### 57455 results for qubit oscillator frequency

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...single-**qubit** case where only one Rabi frequency determines the evolution...two-**qubit** analytic formula matches well to the corresponding numerical...**qubits** are quasi-degenerate, i.e., with **frequencies** much smaller than ...**qubits** are coupled to the **oscillator** so strongly, or are so far detuned...**oscillator**. For an **oscillator** of mass M and **frequency** ω the zero point...**oscillator** is allowed to be an appreciable fraction of the **oscillator** **frequency**. In this parameter regime, the dynamics of the system can neither...one-**qubit** and (b.) two-**qubit** probability dynamics, and (c.) shows that...**qubit**-**qubit** entanglement. Both number state and coherent state preparations...**frequencies** of the **qubits** are much smaller than the **oscillator** **frequency**...**qubit** interacting with a common **oscillator** mode is extended beyond the...two-**qubit** TC model derived within the RWA is valid. At resonance, the ...**qubits** are much smaller than the oscillator frequency and the coupling...two-**qubit** numerical evaluation, which comes from the ω - 2 ω beat note...**oscillator** **frequency**, ω 0 ≪ ω , while the coupling between the **qubits** ...**qubits** can be seen....two-**qubit** case. Qualitative differences between the single-**qubit** and the...two-**qubit** TC model beyond the validity regime of RWA. The regime of parameters...**qubit** interacting with a common oscillator mode is extended beyond the...**qubits**...**qubit**....**oscillator** state with the lowest of the S x states. Note the breakup in...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: Huang, Ren-Shou, Dobrovitski, Viatcheslav, Harmon, Bruce

Date: 2005-04-18

**qubit** and the resonator peak is barely visible. When the **qubit** energy ...**oscillations** of the **qubit** exhibit multiple stages of decay. New approaches...**qubit** decohered by many spins undergoing Rabi **oscillation** by a coherent...**qubit** decohered by many spins undergoing Rabi oscillation by a coherent...**qubit** exhibit multiple stages of decay. New approaches are established...**qubit** coupled to a spurious resonator is also studied, where we proposed...**qubit** dephased by 14 spins with and without a spurious resonator, which...**frequency** ω = 2 α . At high **frequency** the Fourier spectrum is dominated...**qubit** transition frequency. Here this situation is numerically simulated...**oscillation** of a **qubit** coupled to a spurious resonator is also studied...**oscillation**....**qubit** dephased and relaxed by a many-spin system. The parameters are the...**qubit**-spurious resonator system. In both graphs, the vertical axes are...**oscillations** of a **qubit** dephased and relaxed by a many-spin system. The...**qubits** have suggested the existence in the tunnel barrier of bistable ...**qubit** transition **frequency**. Here this situation is numerically simulated...**qubit** energy is detuned from the resonator at 9.95 GHz, the most visible...**qubit** under the direct influence of 1/f noise. In the graph of the Fourier...**oscillation** of one **qubit** coupled with 14 spins at T = 200 mK and T = 10...**Qubit** Rabi Oscillation Decohered by Many Two-Level Systems ... Recent experiments on Josephson junction **qubits** have suggested the existence in the tunnel barrier of bistable two level fluctuators that are responsible for decoherence and 1/f critical current noise. In this article we treat these two-level systems as fictitious spins and investigate their influence quantum mechanically with both analytical and numerical means. We find that the Rabi **oscillations** of the **qubit** exhibit multiple stages of decay. New approaches are established to characterize different decoherence times and to allow for easier feature extraction from experimental data. The Rabi **oscillation** of a **qubit** coupled to a spurious resonator is also studied, where we proposed an idea to explain the serious deterioration of the Rabi osillation amplitude.

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

Date: 2009-07-20

**Oscillator** **frequency** shift as function or the **qubit** splitting ϵ = ω + ...**qubit** splitting ϵ = ω + Δ for the spin state | ↓ obtained (a) within RWA...**qubit** state | ↓ ....**qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and ...**qubit** readout is possible. If several **qubits** are coupled to one resonator...**qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic...**qubits**....**Qubit**-oscillator dynamics in the dispersive regime: analytical theory ...**qubit**-oscillator coupling, we diagonalize the non-RWA Hamiltonian and ...**qubit** state | ↓ , where σ z | ↓ = - | ↓ . The results are depicted in ... We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the **qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive **qubit** readout is possible. If several **qubits** are coupled to one resonator, an effective **qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic interaction. This impacts on the entanglement characteristics of the **qubits**.

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Contributors: Simmonds, R. W., Lang, K. M., Hite, D. A., Pappas, D. P., Martinis, John M.

Date: 2004-02-18

**Qubits** from Junction Resonances...**qubits** show great promise for quantum computing, the origin of dominant...**frequency** resonators impacts the future of all Josephson **qubits** as well...**frequency** ω / 2 π and bias current I for a fixed microwave power. Data...diagram of qubit, showing qubit states and in cubic well at left. Measurement...**frequency**. Dotted vertical lines are centered at spurious resonances...**qubits** as well as existing Josephson technologies. We predict that removing...coupled qubit and resonant states for ω 10 ≃ ω r . Coupling strength ...**qubit**, showing **qubit** states and in cubic well at left. Measurement of...**qubits**, Josephson junction, decoherence...**qubit**, and show that their coherence amplitude is significantly degraded...**oscillation** **frequency** versus microwave amplitude. A linear dependence...**oscillations** for an improved phase **qubit**, and show that their coherence...**qubits**....junction qubit. Junction current bias I is set by I φ and microwave source...**oscillations**. ... Although Josephson junction **qubits** show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. We report Rabi **oscillations** for an improved phase **qubit**, and show that their coherence amplitude is significantly degraded by spurious microwave resonators. These resonators arise from changes in the junction critical current produced by two-level states in the tunnel barrier. The discovery of these high **frequency** resonators impacts the future of all Josephson **qubits** as well as existing Josephson technologies. We predict that removing or reducing these resonators through materials research will improve the coherence of all Josephson **qubits**.

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Contributors: Shevchenko, S. N., Omelyanchouk, A. N., Zagoskin, A. M., Savel'ev, S., Nori, F.

Date: 2007-12-12

**frequency** dependent on the perturbation amplitude. These serve as one ...**oscillations** from their classical Doppelganger....**qubit** in Fig. 4 of Ref. [...**qubit** states....**qubits** (current-biased Josephson junctions) this effect can be mimicked...**frequency**. The parameters used here are: η = 0.95 , E J / ℏ ω p = 300 ...**oscillations** in current-biased Josephson junctions: (a) and (b) show the...**qubits** provide a clear demonstration of quantum coherent behaviour in ...**frequency** in the classical case, in contrast to the positive Bloch-Siegert...**qubit** in state | 1 . Alternatively, instead of an RF readout pulse one...**oscillations** can be produced by the subharmonics of the resonant **frequency**...**qubit** (a) and its Josephson energy (b). The metastable states and can ...**qubit** is a current-biased Josephson junction (see Fig. scheme(a)), and...**frequency** and the amplitude of the **oscillations** respectively for ϵ = 2...**qubit**...**frequency** for relatively weak (a) and strong (b) driving. Different values ... Rabi **oscillations** are coherent transitions in a quantum two-level system under the influence of a resonant perturbation, with a much lower **frequency** dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently [N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. 95, 067001 (2005)] that in phase **qubits** (current-biased Josephson junctions) this effect can be mimicked by classical **oscillations** arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between the classical and quantum effect. First, while the quantum Rabi **oscillations** can be produced by the subharmonics of the resonant **frequency** (multiphoton processes), the classical effect also exists when the system is excited at the overtones. Second, the shape of the resonance is, in the classical case, characteristically asymmetric; while quantum resonances are described by symmetric Lorentzians. Third, the anharmonicity of the potential results in the negative shift of the resonant **frequency** in the classical case, in contrast to the positive Bloch-Siegert shift in the quantum case. We show that in the relevant range of parameters these features allow to confidently distinguish the bona fide Rabi **oscillations** from their classical Doppelganger.

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### Temperature square dependence of the low **frequency** 1/f charge noise in the Josephson junction **qubits**

Contributors: Astafiev, O., Pashkin, Yu. A., Nakamura, Y., Yamamoto, T., Tsai, J. S.

Date: 2006-04-04

**qubit** dephasing during coherent oscillations. The coherent oscillations...**qubits**, we study temperature dependence of the 1/f noise and decay of ...**frequency** integration limit and the high **frequency** cutoff are taken to...**oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated...**oscillations** decay as exp - t 2 / 2 T 2 * 2 with...**frequency** 1/f noise and the quantum f noise recently measured in the Josephson...**qubits** off the electrostatic energy degeneracy point is consistently explained...**qubit** as an SET and measure the low **frequency** charge noise, which causes...**oscillations** measured at T = 50 mK and the dashed envelope exemplifies...**qubit** as an SET and measure the low frequency charge noise, which causes...**frequency** 1/f noise that is observed in the transport measurements....**oscillation** as a function of t away from the degeneracy point ( θ ≠ π ...**qubits**...**qubit** dephasing during coherent **oscillations**. The coherent **oscillations** ... To verify the hypothesis about the common origin of the low **frequency** 1/f noise and the quantum f noise recently measured in the Josephson charge **qubits**, we study temperature dependence of the 1/f noise and decay of coherent **oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge **qubits** off the electrostatic energy degeneracy point is consistently explained by the same low **frequency** 1/f noise that is observed in the transport measurements.

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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
...**qubit** cluster, is designed, and system of equations for
network dynamics...one-**qubit**
gates are suggested. Changing of cluster entanglement degree...**oscillators** is
proposed for modeling of a cluster of entangled **qubits** ...**oscillators** with chaotically modulated limit cycle radii and
**frequencies**...**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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Contributors: Zorin, A. B.

Date: 2003-12-09

**frequency** ω r f ≈ ω 0 , the resonant **frequency** of the uncoupled tank circuit...**qubit** by Duty et al. . Their Al Cooper pair box had E c ≈ 0.8 Δ s c and...**frequency** ω 0 = 2 π × 100 MHz, L T / C T 1 / 2 = 100 Ω , k 2 Q β L = ...**qubit** state with the rf **oscillation** span ± π / 2 is preferable in either...**qubit** based on a superconducting single charge transistor inserted in ...radio-**frequency** readout of the **qubit**. (a) The resonance curves of the ...**qubit** whose value, as well as the produced **frequency** shift δ ω 0 , is ...**qubit** operation. In this basis, the Hamiltonian ( H0) is diagonal,...**oscillations** induced in the **qubit**. Recently, we proposed a transistor ...**qubit**. Another useful quantity is the Josephson inductance of the double...**frequency** of these **oscillations** is sufficiently low, ω r f ≪ Ω , they ...**qubit** dephasing and relaxation due to electric and magnetic control lines...**qubit** states by measuring the effective Josephson inductance of the transistor...**qubit**. Recently, we proposed a transistor configuration of the Cooper ...**qubit** in magic points producing minimum decoherence are given....**qubit** parameters are the same as in Fig. 2....**qubit** inductively coupled to a tank circuit by mutual inductance M . The...radio-**frequency** driven tank circuit enabling the readout of the **qubit** ...**qubit** calculated for the mean Josephson coupling E J 0 ≡ 1 2 E J 1 + E...**qubit** parameters (see caption of Fig. 2)....**frequency** Ω . Increase in amplitude of steady **oscillations** up to φ a ≈...**qubit** parameters (see caption of Fig. 2)....**qubit**....**oscillations** and has a small effect on the rise time of the response signal...**qubit** with radio frequency readout: coupling and decoherence ... The charge-phase Josephson **qubit** based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-**frequency** driven tank circuit enabling the readout of the **qubit** states by measuring the effective Josephson inductance of the transistor. The effect of **qubit** dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the **qubit** in magic points producing minimum decoherence are given.

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Contributors: Wei, L. F., Liu, Yu-xi, Nori, Franco

Date: 2004-02-27

**qubits** without direct interaction can be effectively coupled by sequentially...**oscillator** with adjustable **frequency**. The coupling between any **qubit** and...**qubits**, located on the left of the dashed line, coupled to a large CBJJ...**qubit**-bus system. Here, C g k and 2 ε J k are the gate capacitance and...**qubit** and the bus can be controlled by modulating the magnetic flux applied...**qubits** and the bus. The dashed line only indicates a separation between...**qubit**. ζ k is the maximum strength of the coupling between the k th **qubit**...**qubits** via a current-biased information bus...**frequency** ω b . The detuning between the **qubit** and the bus energies is...**qubit** and the bus energies is ℏ Δ k = ε k - ℏ ω b . n = 0 , 1 is occupation...**qubit**. This tunable and selective coupling provides two-**qubit** entangled ... Josephson **qubits** without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an **oscillator** with adjustable **frequency**. The coupling between any **qubit** and the bus can be controlled by modulating the magnetic flux applied to that **qubit**. This tunable and selective coupling provides two-**qubit** entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality.

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Contributors: Schmidt, Thomas L., Nunnenkamp, Andreas, Bruder, Christoph

Date: 2012-11-09

**qubit**. The central MBSs γ 2 and γ 3 are tunnel-coupled ( t c ) to a topologically...single-**qubit** operations....**qubit** rotations....**qubit** state for a time t * = π / 4 Ω R . In the presence of damping, the...**frequency** | Ω R | in units of c = n p h g c 2 / L for μ = - 100 ϵ L and...**frequency** and damping, Ω R / Γ R , determines the fidelity of **qubit** rotations...**frequency** and damping determined numerically from Eq. ( eq:Dgamma2). Solid...single-**qubit** gate. Supplemented with one braiding operation, this gate...**frequency** is, as expected, exponentially suppressed in the length of the...**qubits** on which certain operations can be performed in a topologically...**qubit** rotations in microwave cavities...**frequency** Ω approaches the critical value | μ | , the prefactor 1 - Ω ...**oscillations** between adjacent Majorana bound states. These **oscillations** ... Majorana bound states have been proposed as building blocks for **qubits** on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi **oscillations** between adjacent Majorana bound states. These **oscillations** can be used to implement an additional single-**qubit** gate. Supplemented with one braiding operation, this gate allows to perform arbitrary single-**qubit** operations.

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