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: Chiarello, F., Paladino, E., Castellano, M. G., Cosmelli, C., D'Arrigo, A., Torrioli, G., Falci, G.

Date: 2011-10-07

qubit is only weakly sensitive to intrinsic noise. We find that this behaviour...qubit in different conditions (different oscillation frequencies) by changing...qubit in different conditions (different oscillation frequencies) by changing...frequency noise contributions, and discuss the experimental results and...qubit manipulation, changing the potential from the two-well “W” case ...qubit, indicated as double SQUID qubit, can be manipulated by rapidly ...qubit manipulated by fast pulses: experimental observation of distinct...oscillations with eq. envelope. The blue line in the left panel is the...oscillations observed for different pulse height. The measured frequency...oscillations exhibiting non-exponential decay, indicating a non trivial...oscillation frequencies observed (about 10-20 GHz), corresponding to the...used for the qubit manipulation, changing the potential from the two-well...frequency Ω / 2 π given by eq.  omega for ϕ x = 0 as a function of ϕ c ... A particular superconducting quantum interference device (SQUID)qubit, indicated as double SQUID qubit, can be manipulated by rapidly modifying its potential with the application of fast flux pulses. In this system we observe coherent oscillations exhibiting non-exponential decay, indicating a non trivial decoherence mechanism. Moreover, by tuning the qubit in different conditions (different oscillation frequencies) by changing the pulse height, we observe a crossover between two distinct decoherence regimes and the existence of an "optimal" point where the qubit is only weakly sensitive to intrinsic noise. We find that this behaviour is in agreement with a model considering the decoherence caused essentially by low frequency noise contributions, and discuss the experimental results and possible issues.

Contributors: Omelyanchouk, A. N., Shevchenko, S. N., Zagoskin, A. M., Il'ichev, E., Nori, Franco

Date: 2007-05-12

the qubit, and I q t the current circulating in the qubit. The persistent...phase qubit (Fig. 2 in  ). The dependence of the frequency of these oscillations...oscillations....frequency ω = 0.612 , and the decay rate γ = 10 -3 . Low-frequency classical...oscillations around a minimum of the potential profile of Fig. fig1 as...frequency ω . The main peak ( ω 0 ≈ 0.6 ) corresponds to the resonance...qubit (Fig. 2 in  ). The dependence of the frequency of these oscillations...high-frequency) harmonic mode of the system, $\omega$. Like in the case...qubits in the classical regime...frequency, M the mutual inductance between the tank and the qubit, and...qubit in the _classical_ regime can produce low-frequency oscillations...qubit in the _classical_ regime can produce low-frequency oscillations...in the qubit circuit produces a magnetic moment, which is measured by ...oscillations are clearly seen. (b) Low-frequency oscillations of the persistent...oscillations, the frequency of these pseudo-Rabi oscillations is much ...frequency $\omega$ and its subharmonics ($\omega/n$), but also at its ...oscillations is in the different scale of the resonance frequency. To ...and the qubit, and I q t the current circulating in the qubit. The persistent...a phase qubit (Fig. 2 in  ). The dependence of the frequency of these ... Nonlinear effects in mesoscopic devices can have both quantum and classical origins. We show that a three-Josephson-junction (3JJ) flux qubit in the _classical_ regime can produce low-frequency oscillations in the presence of an external field in resonance with the (high-frequency) harmonic mode of the system, $\omega$. Like in the case of_quantum_ Rabi oscillations, the frequency of these pseudo-Rabi oscillations is much smaller than $\omega$ and scales approximately linearly with the amplitude of the external field. This classical effect can be reliably distinguished from its quantum counterpart because it can be produced by the external perturbation not only at the resonance frequency $\omega$ and its subharmonics ($\omega/n$), but also at its overtones, $n\omega$.

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: 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: 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: 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.

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.

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 qubit dynamics analytically unwieldy, because the rational function...qubit dynamics are not greatly perturbed by the presence of the oscillator... the qubit 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 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.

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).