### 62592 results for qubit oscillator frequency

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: Chiarello, F., Paladino, E., Castellano, M. G., Cosmelli, C., D'Arrigo, A., Torrioli, G., Falci, G.

Date: 2011-10-07

**qubit** is only weakly sensitive to intrinsic noise. We find that this behaviour...**qubit** in different conditions (different oscillation frequencies) by changing...**qubit** in different conditions (different **oscillation** **frequencies**) by changing...**frequency** noise contributions, and discuss the experimental results and...**qubit** manipulation, changing the potential from the two-well “W” case ...**qubit**, indicated as double SQUID **qubit**, can be manipulated by rapidly ...**qubit** manipulated by fast pulses: experimental observation of distinct...**oscillations** with eq. envelope. The blue line in the left panel is the...**oscillations** observed for different pulse height. The measured **frequency**...**oscillations** exhibiting non-exponential decay, indicating a non trivial...**oscillation** **frequencies** observed (about 10-20 GHz), corresponding to the...used** for **the qubit manipulation, changing the potential from the two-well...**frequency** Ω / 2 π given by eq. omega for ϕ x = 0 as a function of ϕ c ... A particular superconducting quantum interference device (SQUID)**qubit**, indicated as double SQUID **qubit**, can be manipulated by rapidly modifying its potential with the application of fast flux pulses. In this system we observe coherent **oscillations** exhibiting non-exponential decay, indicating a non trivial decoherence mechanism. Moreover, by tuning the **qubit** in different conditions (different **oscillation** **frequencies**) by changing the pulse height, we observe a crossover between two distinct decoherence regimes and the existence of an "optimal" point where the **qubit** is only weakly sensitive to intrinsic noise. We find that this behaviour is in agreement with a model considering the decoherence caused essentially by low **frequency** noise contributions, and discuss the experimental results and possible issues.

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Contributors: Omelyanchouk, A. N., Shevchenko, S. N., Zagoskin, A. M., Il'ichev, E., Nori, Franco

Date: 2007-05-12

the **qubit**, and I q t the current circulating in the **qubit**. The persistent...**phase** **qubit** (Fig. 2 in ). The dependence of the frequency of these oscillations...**oscillations**....**frequency** ω = 0.612 , and the decay rate γ = 10 -3 . Low-**frequency** classical...**oscillations** around a minimum of the potential profile of Fig. fig1 as...**frequency** ω . The main peak ( ω 0 ≈ 0.6 ) corresponds to the resonance...**qubit** (Fig. 2 in ). The dependence of the **frequency** of these **oscillations**...high-**frequency**) harmonic mode of the system, $\omega$. Like in the case...**qubits** in the classical regime...**frequency**, M the mutual inductance between the tank and the **qubit**, and...**qubit** in the _classical_ regime can produce low-frequency oscillations...**qubit** in the _classical_ regime can produce low-**frequency** **oscillations**...in the **qubit** circuit produces a magnetic moment, which is measured by ...**oscillations** are clearly seen. (b) Low-**frequency** **oscillations** of the persistent...**oscillations**, the **frequency** of these pseudo-Rabi **oscillations** is much ...**frequency** $\omega$ and its subharmonics ($\omega/n$), but also at its ...**oscillations** is in the different scale of the resonance **frequency**. To ...and the **qubit**, and I q t the current circulating in the **qubit**. The persistent...a **phase** **qubit** (Fig. 2 in ). The dependence of the frequency of these ... Nonlinear effects in mesoscopic devices can have both quantum and classical origins. We show that a three-Josephson-junction (3JJ) flux **qubit** in the _classical_ regime can produce low-**frequency** **oscillations** in the presence of an external field in resonance with the (high-**frequency**) harmonic mode of the system, $\omega$. Like in the case of_quantum_ Rabi **oscillations**, the **frequency** of these pseudo-Rabi **oscillations** is much smaller than $\omega$ and scales approximately linearly with the amplitude of the external field. This classical effect can be reliably distinguished from its quantum counterpart because it can be produced by the external perturbation not only at the resonance **frequency** $\omega$ and its subharmonics ($\omega/n$), but also at its overtones, $n\omega$.

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Contributors: Strauch, F. W., Dutta, S. K., Paik, Hanhee, Palomaki, T. A., Mitra, K., Cooper, B. K., Lewis, R. M., Anderson, J. R., Dragt, A. J., Lobb, C. J.

Date: 2007-03-02

**frequency**, and two-photon Rabi **frequency** are compared to measurements ...**frequency** Ω R , 01 of the one-photon 0 1 transition as function of microwave...**qubit**, scanned in **frequency** (vertical) and bias current (horizontal). ...**qubit** (current-biased Josephson junction) at high microwave drive power...**qubit** with Nb/AlOx/Nb tunnel junctions. Good agreement is found between...**oscillations** of the escape rate for I a c = 16.5 nA....**oscillations** have been observed in many superconducting devices, and represent...**oscillation** **frequency** Ω ̄ R , 01 as a function of the level spacing ω ...**qubit**...**qubits**) in a quantum computer. We use a three-level multiphoton analysis...phase qubit, scanned in frequency (vertical) and bias current (horizontal ... Rabi **oscillations** have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (**qubits**) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase **qubit** (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi **frequency**, and two-photon Rabi **frequency** are compared to measurements made on a dc SQUID phase **qubit** with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.

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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: Murch, K. W., Ginossar, E., Weber, S. J., Vijay, R., Girvin, S. M., Siddiqi, I.

Date: 2012-08-22

**qubit**-cavity detuning for the **qubit** prepared in the ground state in the...**qubit**, both the effective nonlinearity and the threshold become a non-trivial...**oscillator** Q....**the** **qubit**-oscillator model with N l = 7 show **the** avoided crossings in ...**qubit**-**oscillator** model with N l = 7 show the avoided crossings in the ...and **qubit** junctions (lower and upper insets)....**qubit** junctions (lower and upper insets)....**qubit** and may be used to realize a high fidelity, latching readout whose...**qubit**-**oscillator** detuning. Moreover, the autoresonant threshold is sensitive...**oscillator** is strongly coupled to a quantized superconducting **qubit**, both...**qubit** state. (a) Color plot shows S | 1 versus **qubit** detuning. The dashed... **qubit** state. (a) Color plot shows S | 1 versus **qubit** detuning. The dashed...**qubit**-cavity detuning for **the** **qubit** prepared in **the** ground state in **the**...**frequency** chirped excitation is applied to a classical high-Q nonlinear...**qubit**-oscillator detuning. Moreover, the autoresonant threshold is sensitive...**oscillators** (red) are shown. The arrows indicate the locations of avoided...**the** **qubit** energy levels were modeled as a Duffing nonlinearity. ... When a **frequency** chirped excitation is applied to a classical high-Q nonlinear **oscillator**, its motion becomes dynamically synchronized to the drive and large oscillation amplitude is observed, provided the drive strength exceeds the critical threshold for autoresonance. We demonstrate that when such an **oscillator** is strongly coupled to a quantized superconducting **qubit**, both the effective nonlinearity and the threshold become a non-trivial function of the **qubit**-**oscillator** detuning. Moreover, the autoresonant threshold is sensitive to the quantum state of the **qubit** and may be used to realize a high fidelity, latching readout whose speed is not limited by the **oscillator** Q.

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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: 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: 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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