### 63089 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: 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: 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: 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: 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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