### 62592 results for qubit oscillator frequency

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: Poletto, S, Chiarello, F, Castellano, M G, Lisenfeld, J, Lukashenko, A, Carelli, P, Ustinov, A V

Date: 2009-10-23

**qubit** manipulation allows for much faster coherent operations....**oscillation** of the retrapping probability in one of the wells has a **frequency**...**qubit**. In the phase regime, the manipulation of the energy states is realized...phase qubit....**oscillation** **frequency** versus the normalized amplitude of the microwave...**qubit**, where the coherent evolution between the two flux states is induced... phase qubit by applying microwave pulses at 19 GHz. The oscillation frequency...**frequency** of the Larmor **oscillations**, the microwave-free **qubit** manipulation...**oscillation** and microwave-driven Rabi **oscillation** are rather similar. ...**oscillation** of the double SQUID manipulated as a phase **qubit** by applying...**oscillation** **frequency** changes from 540 MHz to 1.2 GHz by increasing the...**qubit**...**oscillation** **frequencies** versus amplitude of the short flux pulse (full...**qubit**. ... We report on two different manipulation procedures of a tunable rf SQUID. First, we operate this system as a flux **qubit**, where the coherent evolution between the two flux states is induced by a rapid change of the energy potential, turning it from a double well into a single well. The measured coherent Larmor-like **oscillation** of the retrapping probability in one of the wells has a **frequency** ranging from 6 to 20 GHz, with a theoretically expected upper limit of 40 GHz. Furthermore, here we also report a manipulation of the same device as a phase **qubit**. In the phase regime, the manipulation of the energy states is realized by applying a resonant microwave drive. In spite of the conceptual difference between these two manipulation procedures, the measured decay times of Larmor **oscillation** and microwave-driven Rabi **oscillation** are rather similar. Due to the higher **frequency** of the Larmor **oscillations**, the microwave-free **qubit** manipulation allows for much faster coherent operations.

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Contributors: Reuther, Georg M., Hänggi, Peter, Kohler, Sigmund

Date: 2012-05-10

**qubit**-**oscillator** coupling ( g 2 = 0 ), resonant driving, Ω = ω 0 , and...**oscillator** damping γ = 0.02 ϵ . The amplitude A = 0.07 ϵ corresponds to...**oscillator** damping γ . The driving amplitude is A = 3.5 γ , such that ...**qubit**-**oscillator** coupling ( g 1 = 0 ), resonant driving at large **frequency**...**qubit**-**oscillator** Hamiltonian to the dispersive frame and a subsequent ...**qubit** expectation value σ x which exhibits decaying oscillations with ...**qubit** expectation value σ x which exhibits decaying **oscillations** with **frequency** ϵ . The parameters correspond to an intermediate regime between...linear **qubit**-oscillator coupling ( g 2 = 0 ), resonant driving, Ω = ω ...**qubit**-oscillator detuning and by considering also a coupling to the square... **qubit** operator σ x (solid line) and the corresponding purity (dashed)...**qubit** coupled to a resonantly driven dissipative harmonic oscillator. ...**qubit**-oscillator coupling ( g 1 = 0 ), resonant driving at large frequency...**qubit**-**oscillator** master equation in the original frame....**qubit** operator σ x (solid line) and the corresponding purity (dashed) ...**qubit**-oscillator Hamiltonian to the dispersive frame and a subsequent ...**oscillator** damping γ = ϵ , the conditions for the validity of the (Markovian...**qubit** decoherence during dispersive readout...**oscillator** coordinate, which is relevant for flux **qubits**. Analytical results...**qubit** decoherence under generalized dispersive readout, i.e., we investigate...**qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. ...**qubit**-**oscillator** detuning and by considering also a coupling to the square...**qubit**-oscillator master equation in the original frame. ... We study **qubit** decoherence under generalized dispersive readout, i.e., we investigate a **qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. We provide a complete picture by allowing for arbitrarily large **qubit**-**oscillator** detuning and by considering also a coupling to the square of the **oscillator** coordinate, which is relevant for flux **qubits**. Analytical results for the decoherence time are obtained by a transformation of the **qubit**-**oscillator** Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full **qubit**-**oscillator** master equation in the original frame.

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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: Singh, Mandip

Date: 2014-07-01

**flux**-**qubit**-cantilever interrupted by a single Josephson junction is...flux-**qubit**-cantilever corresponds to a quantum entanglement between magnetic...**oscillation** ω i i.e. the **frequency** in absence of magnetic field. The external...**frequency** ( E / h ) is ∼ 4 × 10 11 Hz....**frequency** ( E / h ) is ∼ 3.9 × 10 11 Hz....**oscillator** is introduced that consists of a flux **qubit** in the form of ...**flux** **qubit** with a single Josephson junction is considered throughout this...**oscillates** about an equilibrium angle θ 0 with an intrinsic **frequency** ...flux-**qubit**-cantilever. A part of the flux **qubit** (larger loop) is in the... the **flux**-**qubit**-cantilever to its ground state....**qubit** and the mechanical degrees of freedom of the cantilever are naturally...**oscillation** **frequencies**, consider a flux-**qubit**-cantilever made of niobium...**flux**-**qubit**-cantilever shown in Fig. fig1 where a part of a superconducting...**frequencies** of the flux-**qubit**-cantilever are ω X ≃ 2 π × 7.99 × 10 10 ...**qubit** and the cantilever. An additional magnetic flux threading a DC-SQUID...**qubit** in the form of a cantilever. The magnetic flux linked to the flux...**qubit**...**frequencies** are ω φ ≃ 2 π × 7.99 × 10 10 rad/s, ω δ = 2 π × 22384.5 ...**flux** **qubit** forms a cantilever. The larger loop is interrupted by a smaller ... In this paper a macroscopic quantum **oscillator** is introduced that consists of a flux **qubit** in the form of a cantilever. The magnetic flux linked to the flux **qubit** and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling is controlled through an external magnetic field. The ground state of the introduced flux-**qubit**-cantilever corresponds to a quantum entanglement between magnetic flux and the cantilever displacement.

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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: 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: Meier, Florian, Loss, Daniel

Date: 2004-08-26

**frequency** is comparable to the coupling energy of micro-circuit and fluctuator...**oscillation** visibility. We also calculate the probability for Bogoliubov...**frequencies**, transitions to the second excited state of the superconducting...single-**frequency** **oscillations** with reduced visibility [Fig. Fig2(b)]....**Qubits**...single-**frequency** **oscillations** are restored. The fluctuator leads to a ...**oscillation** experiments....**oscillations** for a squbit-fluctuator system. The probability p 1 t to ...**oscillations** between quantum states of superconducting micro-circuits ...**frequencies** | b x | / h 100 M H z . We show next that, in this regime, ... Coherent Rabi **oscillations** between quantum states of superconducting micro-circuits have been observed in a number of experiments, albeit with a visibility which is typically much smaller than unity. Here, we show that the coherent coupling to background charge fluctuators [R.W. Simmonds et al., Phys. Rev. Lett. 93, 077003 (2004)] leads to a significantly reduced visibility if the Rabi **frequency** is comparable to the coupling energy of micro-circuit and fluctuator. For larger Rabi **frequencies**, transitions to the second excited state of the superconducting micro-circuit become dominant in suppressing the Rabi **oscillation** visibility. We also calculate the probability for Bogoliubov quasi-particle excitations in typical Rabi **oscillation** experiments.

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Contributors: Shi, Zhan, Simmons, C. B., Ward, Daniel. R., Prance, J. R., Mohr, R. T., Koh, Teck Seng, Gamble, John King, Wu, Xian., Savage, D. E., Lagally, M. G.

Date: 2012-08-02

low-**frequency** noise processes are an important dephasing mechanism....**Qubit**...**oscillations** visible near δ t = 0 . The **oscillations** of interest appear...**qubit** states varies with external voltages, consistent with a decoherence...**qubit** in a double quantum dot fabricated in a Si/SiGe heterostructure ...**oscillation** **frequency** f for (a–c), respectively. As t is increased, the...**frequency** at more negative detuning (farther from the anti-crossing). ...**oscillation** **frequency** f for the data in (a–c), respectively. We obtain...**oscillations** at a given **frequency** decays with characteristic time T 2 ...**oscillations** of a charge **qubit** in a double quantum dot fabricated in a...**qubit**'s double-well potential). In the regime with the shortest T2*, applying ... Fast quantum **oscillations** of a charge **qubit** in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2* ranges from 127ps to ~2.1ns; it depends substantially on how the energy difference of the two **qubit** states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise(charge noise that changes the asymmetry of the **qubit**'s double-well potential). In the regime with the shortest T2*, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127ps to 760ps, demonstrating that low-**frequency** noise processes are an important dephasing mechanism.

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Contributors: Eugene Grichuk, Margarita Kuzmina, Eduard Manykin

Date: 2010-09-26

**qubit** simulates the behavior of electric field of
polarized light beam...**qubit** model has been designed as a
stochastic **oscillator** formed by a pair...**qubits** that is
exploited as a computation resource in one-way quantum
...**oscillators** is
proposed for modeling of a cluster of entangled **qubits** ...**oscillators** with chaotically modulated limit cycle radii and
**frequencies**...one-**qubit**
gates are suggested. Changing of cluster entanglement degree...**qubit** cluster, is designed, and system of equations for
network dynamics...**oscillators**...**qubit** model has been designed as a
stochastic oscillator formed by a pair ... A network of coupled stochastic **oscillators** is
proposed for modeling of a cluster of entangled **qubits** that is
exploited as a computation resource in one-way quantum
computation schemes. A **qubit** model has been designed as a
stochastic **oscillator** formed by a pair of coupled limit cycle
**oscillators** with chaotically modulated limit cycle radii and
**frequencies**. The **qubit** simulates the behavior of electric field of
polarized light beam and adequately imitates the states of two-level
quantum system. A cluster of entangled **qubits** can be associated
with a beam of polarized light, light polarization degree being
directly related to cluster entanglement degree. Oscillatory network,
imitating **qubit** cluster, is designed, and system of equations for
network dynamics has been written. The constructions of one-**qubit**
gates are suggested. Changing of cluster entanglement degree caused
by measurements can be exactly calculated.

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