### 63152 results for qubit oscillator frequency

Contributors: Oxtoby, Neil P., Gambetta, Jay, Wiseman, H. M.

Date: 2007-06-24

**qubit**, is used to damp a classical oscillator circuit. The resulting realistic...**frequency** (rf) weak measurements where a low-transparency quantum point... the **qubit** electron, denoted by E 1 and E 0 for the near and far dot, ...low-**frequency** (dc) weak measurements. In this paper we extend realistic...**oscillator** circuit to be a QPC (see Fig. fig:dqdqpc for details). Measurement...**qubit**. A schematic of the isolated DQD and capacitively coupled QPC is...**qubit**. The charge basis states are denoted | 0 and | 1 (see Fig. fig:...**qubit** coupled to a classical L C **oscillator** with inductance L and capacitance...**qubits** is important for quantum computation, particularly for the purposes...radio-**frequency** point contact), with two benefits over the SET — lower...**qubit** using a radio-frequency quantum point contact including experimental...**frequency** is the same as the signal of interest (or very slightly detuned...**qubit**. The rf+dc mode of operation is considered. Here the QPC is biased...charge **qubit** coupled to a classical L C oscillator with inductance L and...**qubit**, is used to damp a classical **oscillator** circuit. The resulting realistic... **qubit** coupled to a classical L C oscillator with inductance L and capacitance...low-**frequency** beats due to mixing the signal with the LO are easily detected...charge-**qubit** detector, that may nevertheless be higher than the dc-QPC...**qubit** and capacitively coupled low-transparency QPC between source (S)...**oscillator**, L O , and then measured. fig:rfcircuit...**oscillator** (relative to the QPC), where the **oscillator** slaves to the **qubit**... **qubit**. The charge basis states are denoted | 0 and | 1 (see Fig. fig ... The extension of quantum trajectory theory to incorporate realistic imperfections in the measurement of solid-state **qubits** is important for quantum computation, particularly for the purposes of state preparation and error-correction as well as for readout of computations. Previously this has been achieved for low-**frequency** (dc) weak measurements. In this paper we extend realistic quantum trajectory theory to include radio **frequency** (rf) weak measurements where a low-transparency quantum point contact (QPC), coupled to a charge **qubit**, is used to damp a classical **oscillator** circuit. The resulting realistic quantum trajectory equation must be solved numerically. We present an analytical result for the limit of large dissipation within the **oscillator** (relative to the QPC), where the **oscillator** slaves to the **qubit**. The rf+dc mode of operation is considered. Here the QPC is biased (dc) as well as subjected to a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be a low-efficiency charge-**qubit** detector, that may nevertheless be higher than the dc-QPC (which is subject to 1/f noise).

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Contributors: Greenberg, Ya. S., Izmalkov, A., Grajcar, M., Il'ichev, E., Krech, W., Meyer, H. -G.

Date: 2002-08-07

**oscillations** in a phase **qubit**. The external source, typically in GHz range...**qubit** levels. The resulting Rabi oscillations of supercurrent in the **qubit**...**qubit**. According to the estimates for dephasing and relaxation times, ...**qubit**. The external source, typically in GHz range, induces transitions...**frequency** in MHz range....three-**junction** **qubit** in classical regime, when the hysteretic dependence...**qubit** in classical regime, when the hysteretic dependence of ground-state...**qubit**...**qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit**...**qubit**. Detailed calculation for zero and non-zero temperature are made...**qubit** coupled to a tank circuit....**oscillations** between quantum states in mesoscopic superconducting systems ... Time-domain observations of coherent **oscillations** between quantum states in mesoscopic superconducting systems were so far restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a new 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**. Detailed calculation for zero and non-zero temperature are made for the case of persistent current **qubit**. According to the estimates for dephasing and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi **frequency** in MHz range.

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

Date: 2012-09-09

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

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

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

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

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

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

**frequency**f n encodes the state of

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

**qubit**, we demonstrated the

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

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

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

**qubits**...

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

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

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

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

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

**qubit**in ...

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

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

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

**qubits**....

**qubits**, we couple each

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

**Josephson junction. Each**

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

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

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

**frequency**, with the

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

**qubits**... We introduce a

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

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

**qubits**, we couple each

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

**qubits**can be read out simultaneously using

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

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

**qubits**.

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Contributors: Hua, Ming, Deng, Fu-Guo

Date: 2013-09-30

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

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

Date: 2011-10-17

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

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Contributors: Catelani, G., Schoelkopf, R. J., Devoret, M. H., Glazman, L. I.

Date: 2011-06-04

**qubit**, such as the transmon and phase **qubits**. We start with the the semiclassical...**ϕ** ̂ / 2 qubit-quasiparticle coupling in Eq. ( HTle) has a striking effect...**qubit** controlled by a magnetic flux, see Eq. ( Hphi). (b) Effective circuit...**qubit** biased at Φ e = Φ 0 / 2 with E J / E L = 10 . The horizontal lines...flux **qubit** biased at Φ e = Φ 0 / 2 with E J / E L = 10 . The horizontal...the flux qubit ground states | - and excited state | + are** the **lowest ...**qubit** sate. The results of Sec. sec:semi are valid for transitions between...**qubits**. The interaction of the **qubit** degree of freedom with the quasiparticles...**frequency** [cf. Eq. ( pl_fr)]...**qubit** frequency in the presence of quasiparticles....**frequency** is given by Eq. ( Gnn) with ϕ 0 = 0 and is independent of n ...**qubit** **frequency** in the presence of quasiparticles.... C , the qubit can be described by** the **effective circuit of Fig. fig1...**oscillations** of the energy levels are exponentially small, see Appendix...**qubit** resonant **frequency**. In the semiclassical regime of small E C , the... a **qubit** controlled by a magnetic flux, see Eq. ( Hphi). (b) Effective...**qubit** properties in devices such as the phase and flux **qubits**, the split...**the** **qubit** sate. The results of Sec. sec:semi are valid for transitions...**qubits**...**frequency** ω p , Eq. ( pl_fr)] and nearly degenerate levels whose energies...**qubit** decay rate induced by quasiparticles, and we study its dependence...**frequency** ω p , Eq. ( pl_fr), and give, for example, the rate Γ 1 0 . ...the flux quantum** the **qubit states | - , | + are respectively symmetric...anharmonic qubit, such as** the **transmon and **phase **qubits. We start with ... As low-loss non-linear elements, Josephson junctions are the building blocks of superconducting **qubits**. The interaction of the **qubit** degree of freedom with the quasiparticles tunneling through the junction represent an intrinsic relaxation mechanism. We develop a general theory for the **qubit** decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the **qubit** properties in devices such as the phase and flux **qubits**, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and non-equilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible non-equilibrium quasiparticle distribution. We also derive expressions for the shift in **qubit** **frequency** in the presence of quasiparticles.

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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: Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Majer, J., Girvin, S. M., Schoelkopf, R. J.

Date: 2005-02-27

**qubit** population P vs. pulse separation Δ t using the pulse sequence shown... to determine **the** **qubit** transition frequency ω a = ω s + 2 π ν R a m s...applying to **the** **qubit** microwave pulses of frequency ω s , which are resonant...**oscillating** at the detuning **frequency** Δ a , s = ω a - ω s ∼ 6 M H z decay...**oscillations** in the **qubit** population P vs. Rabi pulse length Δ t (blue...**qubit** population P vs. pulse separation Δ t using** the **pulse sequence shown...**oscillation** experiment with a superconducting **qubit** we show that a visibility...**qubit** we show that a visibility in the **qubit** excited state population ...**oscillations** in the **qubit** at a **frequency** of ν R a b i = n s g / π , where... φ will be reduced in any **qubit** read-out for which **the** timescale of **the**...**qubit**. In the 2D density plot Fig. fig:2DRabi, Rabi **oscillations** are ...**oscillation** **frequency** ν R a b i with the pulse amplitude ϵ s ∝ n s , see...**qubit** excited state population of more than 90 % can be attained. We perform...**qubit** population P is plotted versus Δ** t** in Fig. fig:rabioscillationsa...**Qubit** with Dispersive Readout...**qubit** state by coupling the **qubit** non-resonantly to a transmission line...**superconducting** **qubit**, a visibility in **the** population of **the** **qubit** excited...**qubit**. In each panel the dashed lines correspond to the expected measurement...**to **the **qubit**. In each panel** the **dashed lines correspond **to **the expected...**oscillations** with Rabi pulse length Δ t , pulse **frequency** ω s and amplitude...**oscillations** in a superconducting **qubit**, a visibility in the population... the **qubit** population P vs. Rabi pulse length Δ t (blue dots) and fit ...**qubit** coherence time is determined to be larger than 500 ns in a measurement...**oscillator** at **frequency** ω L O . The Cooper pair box level separation is ... In a Rabi **oscillation** experiment with a superconducting **qubit** we show that a visibility in the **qubit** excited state population of more than 90 % can be attained. We perform a dispersive measurement of the **qubit** state by coupling the **qubit** non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The **qubit** coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.

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

Date: 2007-10-10

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

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