### 57529 results for qubit oscillator frequency

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

Date: 2006-06-02

two-**qubit** crosstalk....**qubits**. The damped **oscillations** of the superconducting phase after the...**qubit** as a harmonic **oscillator**. However, to analyze the measurement error...**qubits**. The damped oscillations of the superconducting phase after the...second-**qubit** energy E 2 t in the classical model taking into account energy...**qubit** (Fig. f9) shortens significantly the time interval during which...**oscillations** in the “right” well. This dissipative evolution leads to ...**qubit** is treated both classically and quantum-mechanically. The results...**qubit** potential is used; energy relaxation in the second **qubit** is neglected...two-**qubit** imaginary-swap quantum gate....**frequency** of the two-**qubit** imaginary-swap quantum gate....**qubits**....**qubit** may be to a much lower energy than for the **oscillator**; (c) After...**frequency** f d increase, while it starts to decrease at t > 0.52 T 1 (after...**qubit**, which is highly excited after the measurement, is described classically...two-**qubit** operations) for a given tolerable value of the measurement error...**qubit** excitation (though still almost without switching) between 3 ns ...**qubit** energy E 2 (in units of ℏ ω l 2 ) in the **oscillator** model as a function...first-**qubit** **oscillation** **frequency** f d as a function of time t (normalized...**frequencies**, with the difference **frequency** increasing in time, d t ~ 2...**frequency** for the second **qubit**: ω l 2 / 2 π = 10.2 GHz for N l 2 = 10 ...**frequency** of two-**qubit** operations) for a given tolerable value of the ...**qubit** energy in the ground state ≈ ℏ ω l 2 / 2 . Even though the mean ...**frequency** f d of the driving force (Fig. f3) which passes through the...**qubit** may significantly excite the second **qubit**, leading to its measurement...**qubit**. The dashed line in Fig. f8 shows C x , T T 1 dependence in the...**qubits**...**qubit** energy for the same parameters (Fig. f7'), we see that the two ... We analyze the crosstalk error mechanism in measurement of two capacitively coupled superconducting flux-biased phase **qubits**. The damped **oscillations** of the superconducting phase after the measurement of the first **qubit** may significantly excite the second **qubit**, leading to its measurement error. The first **qubit**, which is highly excited after the measurement, is described classically. The second **qubit** is treated both classically and quantum-mechanically. The results of the analysis are used to find the upper limit for the coupling capacitance (thus limiting the **frequency** of two-**qubit** operations) for a given tolerable value of the measurement error probability.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-09-08

**qubit**-oscillator system in the ultrastrong coupling regime, where the ...**qubit**-**oscillator** system in the ultrastrong coupling regime, where the ...**qubit**-oscillator system. The same parameters as in Fig. Fig::Dynam1 are...**oscillator** **frequency** approaches unity or goes beyond, and simultaneously...**qubit** for ε = 0 , Δ / Ω = 0.4 , ω ex / Ω = 5.3 , A / Ω = 8.0 , and temperature...**qubit** energy splitting (extreme driving). Both **qubit**-oscillator coupling...**oscillator** modes in the spectrum, while the latter can bring the **qubit**'s...**oscillations** overlaid. For long times this localization vanishes (see ...**oscillations** between the states | ↓ and | ↑ with the single **frequency** ...**qubit**-oscillator system against the static bias ε for weak coupling g ...**oscillation** **frequencies** are plotted against the dimensionless coupling...**oscillator** degrees of freedom from the density operator of the **qubit**-**oscillator**...**qubit**-**oscillator** system against the static bias ε for weak coupling g ...**qubit** tunneling matrix element of different nature: the former can be ...**qubit** , might occur also for a **qubit**-oscillator system in the ultrastrong...**oscillation** **frequencies** Ω K vanish. However, third-order corrections in...**qubit** energy splitting (extreme driving). Both **qubit**-**oscillator** coupling...**qubit**-oscillator system:...**qubit** , might occur also for a **qubit**-**oscillator** system in the ultrastrong...**Qubit**-oscillator system under ultrastrong coupling and extreme driving...**qubit** ( ε = 0 ). Further, Δ / Ω = 0.4 , ω ex / Ω = 5.3 and A / Ω = 8.0...**qubit**-**oscillator** system. The same parameters as in Fig. Fig::Dynam1 are...**oscillator** states are included. Numerical calculations are shown by red...**qubit**'s dynamics to a standstill at short times (coherent destruction ... We introduce an approach to studying a driven **qubit**-**oscillator** system in the ultrastrong coupling regime, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity or goes beyond, and simultaneously for driving strengths much bigger than the **qubit** energy splitting (extreme driving). Both **qubit**-**oscillator** coupling and external driving lead to a dressing of the **qubit** tunneling matrix element of different nature: the former can be used to suppress selectively certain **oscillator** modes in the spectrum, while the latter can bring the **qubit**'s dynamics to a standstill at short times (coherent destruction of tunneling) even in the case of ultrastrong coupling.

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Contributors: Bennett, Douglas A., Longobardi, Luigi, Patel, Vijay, Chen, Wei, Averin, Dmitri V., Lukens, James E.

Date: 2008-11-14

**qubit** discussed above. This design uses a gradiometric configuration to...**qubit** using pulsed microwaves and rapid flux pulses. The modified rf SQUID...**oscillation's** waveform is compared to analytical results obtained for ...**frequencies** of the Rabi **oscillations** that correspond to these microwave...**Qubits**...**frequency** flux noise....**frequency**); 0 V ’s (no detuning), 0.1 V ∘ ’s (0.21 n s -1 ), 0.45 V ’s...**frequency** flux noise should be seen most dramatically in the decay of ...**Qubits** \and Flux **Qubit** \and SQUIDs...**qubit** from fluctuations in the ambient flux on the length scale (150 μ...**oscillations** for detunings going from top to bottom of 0.094, 0.211, 0.328...**oscillations**. The line is a fit to Eq. fin for δ = 0 averaged over quasi-static...**qubit** cooled through its transition temperature, then the motion of the...**qubit** and the readout magnetometer, (c) a cross section of the wafer around...**frequency** flux noise and is consistent with independent measurement of...**oscillations** is dominated by the lifetime of the excited state and low...**qubit** potential being symmetric without further bias flux....**oscillates** in time, demonstrating the phenomenon of Rabi **oscillations**,...**oscillations** when δ = 0 and the microwave **frequency**, f x r f = 17.9 G ...**qubit** in terms of Ω ....**qubits** . Ω , the **frequency** of the **oscillations** for δ = 0 , is ideally ... We report measurements of coherence times of an rf SQUID **qubit** using pulsed microwaves and rapid flux pulses. The modified rf SQUID, described by an double-well potential, has independent, in situ, controls for the tilt and barrier height of the potential. The decay of coherent **oscillations** is dominated by the lifetime of the excited state and low **frequency** flux noise and is consistent with independent measurement of these quantities obtained by microwave spectroscopy, resonant tunneling between fluxoid wells and decay of the excited state. The **oscillation's** waveform is compared to analytical results obtained for finite decay rates and detuning and averaged over low **frequency** flux noise.

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Contributors: Serban, I., Dykman, M. I., Wilhelm, F. K.

Date: 2009-07-29

**qubit** for the case when its detector, the Josephson bifurcation amplifier...**frequency**. This new **frequency** scale results from the interplay of the ...**qubit** relaxation rates are different in different states. They can display...**qubit** **frequency** and resonant enhancement, which is due to quasienergy ...**qubit** frequency and resonant enhancement, which is due to quasienergy ...**oscillator** approaches bifurcation points where the corresponding attractor...**qubit** **frequency** and twice the modulation **frequency**; Γ 0 = ℏ C Γ r a 2 ...**qubit** measured by a driven Duffing oscillator... **qubit** Γ e ∝ R e ~ N + - ω q - 2 ω F sharply increases if the **qubit** frequency...**qubit** states differs from the thermal Boltzmann distribution. If the **oscillator**-mediated...**qubit** frequency and twice the modulation frequency; Γ 0 = ℏ C Γ r a 2 ... **qubit** decay mechanism, the **qubit** distribution is determined by the ratio...**oscillator** decay rate. The dependence of ν a on the control parameter ...**qubit**, Γ e ≪ κ , it can be satisfied even at resonance....**qubit** Γ e ∝ R e ~ N + - ω q - 2 ω F sharply increases if the **qubit** **frequency**...**qubit** temperature T e f f * = k B T e f f / ℏ ω q as function of the scaled...**qubit**....**frequencies** ν a / | δ ω | for the same κ / | δ ω . Curves 1 and 2 refer...**qubit** relaxation rates noted in Ref. ...**oscillator** changes the effective temperature of the **qubit**. ... We investigate the relaxation of a superconducting **qubit** for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The **qubit** relaxation rates are different in different states. They can display strong dependence on the **qubit** **frequency** and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven **oscillator** changes the effective temperature of the **qubit**.

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Contributors: Fedorov, A., Feofanov, A. K., Macha, P., Forn-Díaz, P., Harmans, C. J. P. M., Mooij, J. E.

Date: 2010-04-09

**qubit**. (c) MW frequency vs f ϵ (controlled by the amplitude of the current...**Qubit** at its Symmetry Point...**oscillator** **frequency** ν o s c ....**qubit** whose gap can be tuned fast and have coupled this **qubit** strongly...**Frequency** of the vacuum Rabi **oscillations** extracted from data (a) and ...**qubit** (green) coupled to a lumped element superconducting LC oscillator...**oscillations** (a) and MW **frequency** (b) vs magnetic f α . In the experiment...**qubit** biased at its symmetry point shows a minimum in the energy splitting...**qubit**-**oscillator** system. The minimum of energy splitting of the **qubit** ...**qubit**-resonator coupling ($g/h\sim0.1\nu_{\rm osc}$). Here being at resonance...**qubit**-resonator system and generate vacuum Rabi oscillations. When the...**oscillator** to the **qubit**. (c) MW **frequency** vs f ϵ (controlled by the amplitude...**qubit**-oscillator system. The minimum of energy splitting of the **qubit** ...**qubit**-oscillator coupling strength reduced by sin η ....**qubit** was kept in its symmetry point ( ϵ = 0 ) by appropriately adjusting...**oscillations**. When the gap is made equal to the **oscillator** **frequency** $...**oscillator**. We show full spectroscopy of the **qubit**-resonator system and ... A flux **qubit** biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a **qubit** whose gap can be tuned fast and have coupled this **qubit** strongly to an LC **oscillator**. We show full spectroscopy of the **qubit**-resonator system and generate vacuum Rabi **oscillations**. When the gap is made equal to the **oscillator** **frequency** $\nu_{osc}$ we find the strongest **qubit**-resonator coupling ($g/h\sim0.1\nu_{\rm osc}$). Here being at resonance coincides with the optimal coherence of the symmetry point. Significant further increase of the coupling is possible.

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Contributors: Zorin, A. B., Chiarello, F.

Date: 2009-08-27

**qubit** which is insensitive to the charge variable, biased in the optimal...**qubit** can be tuned within an appreciable range allowing variable **qubit**-**qubit**...**qubit** **frequency** as a function of parameter β L for fixed L = 50 pH and...**qubit** on the basis of the radio-frequency SQUID with the screening parameter...**frequency** in this **qubit** can be tuned within an appreciable range allowing...**qubit** on the basis of the radio-**frequency** SQUID with the screening parameter...**qubit** with the inductance value L = 50 pH and the set of capacitances...**qubit** ....**qubit** coupled to a resonant circuit and (b) possible equivalent compound...**qubit**-**qubit** coupling....**oscillator**-type states in two separate wells. The spectrum in the central...**qubit** frequency as a function of parameter β L for fixed L = 50 pH and...**qubit** **frequency** within the range of sufficiently large anharmonicity (...**qubit** allowing manipulation within the two basis **qubit** states | 0 and ...**qubit** loop. Capacitance C includes both the self-capacitance of the junction...**qubit** **frequency** ν 10 = Δ E 0 / h and the anharmonicity factor δ computed...**qubit** based on the Josephson oscillator with strong anharmonicity...**frequency** shift in the circuit due to excitation of the **qubit** with the...**qubit** energy dramatically decreases and the **qubit** states are nearly the...**oscillator** type (left inset) to the set of the doublets (right inset),...**qubit** in the ground (solid lines) and excited (dashed lines) states calculated ... We propose a superconducting phase **qubit** on the basis of the radio-**frequency** SQUID with the screening parameter value $\beta_L = (2\pi/\Phi_0)LI_c \approx 1$, biased by a half flux quantum $\Phi_e=\Phi_0/2$. Significant anharmonicity ($> 30%$) can be achieved in this system due to the interplay of the cosine Josephson potential and the parabolic magnetic-energy potential that ultimately leads to the quartic polynomial shape of the well. The two lowest eigenstates in this global minimum perfectly suit for the **qubit** which is insensitive to the charge variable, biased in the optimal point and allows an efficient dispersive readout. Moreover, the transition **frequency** in this **qubit** can be tuned within an appreciable range allowing variable **qubit**-**qubit** coupling.

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Contributors: unknown

Date: 2007-10-22

lower-**frequency** and high-**frequency** cut-off of the baths modes ω0=11Δ, ...**qubits** coupled to an Ohmic bath directly and via an intermediate harmonic...**qubit**-IHO and IHO-bath and the oscillation frequency of the IHO....**qubits** in the two models may have almost same decoherence and relaxation...**oscillator** (IHO). Here, we suppose the **oscillation** **frequencies** of the ...**qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO....**qubit** in the **qubit**-IHO-bath model can be modulated through changing the...**qubit** coupled to an Ohmic bath directly and via an intermediate harmonic ... Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** coupled to an Ohmic bath directly and via an intermediate harmonic **oscillator** (IHO). Here, we suppose the **oscillation** **frequencies** of the bath modes are higher than the IHO’s. When we choose suitable parameters the **qubits** in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the **qubit** in the **qubit**-IHO-bath model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO.

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Contributors: Thrailkill, Z. E., Lambert, J. G., Ramos, R. C.

Date: 2009-09-20

**qubits**. Second, small ripples, or **oscillations**, begin to appear. These...**oscillations** between the **qubits** and resonators....**qubits** will require quantum information to be stored in and transferred...**qubit** from an array of resonators so that it can function within the same...**qubit** (Q) coupled to an array of two resonators (R1, R2) via identical...**Qubits**...**qubit** placed between the resonator array and the active **qubit**. This configuration...**frequencies** to couple **qubits**. We find that an array of resonators with...**frequencies** also cause slight non-uniformities in the high **frequency** **oscillations**...**oscillate** into **qubit** 2, as shown in Fig. fig2 and fig3. As the detuning...**qubits** maintain equal **frequencies** as they are simultaneously detuned from...**qubit** can be effectively used to turn coupling on and off between a **qubit**...**qubits**....**qubit** is characterized as having capacitance C J and critical current ...**qubits** dispersively. We show that a control **qubit** can be used to effectively...**qubit** and the two resonators; since the two resonators are identical here...**qubits** have been shown to be promising components for a future quantum...**oscillations** of the excitation. The detuning of the control **qubit** Q2 can...**qubit** (Q2) between the active **qubit** (Q1) and the resonator array (R1, ...**frequency** of R3 is a little closer to the **frequency** of the **qubits**. The...**qubits**. We find that an array of resonators with different frequencies...**frequency** range used by the resonators....**qubit**-resonator coupling strength is 110 MHz. At zero detuning, the excitation...**qubit** and Q2 is the control **qubit**. In the simulation, the three resonators...**oscillates** slightly faster than in (b) because the small offsets in **frequency**...**frequencies** can be individually addressed to store and retrieve information...**qubit**-**qubit** and **qubit**-resonator coupling strengths. At large detuning,...**oscillates** between the two **qubits** without significant interference from...**qubits** from R2. In (b), the **frequencies** of all three resonators are equal ... Josephson junction-based **qubits** have been shown to be promising components for a future quantum computer. A network of these superconducting **qubits** will require quantum information to be stored in and transferred among them. Resonators made of superconducting metal strips are useful elements for this purpose because they have long coherence times and can dispersively couple **qubits**. We explore the use of multiple resonators with different resonant **frequencies** to couple **qubits**. We find that an array of resonators with different **frequencies** can be individually addressed to store and retrieve information, while coupling **qubits** dispersively. We show that a control **qubit** can be used to effectively isolate an active **qubit** from an array of resonators so that it can function within the same **frequency** range used by the resonators.

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Contributors: Bertet, P., Chiorescu, I., Harmans, C. J. P. M, Mooij, J. E.

Date: 2005-07-13

**qubit** bias point ϵ by ± 2 G H z around 0 . The constants g 1 and g 2 are...**qubit** dephasing time as a function of $\delta \nu_0$. We discuss the specific...**frequency** in the figure). The dashed line indicates the phase-noise insensitive...**oscillator** variables coming from the flux-dependence of the SQUID Josephson...**qubit** is insensitive to the thermal fluctuations of the plasma mode (see...**qubits** is known to arise because of a variety of environmental degrees...**frequency** shift now depends on ϵ . Since g 2 is negative (see figure fig...high-**frequency** noise from the dissipative impedance. The SQUID is threaded...**Qubit** frequency ν q as a function of the bias ϵ for Δ = 5.5 G H z (minimum...**qubit**. Because of the coupling, the **qubit** frequency is shifted by an amount...**qubit**. Because of the coupling, the **qubit** **frequency** is shifted by an amount...flux-**qubit** is the loop in red containing the three junctions of phases...mode-**qubit** interaction hamiltonian which, in addition to the usual Jaynes-Cummings...flux-**qubit** coupled to the plasma mode of its DC-SQUID detector. We first...**qubit** biased by Φ x and SQUID biased by current I b . (b) Simplified electrical...**Frequency** shift per photon δ ν 0 as a function of I b and ϵ . The white...**Qubit** **frequency** ν q as a function of the bias ϵ for Δ = 5.5 G H z (minimum...**qubit** is effectively decoupled from the measuring circuit fluctuations...**qubit**-plasma mode coupling hamiltonian, we will neglect the admittance...SQUID-**qubit** system is seen as an inductance L J connected to the shunct...**qubit** is insensitive to phase noise (due to flux or bias current noise...flux-**qubit** coupled to a harmonic oscillator...SQUID-**qubit** coupling is not symmetric and the junctions critical current...**qubit** transition **frequency** ν q = Δ 2 + ϵ 2 . The corresponding dependence ... Decoherence in superconducting **qubits** is known to arise because of a variety of environmental degrees of freedom. In this article, we focus on the influence of thermal fluctuations in a weakly damped circuit resonance coupled to the **qubit**. Because of the coupling, the **qubit** **frequency** is shifted by an amount $n \delta \nu_0$ if the resonator contains $n$ energy quanta. Thermal fluctuations induce temporal variations $n(t)$ and thus dephasing. We give an approximate formula for the **qubit** dephasing time as a function of $\delta \nu_0$. We discuss the specific case of a flux-**qubit** coupled to the plasma mode of its DC-SQUID detector. We first derive a plasma mode-**qubit** interaction hamiltonian which, in addition to the usual Jaynes-Cummings term, has a coupling term quadratic in the **oscillator** variables coming from the flux-dependence of the SQUID Josephson inductance. Our model predicts that $\delta \nu_0$ cancels in certain non-trivial bias conditions for which dephasing due to thermal fluctuations should be suppressed.

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Contributors: Dial, O. E., Shulman, M. D., Harvey, S. P., Bluhm, H., Umansky, V., Yacoby, A.

Date: 2012-08-09

**qubit** along the y -axis (Fig. t2stara, Fig. S1). Fig. t2starb shows **qubit**...**qubit** loses its quantum information due to interactions with its noisy...**frequencies** in the device....**qubit** and gives good contrast over a wide range of J . b, Exchange **oscillations**...**qubit** during exchange oscillations. Using free evolution and Hahn echo...**frequency** **oscillations** and small d J / d ϵ , a region of large **frequency**...**qubit** with an integrated RF sensing dot. a The detuning ϵ is the voltage...**qubit** is loaded and measured, and the 0 2 region where J is large but ...**oscillations** and large d J / d ϵ , and a region where **oscillations** are...**qubits** are typically operated, the transitional region where J and d J...**qubit** **oscillations** to decay and setting a limit on the fidelity of quantum...**frequencies** are small, allowing the **qubit** to be used as a charge sensor...**qubit** and gives good contrast over a wide range of J . b, Exchange oscillations...**qubit** is allowed to freely precess for a time t under the influence of...**oscillations**. f, Charge **oscillations** measured in 0 2 . This figure portrays...**qubit**,and in metrology the **frequency** of the precession provides a sensitive...**oscillations** in these FID experiments decay due to voltage noise from ...**oscillations**) of these FID **oscillations**, Q ≡ J T 2 * / 2 π ∼ J d J / d...**qubit** during exchange **oscillations**. Using free evolution and Hahn echo...**qubit**-based measurements. Understanding how the **qubit** couples to its environment...**qubit** **oscillations** to decay and limits the fidelity of quantum control...**qubit**,and in metrology the frequency of the precession provides a sensitive...**frequency** and high **frequency** environmental fluctuations, respectively....**qubit** oscillations to decay and limits the fidelity of quantum control...single-**qubit** rotation for a time δ t , and thus reflect the same T 2 *...**oscillations** are dephased by fluctuations in J (Fig. pulsesc) driven, ...**qubit** to be used as a charge sensor with a sensitivity of $2 \times 10...Singlet-Triplet-**Qubit**...**qubit** are grayed out. d, J ϵ and d J / d ϵ in three regions; the 1 1 region ... Two level systems that can be reliably controlled and measured hold promise in both metrology and as qubits for quantum information science (QIS). When prepared in a superposition of two states and allowed to evolve freely, the state of the system precesses with a **frequency** proportional to the splitting between the states. In QIS,this precession forms the basis for universal control of the **qubit**,and in metrology the **frequency** of the precession provides a sensitive measurement of the splitting. However, on a timescale of the coherence time, $T_2$, the **qubit** loses its quantum information due to interactions with its noisy environment, causing **qubit** **oscillations** to decay and setting a limit on the fidelity of quantum control and the precision of **qubit**-based measurements. Understanding how the **qubit** couples to its environment and the dynamics of the noise in the environment are therefore key to effective QIS experiments and metrology. Here we show measurements of the level splitting and dephasing due to voltage noise of a GaAs singlet-triplet **qubit** during exchange **oscillations**. Using free evolution and Hahn echo experiments we probe the low **frequency** and high **frequency** environmental fluctuations, respectively. The measured fluctuations at high **frequencies** are small, allowing the **qubit** to be used as a charge sensor with a sensitivity of $2 \times 10^{-8} e/\sqrt{\mathrm{Hz}}$, two orders of magnitude better than the quantum limit for an RF single electron transistor (RF-SET). We find that the dephasing is due to non-Markovian voltage fluctuations in both regimes and exhibits an unexpected temperature dependence. Based on these measurements we provide recommendations for improving $T_2$ in future experiments, allowing for higher fidelity operations and improved charge sensitivity.

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