### 62772 results for qubit oscillator frequency

Contributors: Hua, Ming, Deng, Fu-Guo

Date: 2013-09-30

**qubit**-state-dependent resonator transition, which means the **frequency** ... qubit-state-dependent resonator transition, which means the frequency...**qubits** assisted by a resonator in the quasi-dispersive regime with a new...three-qubit gate, such as a Fredkin gate on a three-qubit system can also... qubit. (b) The number-state-dependent qubit transition, which means the...**frequency** of two **qubits** between and are chosen as ω 0 , 1 ; 1 / 2 π = ...**oscillations** in our cc-phase gate on a three-charge-**qubit** system. Here...**qubits** can play an important role in shortening largely the operation ... qubits, and q 3 is** the **target** qubit**. The initial state of this system...the** qubit** q in** the **transition between** the **energy levels | i q and | j ...**frequency** shift δ q takes place on the **qubit** due to the photon number ...**qubits**.... the** qubit** q in** the **transition between** the **energy levels | i q and | j...**frequencies** of the **qubits**....**oscillation** (ROT) ROT 0 : | 0 1 | 1 2 | 0 a ↔ | 0 1 | 0 2 | 1 a , while...**qubits**. **Qubits** are placed around the maxima of the electrical field amplitude...**oscillation**, respectively. The MAEV s vary with the transition **frequency**...**frequency** of q 2 (which equals to the transition **frequency** of R a when...**oscillation** varying with the coupling strength g 2 and the **frequency** of...**Qubits** in Circuit QED...**qubit**-state-dependent resonator transition frequency and the tunable period...**qubits**. More interesting, the non-computational third excitation states...**qubits** than previous proposals....second qubit ω 2 . (a) The outcomes for ROT 0 : | 0 1 | 1 2 | 0 a ↔ | ...**oscillation** and an unwanted one. This operation does not require any kind...**qubit**-state-dependent resonator transition **frequency** and the tunable period... qubit and q 2 is** the **target** qubit**. The initial state of** the **system composed...**frequency** on R a becomes ... We present a fast quantum entangling operation on superconducting **qubits** assisted by a resonator in the quasi-dispersive regime with a new effect --- the selective resonance coming from the amplified **qubit**-state-dependent resonator transition **frequency** and the tunable period relation between a wanted quantum Rabi **oscillation** and an unwanted one. This operation does not require any kind of drive fields and the interaction between **qubits**. More interesting, the non-computational third excitation states of the charge **qubits** can play an important role in shortening largely the operation time of the entangling gates. All those features provide an effective way to realize much faster quantum entangling gates on superconducting **qubits** than previous proposals.

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Contributors: Chen, Yu, Sank, D., O'Malley, P., White, T., Barends, R., Chiaro, B., Kelly, J., Lucero, E., Mariantoni, M., Megrant, A.

Date: 2012-09-09

**qubits** can be read out simultaneously using **frequency** multiplexing on ...four-**qubit** sample. F B 1 - 4 are control lines for each **qubit** and R R ...**qubit**, lowering the barrier between the metastable computational energy...**qubits** used in Ref. 6. In this experiment, we drove Rabi **oscillations** ...**qubit** flux bias, with no averaging. See text for details. fig.phase...**qubit** to a separate lumped-element superconducting readout resonator, ...**oscillations** for **qubits** Q 1 - Q 4 respectively, with the **qubits** driven...**qubits** can be read out simultaneously using frequency multiplexing on ... **qubit**’s | g ↔ | e transition and read out the** qubit** states simultaneously... qubits Q 1 to Q 4 . We then drove each

**separately using an on-resonance...**

**qubit****oscillations**in panels (a)-(d) compared to the multiplexed readout in ...

**frequency**for maximum visibility. (b) Reflected phase as a function of...

**qubits**Q 1 - Q 4 respectively, with the

**qubits**driven with 1, 2/3, 1/2...

**frequency**f n encodes the state of

**qubit**n . The phases φ n , n = 1 - ...

**qubit**, we demonstrated the

**frequency**-multiplexed readout by performing...

**frequency**-multiplexed readout. Multiplexed readout signals I p and Q p...

**qubits**, a significant advantage for scaling up to larger numbers of

**qubits**...

**qubits**. Using a quantum circuit with four phase

**qubits**, we couple each...

**qubit**was projected onto the | g or the | e state....

**qubit**in the left ( L , blue) and right ( R , red) wells. Dashed line ...

**qubit**projective measurement, where a current pulse allows a

**qubit**in ...

**frequency**(averaged 900 times), for the

**qubit**in the left ( L , blue) ...

**frequency**-multiplexed readout scheme for superconducting phase

**qubits**....

**qubits**, we couple each

**qubit**to a separate lumped-element superconducting...the

**Josephson junction. Each**

**qubit****is coupled to its readout resonator...**

**qubit****oscillations**measured simultaneously for all the

**qubits**, using the same...

**frequency**, with the

**qubit**prepared first in the left and then in the right...

**qubits**... We introduce a

**frequency**-multiplexed readout scheme for superconducting phase

**qubits**. Using a quantum circuit with four phase

**qubits**, we couple each

**qubit**to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four

**qubits**can be read out simultaneously using

**frequency**multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple

**qubits**, a significant advantage for scaling up to larger numbers of

**qubits**.

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Contributors: Shahriar, M. S., Pradhan, Prabhakar

Date: 2002-12-19

**oscillation** from the plot in (a). (c) The time-dependence of the Rabi **frequency**. Inset: BSO as a function of the absolute phase of the field...**qubit** operations due to the Bloch-Siegert Oscillation...**frequency** is comparable to the Bohr **frequency** so that the rotating wave...low-**frequency** transitions. We present a scheme for observing this effect...**oscillation**. (b) The BSO **oscillation** (amplified scale) by itself, produced...**oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity...**Oscillation** (BSO): (a) The population of state | 1 , as a function of ... We show that if the Rabi **frequency** is comparable to the Bohr **frequency** so that the rotating wave approximation is inappropriate, an extra **oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-**frequency** transitions. We present a scheme for observing this effect in an atomic beam.

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Contributors: Vierheilig, Carmen, Bercioux, Dario, Grifoni, Milena

Date: 2010-10-22

**qubit** dynamics is investigated. In particular, an analytic formula for...**qubit**, an intermediate nonlinear oscillator and an Ohmic bath. linearbath...**qubit** plus **oscillator** system (yellow (light grey) box) and accounts afterwards...**qubit** coupled to a nonlinear quantum **oscillator**, the latter coupled to...nonlinearity onto the qubit dynamics. The comparison of linear versus ...**oscillator** (red (dark grey) box). In the harmonic approximation the effective...**oscillator**. To determine the actual form of the susceptibility, we consider...To read-out the qubit state we couple the qubit linearly to the oscillator...**qubit**, an intermediate nonlinear **oscillator** and an Ohmic bath. linearbath...**qubit**, -the system of interest-, coupled to a nonlinear quantum **oscillator**...also enters the qubit dynamics....**frequency**, as shown in Fig. CompLorentz....**oscillator** within linear response theory in the driving amplitude. Knowing...**qubit** dynamics: In the first approach one determines the eigenvalues and...**qubit** coupled to a nonlinear quantum oscillator, the latter coupled to...**frequencies** with respect to the linear case. As a consequence the relative...the qubit dynamics. The comparison of linear versus nonlinear case is ...**oscillator** and the Ohmic bath are put together, as depicted in Figure ...**qubit** dynamics. This composed system can be mapped onto that of a **qubit**...**qubit**-nonlinear **oscillator** system....**qubit**-nonlinear oscillator system....**qubit**'s population difference is derived. Within the regime of validity...**qubit** plus oscillator system (yellow (light grey) box) and accounts afterwards...determine the qubit dynamics are depicted. In the first approach, which...**qubit** coupled to a dissipative nonlinear quantum oscillator: an effective...**qubit** state we couple the **qubit** linearly to the **oscillator** with the coupling...**qubit** dynamics. ... We consider a **qubit** coupled to a nonlinear quantum **oscillator**, the latter coupled to an Ohmic bath, and investigate the **qubit** dynamics. This composed system can be mapped onto that of a **qubit** coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum **oscillator**. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing **oscillator** within linear response theory in the driving amplitude. Knowing the effective spectral density, the **qubit** dynamics is investigated. In particular, an analytic formula for the **qubit**'s population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the composite **qubit**-nonlinear **oscillator** system.

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Contributors: Zhirov, O. V., Shepelyansky, D. L.

Date: 2007-10-10

**qubit** coupled to a quantum dissipative driven oscillator (resonator). ...**oscillator** with x = â + â / 2 , p = â - â / 2 i (left) and for **qubit** polarization...**frequency** of effective Rabi **oscillations** between quasi-degenerate levels...**oscillator** performs circle rotations in p x plane with **frequency** ω while...synchronization of qubit with radiation suppression **at** qubit frequency...**qubit** radiation spectrum with appearance of narrow lines corresponding...phenomenon of qubit synchronization is illustrated in a more clear way...the **qubit** polarization phase φ vs. oscillator phase ϕ ( p / x = - tan ...**qubit** coupled to a driven dissipative oscillator...**qubit** exhibits tunneling between two orientations with a macroscopic change...**qubit** coupled to a driven **oscillator** with jumps between two metastable...**qubit** radiation ξ z t as function of driving power n p in presence of ...**qubit** rotations become synchronized with the oscillator phase. In the ...direction of qubit polarization also changes in a smooth but nontrivial...rescaled **qubit** frequency Ω / ω 0 for parameters of Fig. fig1; N f are...**qubit** **frequency** Ω / ω 0 for parameters of Fig. fig1; N f are computed...Bistability of **qubit** coupled to a driven oscillator with jumps between...**qubit** polarization phase φ vs. **oscillator** phase ϕ ( p / x = - tan ϕ ) ...shows the **qubit** polarization vector components ξ x (blue/black) and ξ ...**qubit** rotations become synchronized with the **oscillator** phase. In the ...**qubit** with radiation suppression at **qubit** **frequency** Ω = 1.2 ω 0 and appearance...**oscillator** in two metastable states on the driving **frequency** ω (average...**qubit** coupled to a quantum dissipative driven **oscillator** (resonator). ...state** the **degree of qubit polarization ξ = | ξ → | is very close to unity s ... We study numerically the behavior of **qubit** coupled to a quantum dissipative driven **oscillator** (resonator). Above a critical coupling strength the **qubit** rotations become synchronized with the **oscillator** phase. In the synchronized regime, at certain parameters, the **qubit** exhibits tunneling between two orientations with a macroscopic change of number of photons in the resonator. The life times in these metastable states can be enormously large. The synchronization leads to a drastic change of **qubit** radiation spectrum with appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev {\it et al.} Nature {\bf 449}, 588 (2007)].

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Contributors: Makhlin, Yuriy, Shnirman, Alexander

Date: 2003-12-22

**oscillations** of the solid lines are compensated by the dashed line from...low-**frequency**, e.g. 1/f noise, motivated by recent experiments with superconducting...Josephson charge qubit. The simplest Josephson charge qubit is the Cooper-pair...**oscillations** of the solid lines in the diagrams and assuming very slow... ≫ E J for the qubit in Fig. F:qb at the degeneracy point, where the charge...**qubit**. The simplest Josephson charge **qubit** is the Cooper-pair box shown...the qubit’s 2 × 2 density matrix ρ ̂ , exp - i L 0 t θ t , where L 0 is...low-**frequency** noise is equivalent to that of quadratic longitudinal coupling...**frequencies**, we find:...**oscillations** under the influence of both low- and high-**frequency** fluctuations...high-**frequency** dashed line. The relaxation process in e also contributes...**qubit**...the qubit’s density matrix). The term in Fig. F:2ordera gives...**qubits** by transverse low-frequency noise... charge qubit ... We analyze the dissipative dynamics of a two-level quantum system subject to low-**frequency**, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-**frequency** noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent **oscillations** under the influence of both low- and high-**frequency** fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing.

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Contributors: Shevchenko, S. N., Ashhab, S., Nori, Franco

Date: 2011-10-17

**qubit**. In the inverse problem, the response of the **qubit** to external driving...**oscillations** is smaller for ε 0 0 . Therefore, using...**frequency** shift as obtained in the previous Appendix, Eq. ( DwNR)....respective force is...values of the qubit parameters, the model for the dissipative environment...Driving the qubit in a wide range of parameters is done first to plot ...**qubit** - nanomechanical resonator (NR) system, which was realized by LaHaye...**qubit** coupled to a nanomechanical resonator. The charge **qubit** (shown in...changes in the qubit bias result in large changes in the final state, ...**oscillations**, described by Eq. ( Pp2), are demonstrated in Fig. PIPII...**by **the **qubit**-NR coupling constant λ from Ref. [ LaHaye09]: ℏ λ 2 / π E...**oscillations**, which decreases with increasing A / ω . Here we also note...**frequency**: (a) ω / 2 π = 6.5 GHz Δ ...**qubit** is probed through the frequency shift of the low-frequency NR. In...**qubit**, quantum capacitance, nanomechanical
resonator, Landau-Zener ...**frequency** shift repeatedly changes sign. We then formulate and solve the... **qubit** is coupled to the NR (shown in green) through the capacitance C...**qubit**-resonator systems...**qubit**'s state to be known (i.e. measured by some other device) and aim...**qubit**'s Hamiltonian. In particular, for our system the **qubit**'s bias is...**qubit**, and the green parabola on the right shows the potential energy ... **qubit** coupled to a nanomechanical resonator. The charge **qubit** (shown ...**qubit** versus the energy bias ( n g ) and the driving amplitude ( n μ )...**frequency** shift Δ ω N R . (a) The **frequency** shift versus the energy bias...represents a qubit with control parameter ε 0 ; the parabola represents...**oscillations**, interferometry.%
...**qubit** is probed through the **frequency** shift of the low-**frequency** NR. In...**oscillations**, the higher the sensitivity. This is related to the period ... We consider theoretically a superconducting **qubit** - nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)]. First, we study the problem where the state of the strongly driven **qubit** is probed through the **frequency** shift of the low-**frequency** NR. In the case where the coupling is capacitive, the measured quantity can be related to the so-called quantum capacitance. Our theoretical results agree with the experimentally observed result that, under resonant driving, the **frequency** shift repeatedly changes sign. We then formulate and solve the inverse Landau-Zener-Stuckelberg problem, where we assume the driven **qubit**'s state to be known (i.e. measured by some other device) and aim to find the parameters of the **qubit**'s Hamiltonian. In particular, for our system the **qubit**'s bias is defined by the NR's displacement. This may provide a tool for monitoring of the NR's position.

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Contributors: Poletto, S., Chiarello, F., Castellano, M. G., Lisenfeld, J., Lukashenko, A., Cosmelli, C., Torrioli, G., Carelli, P., Ustinov, A. V.

Date: 2008-09-08

**oscillation** **frequency** ω 0 depends on the amplitude of the manipulation...flux **qubit** circuit. (b) The control **flux **Φ c changes the potential barrier...**The** **qubit** is manipulated by changing two magnetic fluxes Φ x and Φ c ,... for **qubit** initialization in **the** left or right well, and Φ x 1 equal to...**the** **qubit** . **The** circuit was manufactured by Hypres using standard Nb/...**the** **qubit** flux is performed by measuring **the** switching current of an unshunted...coherent evolution of **the** **qubit**....**qubits**. An other advantage of this type of **qubit** is its insensitivity ...**oscillation** **frequencies** for the corresponding pulse amplitudes....for **qubit** manipulation at which the **qubit** potential has a shape as indicated...**oscillation** **frequency** could be tuned between 6 and 21 GHz by changing ...**oscillation** **frequencies** for different values of Φ c (open circles). Excellent...**oscillation** **frequency** as shown in Fig. fig:4(a). In Fig. fig:5, we plot...**oscillation** **frequency**, and (b) for different potential symmetry by detuning...**oscillations** of a tunable superconducting flux **qubit** by manipulating its...**qubit** by manipulating its energy potential with a nanosecond-long pulse...**qubit** manipulation at which the **qubit** potential has a shape as indicated...**qubit** circuit. (b) The control flux Φ c changes the potential barrier ...**oscillate** at a **frequency** ranging from 6 GHz to 21 GHz, tunable via the...**qubit** initially prepared in the state, and for (a) different pulse amplitudes...**oscillation** **frequency**, as shown in Fig. fig:4(b), is consistent with ...**qubit** manipulated without microwaves ... We experimentally demonstrate the coherent **oscillations** of a tunable superconducting flux **qubit** by manipulating its energy potential with a nanosecond-long pulse of magnetic flux. The occupation probabilities of two persistent current states **oscillate** at a **frequency** ranging from 6 GHz to 21 GHz, tunable via the amplitude of the flux pulse. The demonstrated operation mode allows to realize quantum gates which take less than 100 ps time and are thus much faster compared to other superconducting **qubits**. An other advantage of this type of **qubit** is its insensitivity to both thermal and magnetic field fluctuations.

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Contributors: Agarwal, S., Rafsanjani, S. M. Hashemi, Eberly, J. H.

Date: 2012-01-13

**qubit** case....**qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system...**qubits** are quasi-degenerate, i.e., with **frequencies** much smaller than ...**qubit**-**qubit** entanglement. Both number state and coherent state preparations...**qubits** are much smaller than the oscillator frequency and the coupling...**oscillator** **frequency**, ω 0 ≪ ω , while the coupling between the **qubits** ... a single qubit....two-qubit case. Qualitative differences between the single-qubit and the...**frequencies** of **oscillation**, 2 Ω N ω and 2 2 Ω N ω . Since three new basis...**oscillator** state with the lowest of the S x states. Note the breakup in... of two-qubit TC model derived within the RWA is valid. At resonance, ...**qubit** system as a consequence of having only one Rabi **frequency** in the...that the two-qubit analytic formula matches well to the corresponding ...**oscillator**. For an **oscillator** of mass M and **frequency** ω the zero point...one-**qubit** and (b.) two-**qubit** probability dynamics, and (c.) shows that... (a.) one-qubit and (b.) two-qubit probability dynamics, and (c.) shows... for the single qubit case....**frequencies** of the **qubits** are much smaller than the **oscillator** **frequency**...**qubit** interacting with a common **oscillator** mode is extended beyond the...single-**qubit** case where only one Rabi **frequency** determines the evolution...single qubit case....multi-qubit cases are highlighted. In particular, we study the collapse...to the two-qubit case. Qualitative differences between the single-qubit...**qubit** interacting with a common oscillator mode is extended beyond the...**qubits**...**qubit**....two-qubit case (Fig. f.collapse_revival_double). The RWA fails to describe...two-**qubit** dynamics that are different from the single **qubit** case, including ... The Tavis-Cummings model for more than one **qubit** interacting with a common **oscillator** mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the **frequencies** of the **qubits** are much smaller than the **oscillator** **frequency** and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single **qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intra-manifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-**qubit** dynamics that are different from the single **qubit** case, including calculations of **qubit**-**qubit** entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.

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

Date: 2004-05-03

**frequency** f 2 at the value f 2 * and measured Rabi **oscillations** (black...**oscillations** with high visibility (65%)....**oscillations**....**frequency** to the **qubit** resonance and measured the switching probability...**qubit** by resonant activation...**frequency** of the **qubit** and (insert) persistent-current versus external...**qubit** and (insert) persistent-current versus external flux. The squares...**qubit** damping time T 1 , to prevent loss of excited state population. ...**qubit** state, which we detect by resonant activation. With a measurement...**frequency**. fig4...**oscillations** at a Larmor **frequency** f q = 7.15 ~ G H z (b) Switching probability...high-**frequency** side of the peak. Thus the plasma **oscillator** non-linearity...**qubit** loop (the scale bar indicates 1 ~ μ m ). Two layers of Aluminium...**frequency** on the **qubit** state, which we detect by resonant activation. ...between the **qubit** states in a time shorter than the **qubit**’s energy relaxation...**oscillation** measured by DC current pulse (grey line, amplitude A = 40 ...**qubit**. It relies on the dependency of the measuring Superconducting Quantum...**qubit** to be in 0 would result into broadening of the curve P s w π ), ...**SQUID** and the **qubit** by fitting the **qubit** “step" appearing in the **SQUID** ... We present the implementation of a new scheme to detect the quantum state of a persistent-current **qubit**. It relies on the dependency of the measuring Superconducting Quantum Interference Device (SQUID) plasma **frequency** on the **qubit** state, which we detect by resonant activation. With a measurement pulse of only 5ns, we observed Rabi **oscillations** with high visibility (65%).

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