### 63089 results for qubit oscillator frequency

Contributors: Fedorov, Kirill G., Shcherbakova, Anastasia V., Schäfer, Roland, Ustinov, Alexey V.

Date: 2013-01-22

flux qubit....through** the **qubit corresponds to** the **changing of** the **persistent currents i...embracing a flux qubit, as shown in Fig. AJJ+Qubit. The current induced...the** flux** qubit with a coupling loop (yellow loop) and control line (green...**frequency** versus magnetic flux through the **qubit** corresponds to the changing... the qubit corresponds to** the **changing of** the **persistent currents in the...**oscillations**, we have performed systematic measurements of the dependence...**frequency** deviation from equilibrium δ ν / ν 0 of the fluxon **oscillation**...**qubit** as a current dipole to the annular junction, we detect periodic ...the** flux** qubit loop....the flux qubit....**oscillation** **frequency** from the unperturbed case δ ν = ν μ - ν 0 , where...**qubit**...**qubit**, **qubit** readout...**qubit**. The time delay of the fluxon can be detected as a **frequency** shift...**oscillation** **frequency** due to the coupling to the flux **qubit**. Every point...current in** the **flux qubit. Thus, the persistent current in** the **qubit manifests...flux qubit. Every point consists of 100 averages. Bias current was set...**frequency** versus bias current. Black line shows the result of perturbation...**oscillation** **frequency** for μ = 0 . Black line in Fig. FD shows the dependence...flux qubit versus magnetic frustration (black line). Red line shows the...**qubits** by using ballistic Josephson vortices are reported. We measured...**qubit**. We found that the scattering of a fluxon on a current dipole can...**oscillation** **frequency** versus magnetic flux through the **qubit**. We found...**qubit** loop....**qubit**. ... Experiments towards realizing a readout of superconducting **qubits** by using ballistic Josephson vortices are reported. We measured the microwave radiation induced by a fluxon moving in an annular Josephson junction. By coupling a flux **qubit** as a current dipole to the annular junction, we detect periodic variations of the fluxon's **oscillation** **frequency** versus magnetic flux through the **qubit**. We found that the scattering of a fluxon on a current dipole can lead to the acceleration of a fluxon regardless of a dipole polarity. We use the perturbation theory and numerical simulations of the perturbed sine-Gordon equation to analyze our results.

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Contributors: Saito, Keiji, Wubs, Martijn, Kohler, Sigmund, Hanggi, Peter, Kayanuma, Yosuke

Date: 2006-03-07

**qubit** and the oscillator, and can be written as...**qubit**, being independent of the frequency of the QED mode. Possible applications...**qubit** flip, the resulting dynamics is restricted to the states | ↑ , 2...**qubit** and the **oscillator**, and can be written as...**frequencies** Ω . The dashed line marks the Ω -independent, final probability...individual qubit-oscillator states for a coupling strength γ = 0.6 ℏ v...large **qubit**-oscillator coupling γ / ℏ Ω = 0.5 , reliable single-photon...**frequency** Ω = 0.5 v / ℏ ....**oscillator** **frequency**, P ↑ ↓ t resembles the standard LZ transition with...**frequency** Ω and the **qubit**-**oscillator** coupling γ are determined by the ...**qubit**, being independent of the **frequency** of the QED mode. Possible applications...**qubit**-**oscillator** entanglement....**qubit**-**oscillator** states for a coupling strength γ = 0.6 ℏ v and **oscillator**...**qubit** comes into resonance with the **oscillator** sometime during the sweep...**qubit** undergoing Landau-Zener transitions enabled by the coupling to a...**oscillator** **frequency** Ω , despite the fact that this is not the case for...**qubit** is in state | ↓ is depicted in Fig. fig:one-osc. It demonstrates...the **qubit** comes into resonance with the oscillator sometime during the...**qubit**-oscillator entanglement....**oscillations** that are typical for the tail of a LZ transition are averaged ... We study a **qubit** undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the **qubit**, being independent of the **frequency** of the QED mode. Possible applications are single-photon generation and the controllable creation of **qubit**-**oscillator** entanglement.

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Contributors: Martijn Wubs, Sigmund Kohler, Peter Hänggi

Date: 2007-10-01

**qubit** may undergo Landau–Zener transitions due to its coupling to one ...a qubit coupled to two oscillators. Parameters: γ=0.25ℏv and Ω2=100ℏv,...**qubit**–oscillator entanglement, with state-of-the-art circuit QED as a ...**qubit** are well suited for the robust creation of entangled cavity states...**qubit** that is coupled to one **oscillator**. Starting in the ground state ...**qubit** coupled to one **oscillator**, far outside the RWA regime: γ=ℏΩ=0.25ℏv...**qubit** coupled to two cavities, we show that Landau–Zener sweeps of the...**oscillator** **frequencies**, both inside and outside the regime where a rotating-wave...**qubit** coupled to two **oscillators**. Parameters: γ=0.25ℏv, ℏΩ1=90ℏv, and ...case** the **qubit would be measured |↑〉.
...**oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau–Zener... the qubit–oscillator coupling γ. Parameters: γ=0.25ℏv and ℏΩ2=100ℏv, ...**qubit** coupled to one oscillator, Landau–Zener transitions can be used ...**oscillator** if the **qubit** would be measured in state |↓〉; the dash-dotted...**qubit** coupled to two **oscillators** with degenerate energies. Parameters:...**sweep** of a qubit coupled to two oscillators with degenerate energies. ...**qubit**–**oscillator** entanglement, with state-of-the-art circuit QED as a ...LZ **sweep** of a qubit coupled to two oscillators. Parameters: γ=0.25ℏv, ... A **qubit** may undergo Landau–Zener transitions due to its coupling to one or several quantum harmonic **oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau–Zener transitions can be used for single-photon generation and for the controllable creation of **qubit**–**oscillator** entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a **qubit** coupled to two cavities, we show that Landau–Zener sweeps of the **qubit** are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the **qubit** acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau–Zener transition probability for the **qubit**, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the **oscillator** **frequencies**, both inside and outside the regime where a rotating-wave approximation is valid.

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Contributors: Greenberg, Ya. S.

Date: 2003-03-04

**oscillations** in a phase **qubit**. The external source, typically in GHz range...**qubit** states, nevertheless the voltage across the tank **oscillates** with...**qubit** coupled to a dissipative tank circuit. The evolution of A exhibits...**qubit**). We explicitly account for the back action of a tank circuit and...**oscillations** with lower **frequency**. Deterministic case (a) together with...L...destroys the phase coherence between qubit states, nevertheless the voltage...**qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit**...speaking, consider qubit as having definite wave function. However, if...P...**qubit**. The external source, typically in GHz range, induces transitions...of qubit evolution as the coupling between the qubit and the tank is increased...loss-free qubit coupled to the dissipative tank circuit. The system is...loss-free **qubit** coupled to a loss-free tank circuit. Oscillations of A...**oscillates** with a high **frequency** which is about 10 GHz in our case. As...**qubit** loop. As is seen from the Fig. fig4a, A **oscillates** with Rabi **frequency**...case....**qubit** levels. The resulting Rabi oscillations of supercurrent in the **qubit**...**qubit**. Computer simulations...**oscillations** correspond to Rabi **frequency**....**oscillates** with gap **frequency**, while the **frequency** of A is almost ten ...**oscillates** also with Rabi **frequency** which is equal to 50 MHz in our case... to show the effect of qubit evolution as the coupling between the qubit... **qubit** coupled to a dissipative tank circuit Q T = 100 . The voltage across...**qubit** coupled to a loss-free tank circuit. **Oscillations** of A. Deterministic... A and B for **qubit** without dissipation....**qubit** without dissipation....**frequency**. Deterministic case (a) together with one realization (b) are...**oscillations** in MHz range can be detected using conventional NMR pulse...**oscillations** between quantum states in mesoscopic superconducting systems...**qubit**. Here we present the results of detailed computer simulations of ... Time-domain observations of coherent **oscillations** between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a 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**. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase **qubit**). We explicitly account for the back action of a tank circuit and for the unpredictable nature of outcome of a single measurement. According to the results of our simulations the Rabi **oscillations** in MHz range can be detected using conventional NMR pulse Fourier technique.

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Contributors: Lisenfeld, Juergen, Mueller, Clemens, Cole, Jared H., Bushev, Pavel, Lukashenko, Alexander, Shnirman, Alexander, Ustinov, Alexey V.

Date: 2009-09-18

**frequencies**. Each trace was recorded after adjusting the **qubit** bias to...**frequency** while the **qubit** was kept detuned. A π pulse was applied to measure...**qubit**-fluctuator system...the **qubit** in the excited state, P t , vs. driving frequency; (b) Fourier-transform...phase **qubit** circuit. (b) Probability to measure the excited **qubit** state...**the** **qubit** was kept detuned. A π pulse was applied to measure **the** energy...**oscillations**
...**qubits** often show signatures of coherent coupling to microscopic two-level...**frequency** of 7.805 GHz (indicated by a dashed line)....**qubits**, Josephson junctions, two-level
fluctuators, microwave spectroscopy...**qubit** and fluctuator v ⊥ and to the microwave field Ω q and Ω f v ....**qubit** in the excited state, P t , vs. driving **frequency**; (b) Fourier-transform...**qubit** levels....**qubit** as and and those of the TLF as and . Arrows indicate the couplings...** qubit’s** Rabi

**frequency**Ω q / h is set to 48 MHz....

**qubit**, in which we induce Rabi oscillations by resonant microwave driving...

**oscillations**observed experimentally....

**frequency**, revealing the coupling to a two-level defect state having a...

**the**

**qubit**loop. The

**qubit**state is controlled by an externally applied...levels

**in**

**the**

**qubit**....

**qubit**, in which we induce Rabi

**oscillations**by resonant microwave driving...

**qubit**is tuned close to the resonance with an individual TLF and the Rabi...

**frequency**components.

**Frequency**and visibility of each component depend...

**qubit**relative to the TLF’s resonance

**frequency**, which is indicated in...

**qubit**transition. In this work, we studied

**the**

**qubit**interacting with ...

**qubit**above or below the fluctuator's level-splitting. Theoretical analysis...

**qubit**circuit. (b) Probability to measure the excited

**qubit**state (color-coded...

**qubit**-TLF coupling), interesting 4-level dynamics are observed. The experimental...

**frequency**of order of the

**qubit**-TLF coupling), interesting 4-level dynamics...in the

**qubit**. (As the anharmonicity Δ / h ∼ 100 MHz in our circuit is...

**the**phase

**qubit**circuit (

**the**

**qubit**subspace) and disregard

**the**longitudinal ... Superconducting

**qubits**often show signatures of coherent coupling to microscopic two-level fluctuators (TLFs), which manifest themselves as avoided level crossings in spectroscopic data. In this work we study a phase

**qubit**, in which we induce Rabi

**oscillations**by resonant microwave driving. When the

**qubit**is tuned close to the resonance with an individual TLF and the Rabi driving is strong enough (Rabi

**frequency**of order of the

**qubit**-TLF coupling), interesting 4-level dynamics are observed. The experimental data shows a clear asymmetry between biasing the

**qubit**above or below the fluctuator's level-splitting. Theoretical analysis indicates that this asymmetry is due to an effective coupling of the TLF to the external microwave field induced by the higher

**qubit**levels.

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Contributors: Higgins, Kieran D. B., Lovett, Brendon W., Gauger, Erik M.

Date: 2012-03-27

**qubit** design but with an **oscillating** voltage applied to the CPB bias gate... qubits. The criterion for the single term approximation to be valid is...**qubit** and **oscillator**, thus requiring a theoretical treatment beyond the...**qubit** and oscillator, thus requiring a theoretical treatment beyond the...the qubit frequency Ω with temperature. The upper inset shows the dependence...**qubit** thermometry of an oscillator....**qubit** dynamics in this regime, based on an **oscillator** correlation function...**qubit** thermometry: T i n is the temperature supplied to the numerical ...**oscillations** with **frequency** ( eqn:rho3) to it. The blue line is the data...**qubit** thermometry of an **oscillator**....**qubit** dynamics. We obtain a new expression for the ac Stark shift and ...**qubit** dynamics in this regime, based on an oscillator correlation function...**oscillations** are also shown as a reference (green). Left: the population...**oscillator** Hilbert space at a point where the dynamics have converged ... the** qubit**. These parameters can be achieved experimentally using the

**sam**...

**frequency**of the

**qubit**dynamics is still adequately captured by our single...

**qubit**dynamics is still adequately captured by our single term approximation...

**qubit**

**frequency**Ω with temperature. The upper inset shows the dependence...

**oscillator**on the

**qubit**. These parameters can be achieved experimentally...

**oscillator**represents a ubiquitous physical system. New experiments in...

**frequency**domain. The full numerical solution was Fourier transformed ...the

**dynamics analytically unwieldy, because the rational function...**

**qubit****qubit**dynamics are not greatly perturbed by the presence of the

**oscillator**... the

**dynamics are not greatly perturbed by the presence of the oscillator...of qubit thermometry: T i n is the temperature supplied to the numerical ... A quantum two level system coupled to a harmonic**

**qubit****oscillator**represents a ubiquitous physical system. New experiments in circuit QED and nano-electromechanical systems (NEMS) achieve unprecedented coupling strength at large detuning between

**qubit**and

**oscillator**, thus requiring a theoretical treatment beyond the Jaynes Cummings model. Here we present a new method for describing the

**qubit**dynamics in this regime, based on an

**oscillator**correlation function expansion of a non-Markovian master equation in the polaron frame. Our technique yields a new numerical method as well as a succinct approximate expression for the

**qubit**dynamics. We obtain a new expression for the ac Stark shift and show that this enables practical and precise

**qubit**thermometry of an

**oscillator**.

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

Date: 2004-07-30

**oscillator**. We achieve generation and control of the entangled state by...**frequencies** are shown by the filled squares in b). b, Rabi **frequency**, .......**oscillations**: after a π pulse on the **qubit** resonance ( | 00 → | 10 ) we...flux **qubit** (the smallest loop closed by three junctions); the **qubit** to...**frequencies** indicated by peaks in the SQUID switching probability when...**qubit** - **oscillator** system for some given bias point. The blue and red ...**oscillations** of the coupled system....**oscillations** at the **qubit** symmetry point Δ = 5.9 GHz. a, Switching probability...**qubit** symmetry point Δ = 5.9 GHz. a, Switching probability as a function...**oscillator**, as demonstrated in ion/atom-trap experiments or cavity quantum...**qubit** (a two-level system) and a superconducting quantum interference ...**qubits**. Single-**qubit** operations, direct coupling between two **qubits**, and... the **qubit** transition. In the upper scan, the system is first excited ...through the **qubit** area away from the **qubit** symmetry point. Inset, energy...**qubit** coupled to a harmonic oscillator...Qub ... In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits or **qubits**. Single-**qubit** operations, direct coupling between two **qubits**, and the realization of a quantum gate have been reported. However, complex manipulation of entangled states - such as the coupling of a two-level system to a quantum harmonic **oscillator**, as demonstrated in ion/atom-trap experiments or cavity quantum electrodynamics - has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux **qubit** (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic **oscillator**. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi **oscillations** of the coupled system.

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Contributors: Wubs, Martijn, Kohler, Sigmund, Hanggi, Peter

Date: 2007-03-15

**the** **qubit** would be measured | ↑ . fig:photon_averages...**the** **qubit** would be measured in state | ↓ ; **the** dash-dotted blue curve ...**qubit**-**oscillator** coupling γ . Parameters: γ = 0.25 ℏ v and ℏ Ω 2 = 100...**oscillator** depend on the state of the **qubit**....**qubit** coupled to one oscillator, far outside **the** RWA regime: γ = ℏ Ω =...the qubit. In general not much can be said about this final state, but...**qubit** coupled to two cavities, we show that Landau-Zener sweeps of the...**oscillator** **frequency**. In Fig. fig:photon_averages we depict how for a...**qubit** coupled to two **oscillators**. Parameters: γ = 0.25 ℏ v and Ω 2 = 100...**qubit**-**oscillator** coupling, then the dynamics can very well be approximated...**oscillator** if the **qubit** would be measured in state | ↓ ; the dash-dotted...**qubit**-oscillator entanglement, with state-of-the-art circuit QED as a ...**qubit**-**oscillator** entanglement, with state-of-the-art circuit QED as a ...**oscillator** energies ℏ Ω 1 , 2 are much larger than the **qubit**-**oscillator**...**qubit** are well suited for the robust creation of entangled cavity states...**qubit** coupled to one **oscillator**, far outside the RWA regime: γ = ℏ Ω =... of a qubit coupled to two oscillators. Parameters: γ = 0.25 ℏ v and Ω...**qubit** may undergo Landau-Zener transitions due to its coupling to one ...**qubit**-oscillator coupling γ . Parameters: γ = 0.25 ℏ v and ℏ Ω 2 = 100...final qubit-two-oscillator state | ψ ∞ rather than merely the transition...**oscillator** **frequencies**, both inside and outside the regime where a rotating-wave... final qubit state is | ↑ . We call this dynamical selection rule the ...**qubit** coupled to two **oscillators**. Parameters: γ = 0.25 ℏ v , ℏ Ω 1 = 90...**oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau-Zener...state of the qubit....**qubit** coupled to two oscillators with large energies, and with detunings...**qubit** coupled to one oscillator, Landau-Zener transitions can be used ...**qubit** coupled to two **oscillators** with degenerate energies. Parameters: ... A **qubit** may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic **oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of **qubit**-**oscillator** entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a **qubit** coupled to two cavities, we show that Landau-Zener sweeps of the **qubit** are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the **qubit** acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the **qubit**, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the **oscillator** **frequencies**, both inside and outside the regime where a rotating-wave approximation is valid.

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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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