### 63157 results for qubit oscillator frequency

Contributors: Wirth, T., Lisenfeld, J., Lukashenko, A., Ustinov, A. V.

Date: 2010-10-05

**qubit**. A capacitively shunted dc-SQUID is used as a nonlinear resonator...**oscillations** of the **qubit** for different driving powers, from bottom to...flux of** the **qubit state....**frequency** of 1.9 GHz. As the two **qubit** states differ by magnetic flux ...**qubit** state measurement time down to 25 microseconds, which is much faster...**qubit** microwave driving. As it is expected, the **frequency** of Rabi **oscillations**...**qubit** for future experiments. Fig. fig:3 (b) shows the same **frequency**...**qubits**, phase **qubit**, dispersive readout, SQUID...**qubits** using a single microwave line by employing frequency-division multiplexing... qubit Josephson junction .... qubit itself. We verified this fact by measuring** the **same qubit with ...**frequency** applied to the SQUID vs. externally applied flux. The measurement...the qubit. The pulsed microwave signal is applied via a cryogenic circulator...**oscillations** of the **qubit** measured for different driving powers of the... qubit for different driving powers, from bottom to top: -18 dBm, -15 ...**qubit**. The pulsed microwave signal is applied via a cryogenic circulator...the qubit changing its magnetic flux by approximately Φ 0 . (a) In the... qubit measured for different driving powers of** the **qubit microwave driving...**qubits** using a single microwave line by employing **frequency**-division multiplexing...**frequency** shift induced by the **qubit** is shown in detail in Fig. fig:3...**qubit**...biasing** the **qubit**. The** qubit is controlled by microwave pulses which are...**qubit**. We detect the flux state of the **qubit** by measuring the amplitude...**frequency** of the SQUID resonator by 30 MHz due to the **qubit** changing its ... We present experimental results on a dispersive scheme for reading out a Josephson phase **qubit**. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the **qubit**. We detect the flux state of the **qubit** by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the **qubit** state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows for reading out multiple **qubits** using a single microwave line by employing **frequency**-division multiplexing.

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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: 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: Huang, Ren-Shou, Dobrovitski, Viatcheslav, Harmon, Bruce

Date: 2005-04-18

one qubit coupled with 14 spins at T = 200 mK and T = 10 mK. The left ...**qubit** decohered by many spins undergoing Rabi **oscillation** by a coherent...where the qubit is coupled to a spurious resonator, and the dotted line...result **of a **qubit dephased by 14 spins with and without a spurious resonator...**frequency** ω = 2 α . At high **frequency** the Fourier spectrum is dominated...result produced by a qubit under the direct influence** of** 1/f noise. In...**oscillations** of a **qubit** dephased and relaxed by a many-spin system. The...**qubits** have suggested the existence in the tunnel barrier of bistable ... of the qubit transition frequency. Here this situation is numerically...**qubit** transition **frequency**. Here this situation is numerically simulated...is the qubit and the resonator peak is barely visible. When the qubit ...**oscillation** of one **qubit** coupled with 14 spins at T = 200 mK and T = 10...spectroscopic data** of** the qubit transition frequency. Here this situation...**qubit** and the resonator peak is barely visible. When the **qubit** energy ...**oscillations** of the **qubit** exhibit multiple stages of decay. New approaches...**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...oscillations **of a **qubit dephased and relaxed by a many-spin system. The...**oscillation** of a **qubit** coupled to a spurious resonator is also studied...**oscillation**....of the qubit decohered by many spins undergoing Rabi oscillation by a ... a qubit dephased and relaxed by a many-spin system. The parameters are...**qubit** under the direct influence of 1/f noise. In the graph of the Fourier...**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: 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...**of** **qubit**, **showing** **qubit** states and in cubic well at left. Measurement...**frequency** ω / 2 π and bias current I for a fixed microwave power. Data...**frequency**. Dotted vertical lines are centered at spurious resonances...**qubits** as well as existing Josephson technologies. We predict that removing...**qubit**. Junction current bias I is set by I φ and microwave source I μ...**qubit**, showing **qubit** states and in cubic well at left. Measurement of...**qubits**, Josephson junction, decoherence...**diagram** for coupled **qubit** and resonant states for ω 10 ≃ ω r . Coupling...**oscillation** **frequency** versus microwave amplitude. A linear dependence...**oscillations** for an improved phase **qubit**, and show that their coherence...**qubit**, and show that their coherence amplitude is significantly degraded...**qubits**....**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: 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....by rotating the qubit state for a time t * = π / 4 Ω R . In the presence...**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...logical qubit. The central MBSs γ 2 and γ 3 are tunnel-coupled ( t c )...**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**... the fidelity of qubit rotations. ... 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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Contributors: Liang, Xian-Ting

Date: 2009-08-26

**qubit** coupled to an intermediate harmonic **oscillator** has longer decoherence...**frequencies** of baths be infinite and finite. Secondly, we investigate ...**qubits** we use a numerically exact algorithm, iterative tensor multiplication...**frequency**;
Decorerence and Relaxation times
...**frequency** of the bath ω c...**qubit** governed by J A I ω vs by J A F ω in different values of ω c . Top...**qubit** has different dynamics governed by the two kinds of spectral density...**qubit** in model C versus in model D governed by the ESDFs J C I / F ω and... **qubit** in model B governed by J B I ω vs by J B F ω in different values...**frequency** ω c different values. It is shown that the absolute values of...**qubit** in model B governed by J B I ω vs by J B F ω in different values...**qubit** coupled to an intermediate harmonic oscillator has longer decoherence...**qubits** in four kinds of systems constructed with the basic spin-boson ... In this paper we firstly obtain two kinds of effective spectral density functions by setting the cut-off **frequencies** of baths be infinite and finite. Secondly, we investigate the reduced dynamics of open **qubits** in four kinds of systems constructed with the basic spin-boson model. It is shown that the **qubit** has different dynamics governed by the two kinds of spectral density functions. In addition, we obtained that a **qubit** coupled to an intermediate harmonic **oscillator** has longer decoherence and relaxation times as they are coupled to a common bath than to their respective baths. In solving the dynamics of **qubits** we use a numerically exact algorithm, iterative tensor multiplication algorithm based on the quasiadiabatic propagator path integral scheme.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-07-30

**oscillator** **frequency** approaches unity and goes beyond. In this regime ...**oscillator** **frequency** Ω , ε = l Ω . In this case we found that the levels...**qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore...**frequency** peaks coming from the two dressed **oscillation** **frequencies** Ω ...**Qubit**-oscillator system: An analytical treatment of the ultra-strong coupling...**qubit** for an **oscillator** at low temperature. We consider the coupling strength...**oscillations** **frequency** Ω j l . For l being not an integer those doublets...**qubit**-oscillator detuning. Furthermore, the dynamics is not governed anymore...**qubit** for an oscillator at low temperature. We consider the coupling strength...**qubit** ( ε / Ω = 0.5 ) at resonance with the oscillator Δ b = Ω in the ...**frequencies** through a variation of the coupling....**qubit** ( ε / Ω = 0.5 ) at resonance with the **oscillator** Δ b = Ω in the ...**frequency** range. The lowest **frequency** peaks originate from transitions...**qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime...**oscillations**. With increasing time small differences between numerical...**oscillation** **frequency** Ω j 0 . Numerical calculations and VVP predict group...**oscillation** **frequencies** Ω j 1 and Ω j 2 influence the longtime dynamics...**qubit** ( ε / Ω = 0.5 ) being at resonance with the **oscillator** ( Δ b = Ω ... We examine a two-level system coupled to a quantum **oscillator**, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the **qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including in particular also the finite bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the **qubit** for an **oscillator** at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many **frequencies** are contributing to the dynamics. They are gathered into groups whose spacing depends on the **qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a non-trivial dressing of the tunneling matrix element, which can be used to suppress specific **frequencies** through a variation of the coupling.

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Contributors: Zorin, A. B.

Date: 2003-12-09

**qubit** state with the rf oscillation span ± π / 2 is preferable in either...**frequency** ω r f ≈ ω 0 , the resonant **frequency** of the uncoupled tank circuit...**frequency** ω 0 = 2 π × 100 MHz, L T / C T 1 / 2 = 100 Ω , k 2 Q β L = ...lines). The **qubit** parameters are the same as in Fig. 2....**qubit** state with the rf **oscillation** span ± π / 2 is preferable in either...radio-**frequency** readout of the **qubit**. (a) The resonance curves of the ...**qubit** based on a superconducting single charge transistor inserted in ...states of the **qubit**....**given** **qubit** parameters (see caption of Fig. 2)....**qubit** whose value, as well as the produced **frequency** shift δ ω 0 , is ...The **qubit** is controlled by charge Q 0 generated by the gate and flux Φ...charge-flux **qubit** are characterized by self-capacitances C 1 and C 2 and...**oscillations** induced in the **qubit**. Recently, we proposed a transistor ...**frequency** of these **oscillations** is sufficiently low, ω r f ≪ Ω , they ...**qubit** whose value, as well as the produced frequency shift δ ω 0 , is ...**e for** the **given** **qubit** parameters (see caption of Fig. 2)....**qubit** dephasing and relaxation due to electric and magnetic control lines...**qubit** states by measuring the effective Josephson inductance of the transistor...**qubit** dephasing is of minor importance, while the requirement of a sufficiently...**qubit** in magic points producing minimum decoherence are given....**qubit** parameters are the same as in Fig. 2....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...**frequency** Ω . Increase in amplitude of steady **oscillations** up to φ a ≈...**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**, located on the left of the dashed line, coupled to a large CBJJ...**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**. This tunable and selective coupling provides two-**qubit** entangled... qubit-bus system. Here, C g k and 2 ε J k are the gate capacitance and...**qubits** without direct interaction can be effectively coupled by sequentially...**oscillator** with adjustable **frequency**. The coupling between any **qubit** and...**qubit**-bus system. Here, C g k and 2 ε J k are the gate capacitance and... qubit and the bus energies is ℏ Δ k = ε k - ℏ ω b . n = 0 , 1 is occupation...**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. ζ k is the maximum strength of the coupling between the k th qubit ... 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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