Contributors: Strauch, F. W., Dutta, S. K., Paik, Hanhee, Palomaki, T. A., Mitra, K., Cooper, B. K., Lewis, R. M., Anderson, J. R., Dragt, A. J., Lobb, C. J.

Date: 2007-03-02

frequency, and two-photon Rabi frequency are compared to measurements ...frequency Ω R , 01 of the one-photon 0 1 transition as function of microwave...qubit, scanned in frequency (vertical) and bias current (horizontal). ...qubit (current-biased Josephson junction) at high microwave drive power...qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between...oscillations of the escape rate for I a c = 16.5 nA....oscillations have been observed in many superconducting devices, and represent...oscillation frequency Ω ̄ R , 01 as a function of the level spacing ω ...qubit...qubits) in a quantum computer. We use a three-level multiphoton analysis...phase qubit, scanned in frequency (vertical) and bias current (horizontal ... Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and two-photon Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.

Contributors: Averin, D. V.

Date: 2002-02-05

qubit, σ z and σ y , as required in the QND Hamiltonian ( 2). For discussion...oscillations avoiding the detector-induced dephasing that affects the ... qubit. The oscillations are represented as a spin rotation in the z -...frequency Δ . QND measurement is realized if the measurement frame (dashed...qubit structure that enables measurements of the two non-commuting observables...oscillations in an individual two-state system. Such a measurement enables...frequency Ω ≃ Δ ....qubits which combine flux and charge dynamics....qubit...oscillations of a qubit. The oscillations are represented as a spin rotation ... The concept of quantum nondemolition (QND) measurement is extended to coherent oscillations in an individual two-state system. Such a measurement enables direct observation of intrinsic spectrum of these oscillations avoiding the detector-induced dephasing that affects the standard (non-QND) measurements. The suggested scheme can be realized in Josephson-junction qubits which combine flux and charge dynamics.

Contributors: Murch, K. W., Ginossar, E., Weber, S. J., Vijay, R., Girvin, S. M., Siddiqi, I.

Date: 2012-08-22

qubit-cavity detuning for the qubit prepared in the ground state in the...qubit, both the effective nonlinearity and the threshold become a non-trivial...oscillator Q....the qubit-oscillator model with N l = 7 show the avoided crossings in ...qubit-oscillator model with N l = 7 show the avoided crossings in the ...and qubit junctions (lower and upper insets)....qubit junctions (lower and upper insets)....qubit and may be used to realize a high fidelity, latching readout whose...qubit-oscillator detuning. Moreover, the autoresonant threshold is sensitive...oscillator is strongly coupled to a quantized superconducting qubit, both...qubit state. (a) Color plot shows S | 1 versus qubit detuning. The dashed... qubit state. (a) Color plot shows S | 1 versus qubit detuning. The dashed...qubit-cavity detuning for the qubit prepared in the ground state in the...frequency chirped excitation is applied to a classical high-Q nonlinear...qubit-oscillator detuning. Moreover, the autoresonant threshold is sensitive...oscillators (red) are shown. The arrows indicate the locations of avoided...the qubit energy levels were modeled as a Duffing nonlinearity. ... When a frequency chirped excitation is applied to a classical high-Q nonlinear oscillator, its motion becomes dynamically synchronized to the drive and large oscillation amplitude is observed, provided the drive strength exceeds the critical threshold for autoresonance. We demonstrate that when such an oscillator is strongly coupled to a quantized superconducting qubit, both the effective nonlinearity and the threshold become a non-trivial function of the qubit-oscillator detuning. Moreover, the autoresonant threshold is sensitive to the quantum state of the qubit and may be used to realize a high fidelity, latching readout whose speed is not limited by the oscillator Q.

Contributors: Mandip Singh

Date: 2015-07-14

flux-qubit in the form of a cantilever. The net magnetic flux threading...superconducting-loop-oscillator when the intrinsic frequency is 10 kHz...flux-qubit and the mechanical degrees of freedom of the cantilever are...flux-qubit-cantilever turns out to be an entangled quantum state, where...superconducting-loop-oscillator with its axis of rotation along the z-axis... flux-qubit and the cantilever. An additional magnetic flux threading ...frequency (E/h) is ∼4×1011 Hz. ... flux-qubit-cantilever. A part of the flux-qubit (larger loop) is projected...oscillator is proposed, which consists of a flux-qubit in the form of ...flux-qubit-cantilever without a Josephson junction, is also discussed....flux-qubit-cantilever. A part of the flux-qubit (larger loop) is projected...qubit...frequency (E/h) is ∼3.9×1011 Hz. ... In this paper a macroscopic quantum oscillator is proposed, which consists of a flux-qubit in the form of a cantilever. The net magnetic flux threading through the flux-qubit and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling between the cantilever and the magnetic flux is controlled through an external magnetic field. The ground state of the flux-qubit-cantilever turns out to be an entangled quantum state, where the cantilever deflection and the magnetic flux are the entangled degrees of freedom. A variant, which is a special case of the flux-qubit-cantilever without a Josephson junction, is also discussed.

Contributors: Whittaker, J. D., da Silva, F. C. S., Allman, M. S., Lecocq, F., Cicak, K., Sirois, A. J., Teufel, J. D., Aumentado, J., Simmonds, R. W.

Date: 2014-08-08

i n ≈ 4 , qubit lifetimes are relatively large across the full qubit ...Qubits...oscillations for frequencies near f 01 = 7.38 GHz. (b) Line-cut on-resonance...qubit anharmonicity, qubit-cavity coupling and detuning. A tunable cavity...a) Relative qubit anharmonicity α r versus qubit frequency ω 01 / 2 π ...is the qubit junction critical current, with the phase difference across the...qubit anharmonicity α r versus qubit frequency ω 01 / 2 π (design A )....qubit inductively coupled to a single-mode, resonant cavity with a tunable...minima....QB...qubit frequency change both Δ 01 and the qubit’s anharmonicity α . In ...qubit far detuned, biased at its maximum frequency. The solid line is ...qubit and cavity frequencies and the dashed lines show the new coupled...qubits....qubit frequency, at f 01 = 7.98 GHz, Ramsey oscillations gave T 2 * = ...qubit-cavity system, we show that dynamic control over the cavity frequency...measure of the qubit anharmonicity as shown later in Fig.  Fig9....phase qubit (design A ) remains stable enough for operation (see text)...qubit frequencies. In order to capture the maximum dispersive frequency...qubit, and residual bus coupling for a system with multiple qubits. With...qubit evolutions and optimize state readout during qubit measurements....frequency of f c m a x = 7.07  GHz while sweeping the qubit flux bias ...oscillation decay time of T ' = 409  ns. (c) Ramsey oscillations versus...oscillations gave T ' = 727  ns, a separate measurement of qubit energy...the qubit flux bias is swept. Two different data sets (with the qubit ...  GHz while sweeping the qubit flux bias φ q . In both cases, when the ...frequency provides a way to strongly vary both the qubit-cavity detuning...cavity (qubit) (see text)....frequency that allows for both microwave readout of tunneling and dispersive...resultant flux coupling of the qubit bias coil, M q B = 10.9  pH. The ... We describe a tunable-cavity QED architecture with an rf SQUID phase qubit inductively coupled to a single-mode, resonant cavity with a tunable frequency that allows for both microwave readout of tunneling and dispersive measurements of the qubit. Dispersive measurement is well characterized by a three-level model, strongly dependent on qubit anharmonicity, qubit-cavity coupling and detuning. A tunable cavity frequency provides a way to strongly vary both the qubit-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the qubit, and residual bus coupling for a system with multiple qubits. With our qubit-cavity system, we show that dynamic control over the cavity frequency enables one to avoid Purcell losses during coherent qubit evolutions and optimize state readout during qubit measurements. The maximum qubit decay time $T_1$ = 1.5 $\mu$s is found to be limited by surface dielectric losses from a design geometry similar to planar transmon qubits.

Contributors: Serban, I., Solano, E., Wilhelm, F. K.

Date: 2007-02-28

between qubit and oscillator. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and... seen by the qubit. The dephasing rate is also expected to diverge. The...qubit has been lost....qubit and oscillator or between oscillator and bath, corrections of the...qubit and the oscillator by means of their full Floquet state master equations...qubit and oscillator. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and ℏ ν / k...through the qubit loop is Φ q and through the SQUID is Φ S .... of a qubit with one Josephson junction (phase γ , capacitance C q and...qubit quadratically coupled to its detector, a damped harmonic oscillator...effect after the qubit and the oscillator become entangled. The dephasing...qubit and oscillator. We also show that the pointer becomes measurable...states of the qubit split already during the transient motion of p ̂ t...qubit quadratically coupled to its detector, a damped harmonic oscillator...qubit with one Josephson junction (phase γ , capacitance C q and inductance...qubit and the oscillator by means of their full Floquet state master equations...frequency is at resonance with the harmonic oscillator — we have a continuum...qubit loop is Φ q and through the SQUID is Φ S ....qubit and oscillator. We also show that the pointer becomes measurable...qubit and the oscillator become entangled. The dephasing rate drops again...frequencies to the value obtained in the case without driving....frequency ν for different vales of κ ( Δ / Ω = 0.5 ). Here ℏ Ω / k B T...qubit states (c). Here ℏ Ω / k B T = 2 , Δ / Ω = 0.45 , κ / Ω = 0.025 ...qubit and explore several measurement protocols, which include a long-term...different qubit states (c). Here ℏ Ω / k B T = 2 , Δ / Ω = 0.45 , κ / ... we later approximate the qubit as a two-level system. The qubit used ...qubits...oscillator has the frequency Ω because it has not yet "seen" the qubit...about the qubit state, and has the advantage of avoiding decoeherence ... Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full read-out cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.

Contributors: Poletto, S, Chiarello, F, Castellano, M G, Lisenfeld, J, Lukashenko, A, Carelli, P, Ustinov, A V

Date: 2009-10-23

qubit manipulation allows for much faster coherent operations....oscillation of the retrapping probability in one of the wells has a frequency...qubit. In the phase regime, the manipulation of the energy states is realized...phase qubit....oscillation frequency versus the normalized amplitude of the microwave...qubit, where the coherent evolution between the two flux states is induced... phase qubit by applying microwave pulses at 19 GHz. The oscillation frequency...frequency of the Larmor oscillations, the microwave-free qubit manipulation...oscillation and microwave-driven Rabi oscillation are rather similar. ...oscillation of the double SQUID manipulated as a phase qubit by applying...oscillation frequency changes from 540 MHz to 1.2 GHz by increasing the...qubit...oscillation frequencies versus amplitude of the short flux pulse (full...qubit. ... We report on two different manipulation procedures of a tunable rf SQUID. First, we operate this system as a flux qubit, where the coherent evolution between the two flux states is induced by a rapid change of the energy potential, turning it from a double well into a single well. The measured coherent Larmor-like oscillation of the retrapping probability in one of the wells has a frequency ranging from 6 to 20 GHz, with a theoretically expected upper limit of 40 GHz. Furthermore, here we also report a manipulation of the same device as a phase qubit. In the phase regime, the manipulation of the energy states is realized by applying a resonant microwave drive. In spite of the conceptual difference between these two manipulation procedures, the measured decay times of Larmor oscillation and microwave-driven Rabi oscillation are rather similar. Due to the higher frequency of the Larmor oscillations, the microwave-free qubit manipulation allows for much faster coherent operations.

Contributors: Ginossar, Eran, Bishop, Lev S., Girvin, S. M.

Date: 2012-07-19

qubit state measurement in circuit quantum electrodynamics...qubit and cavity are on resonance or far off-resonance (dispersive)....superconducting transmon qubits...frequency and amplitude. The region of bifurcation...oscillator with its set of transition frequencies depending on the state...qubit and cavity are strongly coupled. We focus on the parameter ranges...qubit decay . T 1 . has . distinct influence on the lifetime of the QCS...qubit quantum state discrimination and we present initial results for ...frequency).... 4 transmon qubits transmonat 7.0 . 7.5 . 8.0 . 12.3 . H z . All qubits...oscillator...qubits in the circuit quantum electrodynamics architecture, where the ...oscillator and we analyze the quantum and semi-classical dynamics. One...oscillator (Duffing oscillator) Duffing oscillator, constructed by making... the qubit is detuned from the cavity . ω q . ω c . 2 π . 2 g ). It is...disruptive to the qubit state and it is realized where the cavity and ... qubit (Fig.  gino:chirp_figure). This selective dynamical mapping of th...frequency. For (b), if the state of one (‘spectator’) qubit is held constant...frequency response bifurcates, and the JC oscillator enters a region of...frequency and amplitude. Despite the presence of 4 qubits in the device...one qubit, see Fig.  gino:fig:return. Such an asymmetric qubit dependent...qubit frequency. (c) Wave packet snapshots at selected times (indicated...anharmonic transmon....the qubit being detuned. Due to the interaction with the qubit, the cavity...frequency of panel (b) conditioned on the initial state of the qubit. ...qubit state q : (a) for the JC model, parameters as in Figs.  gino:fig ... In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the qubit and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon qubits in the circuit quantum electrodynamics architecture, where the system behaves essentially as a nonlinear quantum oscillator and we analyze the quantum and semi-classical dynamics. One of the central motivations is that under strong excitation tones, the nonlinear response can lead to qubit quantum state discrimination and we present initial results for the cases when the qubit and cavity are on resonance or far off-resonance (dispersive).

Contributors: Lisenfeld, Juergen, Mueller, Clemens, Cole, Jared H., Bushev, Pavel, Lukashenko, Alexander, Shnirman, Alexander, Ustinov, Alexey V.

Date: 2009-09-18

frequencies. Each trace was recorded after adjusting the qubit bias to...frequency while the qubit was kept detuned. A π pulse was applied to measure...qubit-fluctuator system...the qubit in the excited state, P t , vs. driving frequency; (b) Fourier-transform...phase qubit circuit. (b) Probability to measure the excited qubit state...the qubit was kept detuned. A π pulse was applied to measure the energy...oscillations ...qubits often show signatures of coherent coupling to microscopic two-level...frequency of 7.805 GHz (indicated by a dashed line)....qubits, Josephson junctions, two-level fluctuators, microwave spectroscopy...qubit and fluctuator v ⊥ and to the microwave field Ω q and Ω f v ....qubit in the excited state, P t , vs. driving frequency; (b) Fourier-transform...qubit levels....qubit as and and those of the TLF as and . Arrows indicate the couplings...qubit’s Rabi frequency Ω q / h is set to 48 MHz....qubit, in which we induce Rabi oscillations by resonant microwave driving...oscillations observed experimentally....frequency, revealing the coupling to a two-level defect state having a... the qubit loop. The qubit state is controlled by an externally applied...levels in the qubit....qubit, in which we induce Rabi oscillations by resonant microwave driving...qubit is tuned close to the resonance with an individual TLF and the Rabi...frequency components. Frequency and visibility of each component depend...qubit relative to the TLF’s resonance frequency, which is indicated in...qubit transition. In this work, we studied the qubit interacting with ...qubit above or below the fluctuator's level-splitting. Theoretical analysis...qubit circuit. (b) Probability to measure the excited qubit state (color-coded...qubit-TLF coupling), interesting 4-level dynamics are observed. The experimental...frequency of order of the qubit-TLF coupling), interesting 4-level dynamics...in the qubit. (As the anharmonicity Δ / h ∼ 100  MHz in our circuit is... the phase qubit circuit (the qubit subspace) and disregard the longitudinal ... Superconducting qubits often show signatures of coherent coupling to microscopic two-level fluctuators (TLFs), which manifest themselves as avoided level crossings in spectroscopic data. In this work we study a phase qubit, in which we induce Rabi oscillations by resonant microwave driving. When the qubit is tuned close to the resonance with an individual TLF and the Rabi driving is strong enough (Rabi frequency of order of the qubit-TLF coupling), interesting 4-level dynamics are observed. The experimental data shows a clear asymmetry between biasing the qubit above or below the fluctuator's level-splitting. Theoretical analysis indicates that this asymmetry is due to an effective coupling of the TLF to the external microwave field induced by the higher qubit levels.

Contributors: Shi, Zhan, Simmons, C. B., Ward, Daniel. R., Prance, J. R., Mohr, R. T., Koh, Teck Seng, Gamble, John King, Wu, Xian., Savage, D. E., Lagally, M. G.

Date: 2012-08-02

low-frequency noise processes are an important dephasing mechanism....Qubit...oscillations visible near δ t = 0 . The oscillations of interest appear...qubit states varies with external voltages, consistent with a decoherence...qubit in a double quantum dot fabricated in a Si/SiGe heterostructure ...oscillation frequency f for (a–c), respectively. As t is increased, the...frequency at more negative detuning (farther from the anti-crossing). ...oscillation frequency f for the data in (a–c), respectively. We obtain...oscillations at a given frequency decays with characteristic time T 2 ...oscillations of a charge qubit in a double quantum dot fabricated in a...qubit's double-well potential). In the regime with the shortest T2*, applying ... Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2* ranges from 127ps to ~2.1ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise(charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T2*, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127ps to 760ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.