### 62680 results for qubit oscillator frequency

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

Date: 2003-03-04

**oscillations** in a phase **qubit**. The external source, typically in GHz range...**qubit** states, nevertheless the voltage across the tank **oscillates** with...**qubit** coupled to a dissipative tank circuit. The evolution of A exhibits...**qubit**). We explicitly account for the back action of a tank circuit and...**oscillations** with lower **frequency**. Deterministic case (a) together with...L...destroys the phase coherence between qubit states, nevertheless the voltage...**qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit**...speaking, consider qubit as having definite wave function. However, if...P...**qubit**. The external source, typically in GHz range, induces transitions...of qubit evolution as the coupling between the qubit and the tank is increased...loss-free qubit coupled to the dissipative tank circuit. The system is...loss-free **qubit** coupled to a loss-free tank circuit. Oscillations of A...**oscillates** with a high **frequency** which is about 10 GHz in our case. As...**qubit** loop. As is seen from the Fig. fig4a, A **oscillates** with Rabi **frequency**...case....**qubit** levels. The resulting Rabi oscillations of supercurrent in the **qubit**...**qubit**. Computer simulations...**oscillations** correspond to Rabi **frequency**....**oscillates** with gap **frequency**, while the **frequency** of A is almost ten ...**oscillates** also with Rabi **frequency** which is equal to 50 MHz in our case... to show the effect of qubit evolution as the coupling between the qubit... **qubit** coupled to a dissipative tank circuit Q T = 100 . The voltage across...**qubit** coupled to a loss-free tank circuit. **Oscillations** of A. Deterministic... A and B for **qubit** without dissipation....**qubit** without dissipation....**frequency**. Deterministic case (a) together with one realization (b) are...**oscillations** in MHz range can be detected using conventional NMR pulse...**oscillations** between quantum states in mesoscopic superconducting systems...**qubit**. Here we present the results of detailed computer simulations of ... Time-domain observations of coherent **oscillations** between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi **oscillations** in a phase **qubit**. The external source, typically in GHz range, induces transitions between the **qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit** loop are detected by a high quality resonant tank circuit, inductively coupled to the phase **qubit**. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase **qubit**). We explicitly account for the back action of a tank circuit and for the unpredictable nature of outcome of a single measurement. According to the results of our simulations the Rabi **oscillations** in MHz range can be detected using conventional NMR pulse Fourier technique.

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Contributors: Beaudoin, Félix, da Silva, Marcus P., Dutton, Zachary, Blais, Alexandre

Date: 2012-08-09

**qubits** have **frequencies** separated enough that they do not overlap during...**the** **second** **qubit**. The fidelity is extracted by injecting these unitaries...two-**qubit** operations in circuit QED. ϵ is the strength of the drive used...**qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how...anticrossings in the qubit-resonator or qubit-qubit spectrum. They are...**qubit** or the resonator, with the significant disadvantage that such implementations...of the fidelity on qubit relaxation and dephasing is similar....**oscillator** with **frequency** ω r = 7.8 GHz. As explained in Section sec:...**qubit** at the red sideband **frequency** assuming the second **qubit** is in its...two-**qubit** operations in circuit QED. ϵ is **the** strength of **the** drive used...**qubit** frequency modulation...**oscillators** (see Section sec:Duffing) with E J 1 = 25 GHz, E J 2 = 35...**qubit** splitting is modulated at a **frequency** that lies exactly between ...**frequency** associated to the operating point φ i . This **frequency** is illustrated...coming from the spectator qubit (see Section sec:SB)....prepare qubit-qubit entangled states. The parameters of every pulses entering...**qubits** and microwave resonators. Up to now, these transitions have been...**qubit** frequency using a flux-bias line. Not only can first-order transitions...**oscillations** have been seen to be especially large for big relevant ε ...**eqn**:trace). The qubits are taken to be transmons, which are modelled as...**oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can...**oscillations** in the Rabi **oscillations** that reduce the fidelity. These ...**qubit** transition **frequencies** in and out of resonance without crossing ...**second** **qubit** is excited. Blue dashed line: population transfer error 1...**qubit** at **the** red sideband frequency assuming **the** **second** **qubit** is in its ... Sideband transitions have been shown to generate controllable interaction between superconducting **qubits** and microwave resonators. Up to now, these transitions have been implemented with voltage drives on the **qubit** or the resonator, with the significant disadvantage that such implementations only lead to second-order sideband transitions. Here we propose an approach to achieve first-order sideband transitions by relying on controlled **oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can first-order transitions be significantly faster, but the same technique can be employed to implement other tunable **qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how such first-order sideband transitions can be used to implement a high fidelity controlled-NOT operation between two transmons coupled to the same resonator.

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Contributors: Saito, Keiji, Wubs, Martijn, Kohler, Sigmund, Hanggi, Peter, Kayanuma, Yosuke

Date: 2006-03-07

**qubit** and the oscillator, and can be written as...**qubit**, being independent of the frequency of the QED mode. Possible applications...**qubit** flip, the resulting dynamics is restricted to the states | ↑ , 2...**qubit** and the **oscillator**, and can be written as...**frequencies** Ω . The dashed line marks the Ω -independent, final probability...individual qubit-oscillator states for a coupling strength γ = 0.6 ℏ v...large **qubit**-oscillator coupling γ / ℏ Ω = 0.5 , reliable single-photon...**frequency** Ω = 0.5 v / ℏ ....**oscillator** **frequency**, P ↑ ↓ t resembles the standard LZ transition with...**frequency** Ω and the **qubit**-**oscillator** coupling γ are determined by the ...**qubit**, being independent of the **frequency** of the QED mode. Possible applications...**qubit**-**oscillator** entanglement....**qubit**-**oscillator** states for a coupling strength γ = 0.6 ℏ v and **oscillator**...**qubit** comes into resonance with the **oscillator** sometime during the sweep...**qubit** undergoing Landau-Zener transitions enabled by the coupling to a...**oscillator** **frequency** Ω , despite the fact that this is not the case for...**qubit** is in state | ↓ is depicted in Fig. fig:one-osc. It demonstrates...the **qubit** comes into resonance with the oscillator sometime during the...**qubit**-oscillator entanglement....**oscillations** that are typical for the tail of a LZ transition are averaged ... We study a **qubit** undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the **qubit**, being independent of the **frequency** of the QED mode. Possible applications are single-photon generation and the controllable creation of **qubit**-**oscillator** entanglement.

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Contributors: Yoshihara, Fumiki, Nakamura, Yasunobu, Yan, Fei, Gustavsson, Simon, Bylander, Jonas, Oliver, William D., Tsai, Jaw-Shen

Date: 2014-02-06

**oscillation**, $1/f$ noise...parallel to the qubit’s energy eigenbasis; this component is not averaged...**oscillation** curves with different Rabi **frequencies** Ω R measured at different...** qubit’s** energy eigenbasis; this component is not averaged out when Ω R...

**frequency**δ ω (black open circles) and the Bloch–Siegert shift δ ω B S...

**qubit**'s level splitting of 4.8 GHz, a regime where the rotating-wave approximation...

**oscillations**due to quasistatic flux noise. “Optimal" in the last column...

**oscillation**measurements, a microwave pulse is applied to the

**qubit**followed...

**oscillation**decay at ε = 0 , where the quasistatic noise contribution ...

**qubit**noise spectroscopy using Rabi oscillations under strong driving ...

**qubit**and its strong inductive coupling to a microwave line enabled high-amplitude...

**frequency**of ω m w / 2 π = 6.1 GHz, has a minimum of approximately ω ...

**frequency**range decreases with increasing

**frequency**up to 300 MHz, where...

**frequencies**up to 1.7 GHz were achieved, approaching the

**qubit**'s level...

**frequency**Ω R 0 at the shifted resonance decreases as ε increases, while...

**frequency**, and cal: Γ R s t δ ω m w stands for the calculation to study...

**oscillations**under strong driving conditions. The large anharmonicity ...

**qubit**by studying the decay of Rabi oscillations under strong driving ...the qubit followed by a readout pulse, and P s w as a function of the ...to the qubit followed by a readout pulse, and P s w as a function of the... qubit by a mutual inductance of 1.2 pH and nominally cooled to 35 mK....high-

**frequency**flux noise spectrum in a superconducting flux

**qubit**by ...

**qubit**by a mutual inductance of 1.2 pH and nominally cooled to 35 mK. ... We infer the high-

**frequency**flux noise spectrum in a superconducting flux

**qubit**by studying the decay of Rabi

**oscillations**under strong driving conditions. The large anharmonicity of the

**qubit**and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi

**frequencies**up to 1.7 GHz were achieved, approaching the

**qubit**'s level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide

**frequency**range decreases with increasing

**frequency**up to 300 MHz, where the spectral density is not very far from the extrapolation of the 1/f spectrum obtained from the free-induction-decay measurements. We discuss a possible origin of the flux noise due to surface electron spins.

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Contributors: Wubs, Martijn, Kohler, Sigmund, Hanggi, Peter

Date: 2007-03-15

**the** **qubit** would be measured | ↑ . fig:photon_averages...**the** **qubit** would be measured in state | ↓ ; **the** dash-dotted blue curve ...**qubit**-**oscillator** coupling γ . Parameters: γ = 0.25 ℏ v and ℏ Ω 2 = 100...**oscillator** depend on the state of the **qubit**....**qubit** coupled to one oscillator, far outside **the** RWA regime: γ = ℏ Ω =...the qubit. In general not much can be said about this final state, but...**qubit** coupled to two cavities, we show that Landau-Zener sweeps of the...**oscillator** **frequency**. In Fig. fig:photon_averages we depict how for a...**qubit** coupled to two **oscillators**. Parameters: γ = 0.25 ℏ v and Ω 2 = 100...**qubit**-**oscillator** coupling, then the dynamics can very well be approximated...**oscillator** if the **qubit** would be measured in state | ↓ ; the dash-dotted...**qubit**-oscillator entanglement, with state-of-the-art circuit QED as a ...**qubit**-**oscillator** entanglement, with state-of-the-art circuit QED as a ...**oscillator** energies ℏ Ω 1 , 2 are much larger than the **qubit**-**oscillator**...**qubit** are well suited for the robust creation of entangled cavity states...**qubit** coupled to one **oscillator**, far outside the RWA regime: γ = ℏ Ω =... of a qubit coupled to two oscillators. Parameters: γ = 0.25 ℏ v and Ω...**qubit** may undergo Landau-Zener transitions due to its coupling to one ...**qubit**-oscillator coupling γ . Parameters: γ = 0.25 ℏ v and ℏ Ω 2 = 100...final qubit-two-oscillator state | ψ ∞ rather than merely the transition...**oscillator** **frequencies**, both inside and outside the regime where a rotating-wave... final qubit state is | ↑ . We call this dynamical selection rule the ...**qubit** coupled to two **oscillators**. Parameters: γ = 0.25 ℏ v , ℏ Ω 1 = 90...**oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau-Zener...state of the qubit....**qubit** coupled to two oscillators with large energies, and with detunings...**qubit** coupled to one oscillator, Landau-Zener transitions can be used ...**qubit** coupled to two **oscillators** with degenerate energies. Parameters: ... A **qubit** may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic **oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of **qubit**-**oscillator** entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a **qubit** coupled to two cavities, we show that Landau-Zener sweeps of the **qubit** are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the **qubit** acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the **qubit**, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the **oscillator** **frequencies**, both inside and outside the regime where a rotating-wave approximation is valid.

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Contributors: Higgins, Kieran D. B., Lovett, Brendon W., Gauger, Erik M.

Date: 2012-03-27

**qubit** design but with an **oscillating** voltage applied to the CPB bias gate... qubits. The criterion for the single term approximation to be valid is...**qubit** and **oscillator**, thus requiring a theoretical treatment beyond the...**qubit** and oscillator, thus requiring a theoretical treatment beyond the...the qubit frequency Ω with temperature. The upper inset shows the dependence...**qubit** thermometry of an oscillator....**qubit** dynamics in this regime, based on an **oscillator** correlation function...**qubit** thermometry: T i n is the temperature supplied to the numerical ...**oscillations** with **frequency** ( eqn:rho3) to it. The blue line is the data...**qubit** thermometry of an **oscillator**....**qubit** dynamics. We obtain a new expression for the ac Stark shift and ...**qubit** dynamics in this regime, based on an oscillator correlation function...**oscillations** are also shown as a reference (green). Left: the population...**oscillator** Hilbert space at a point where the dynamics have converged ... the** qubit**. These parameters can be achieved experimentally using the

**sam**...

**frequency**of the

**qubit**dynamics is still adequately captured by our single...

**qubit**dynamics is still adequately captured by our single term approximation...

**qubit**

**frequency**Ω with temperature. The upper inset shows the dependence...

**oscillator**on the

**qubit**. These parameters can be achieved experimentally...

**oscillator**represents a ubiquitous physical system. New experiments in...

**frequency**domain. The full numerical solution was Fourier transformed ...the

**dynamics analytically unwieldy, because the rational function...**

**qubit****qubit**dynamics are not greatly perturbed by the presence of the

**oscillator**... the

**dynamics are not greatly perturbed by the presence of the oscillator...of qubit thermometry: T i n is the temperature supplied to the numerical ... A quantum two level system coupled to a harmonic**

**qubit****oscillator**represents a ubiquitous physical system. New experiments in circuit QED and nano-electromechanical systems (NEMS) achieve unprecedented coupling strength at large detuning between

**qubit**and

**oscillator**, thus requiring a theoretical treatment beyond the Jaynes Cummings model. Here we present a new method for describing the

**qubit**dynamics in this regime, based on an

**oscillator**correlation function expansion of a non-Markovian master equation in the polaron frame. Our technique yields a new numerical method as well as a succinct approximate expression for the

**qubit**dynamics. We obtain a new expression for the ac Stark shift and show that this enables practical and precise

**qubit**thermometry of an

**oscillator**.

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Contributors: Liberti, G., Zaffino, R. L., Piperno, F., Plastina, F.

Date: 2005-11-21

**qubit** is coupled to a single **oscillator** mode. 99 weiss U. Weiss, Quantum...**frequency** and the level asymmetry of the **qubit**. This is done in the adiabatic...**qubit**. This is done in the adiabatic regime in which the time evolution...of a qubit with an ohmic environment was numerically analyzed. It turns...of the **qubit** tunnelling amplitude D . One can appreciate that the result...**oscillator** in the lower adiabatic potential, for D = 10 and α = 2 and ...**qubit** is much faster than the oscillator one. Within the adiabatic approximation...**oscillator** defined in Eq. ( due1), centered in Q = ± Q 0 , respectively...**qubit** ( W = D = 0 ) would have given a pair of independent parabolas instead...the qubit is coupled to a single oscillator mode....**qubit** tunnelling amplitude D . One can appreciate that the result of Eq...**qubit** strongly interacting with an oscillator mode, as a function of the...asymmetry in the qubit Hamiltonian. As mentioned in section sect2 above...**qubit** coupled to a resonator in the adiabatic regime...**qubit** and the environmental **oscillator**. Unfortunately, the coupling strength...to the reduced qubit state. For example, for a large enough interaction...**oscillator** localizes in one of the wells of its effective potential and...**qubit** is much faster than the **oscillator** one. Within the adiabatic approximation...the qubit and the environmental oscillator. Unfortunately, the coupling...**qubit** strongly interacting with an **oscillator** mode, as a function of the ... We discuss the ground state entanglement of a bi-partite system, composed by a **qubit** strongly interacting with an **oscillator** mode, as a function of the coupling strenght, the transition **frequency** and the level asymmetry of the **qubit**. This is done in the adiabatic regime in which the time evolution of the **qubit** is much faster than the **oscillator** one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.

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

Date: 2012-05-10

**qubit**-**oscillator** coupling ( g 2 = 0 ), resonant driving, Ω = ω 0 , and...**oscillator** damping γ = 0.02 ϵ . The amplitude A = 0.07 ϵ corresponds to...**oscillator** damping γ . The driving amplitude is A = 3.5 γ , such that ...**qubit**-**oscillator** coupling ( g 1 = 0 ), resonant driving at large **frequency**...**qubit**-**oscillator** Hamiltonian to the dispersive frame and a subsequent ...**qubit** expectation value σ x which exhibits decaying oscillations with ...**qubit** expectation value σ x which exhibits decaying **oscillations** with **frequency** ϵ . The parameters correspond to an intermediate regime between...linear **qubit**-oscillator coupling ( g 2 = 0 ), resonant driving, Ω = ω ...**qubit**-oscillator detuning and by considering also a coupling to the square... **qubit** operator σ x (solid line) and the corresponding purity (dashed)...**qubit** coupled to a resonantly driven dissipative harmonic oscillator. ...**qubit**-oscillator coupling ( g 1 = 0 ), resonant driving at large frequency...**qubit**-**oscillator** master equation in the original frame....**qubit** operator σ x (solid line) and the corresponding purity (dashed) ...**qubit**-oscillator Hamiltonian to the dispersive frame and a subsequent ...**oscillator** damping γ = ϵ , the conditions for the validity of the (Markovian...**qubit** decoherence during dispersive readout...**oscillator** coordinate, which is relevant for flux **qubits**. Analytical results...**qubit** decoherence under generalized dispersive readout, i.e., we investigate...**qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. ...**qubit**-**oscillator** detuning and by considering also a coupling to the square...**qubit**-oscillator master equation in the original frame. ... We study **qubit** decoherence under generalized dispersive readout, i.e., we investigate a **qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. We provide a complete picture by allowing for arbitrarily large **qubit**-**oscillator** detuning and by considering also a coupling to the square of the **oscillator** coordinate, which is relevant for flux **qubits**. Analytical results for the decoherence time are obtained by a transformation of the **qubit**-**oscillator** Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full **qubit**-**oscillator** master equation in the original frame.

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

Date: 2004-07-30

**oscillator**. We achieve generation and control of the entangled state by...**frequencies** are shown by the filled squares in b). b, Rabi **frequency**, .......**oscillations**: after a π pulse on the **qubit** resonance ( | 00 → | 10 ) we...flux **qubit** (the smallest loop closed by three junctions); the **qubit** to...**frequencies** indicated by peaks in the SQUID switching probability when...**qubit** - **oscillator** system for some given bias point. The blue and red ...**oscillations** of the coupled system....**oscillations** at the **qubit** symmetry point Δ = 5.9 GHz. a, Switching probability...**qubit** symmetry point Δ = 5.9 GHz. a, Switching probability as a function...**oscillator**, as demonstrated in ion/atom-trap experiments or cavity quantum...**qubit** (a two-level system) and a superconducting quantum interference ...**qubits**. Single-**qubit** operations, direct coupling between two **qubits**, and... the **qubit** transition. In the upper scan, the system is first excited ...through the **qubit** area away from the **qubit** symmetry point. Inset, energy...**qubit** coupled to a harmonic oscillator...Qub ... In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits or **qubits**. Single-**qubit** operations, direct coupling between two **qubits**, and the realization of a quantum gate have been reported. However, complex manipulation of entangled states - such as the coupling of a two-level system to a quantum harmonic **oscillator**, as demonstrated in ion/atom-trap experiments or cavity quantum electrodynamics - has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux **qubit** (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic **oscillator**. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi **oscillations** of the coupled system.

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