is sufficiently low, ω r f ≪ Ω , they ...**qubit** whose value, as well as the produced frequency shift δ ω 0 , is ...**e for** the **given** **qubit** parameters (see caption of Fig. 2)....**qubit** dephasing and relaxation due to electric and magnetic control lines...**qubit** states by measuring the effective Josephson inductance of the transistor...**qubit** dephasing is of minor importance, while the requirement of a sufficiently...**qubit** in magic points producing minimum decoherence are given....**qubit** parameters are the same as in Fig. 2....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...**frequency** Ω . Increase in amplitude of steady **oscillations** up to φ a ≈...**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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Contributors: Kim, Mun Dae

Date: 2008-09-02

**oscillating** field it is shown that the high fidelity of the CNOT gate ... qubits. (b) Occupation probabilities of | ρ ρ ' states during Rabi-type...coupled-**qubit** states with the initial state, | ψ 0 = | 00 + | 10 / 2 for...**Qubits**...two-**qubit** **oscillation** deviates seriously from the Rabi **oscillation** and...**oscillations** of occupation probability of coupled-**qubit** states with the...**oscillating** field amplitude for any given values of **qubit** energy gap and...**oscillation**. Here, the unit of all numbers is GHz....**qubit** energy gap ω 0 . For small ω 0 and large J the **oscillations** are ... **qubit** energy gap ω 0 / 2 π =4GHz, and Rabi frequency Ω 0 / 2 π = 600 ...that the target qubit flips for a specific state of control qubit such...**oscillating** field with the resonant **frequency** ω = ω 0 < ω 1 ....values of qubit energy gap and coupling strength between qubits. While... qubits, where ρ , ρ ' ∈ 0 1 . E s s ' with s , s ' ∈ are shown as thin...coupled-**qubit** oscillation driven by an oscillating field. When the period...**qubit** energy gap ω 0 . For small ω 0 and large J the oscillations are ...**qubit** energy gap ω 0 / 2 π =4GHz, and Rabi **frequency** Ω 0 / 2 π = 600 MHz...coupled-**qubit** **oscillation** driven by an **oscillating** field. When the period...**qubit** energy gap in experiments....**oscillation** for strongly coupled **qubits**. While the P 00 ( P 01 ) is reversed...**oscillation**, we show that the controlled-NOT (CNOT) gate operation can...two-qubit oscillation deviates seriously from the Rabi oscillation and...**oscillations**, while for a sufficiently strong coupling it can be done ...**qubits**, where ρ , ρ ' ∈ 0 1 . E s s ' with s , s ' ∈ are shown as thin...to shift the qubits slightly away from the degeneracy point to detect ... We study the coupled-**qubit** **oscillation** driven by an **oscillating** field. When the period of the non-resonant mode is commensurate with that of the resonant mode of the Rabi **oscillation**, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate **oscillations**, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of **oscillating** field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and **qubit** energy gap in experiments.

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