Contributors: unknown

Date: 2015-05-18

flux-qubit in the form of a cantilever. The net magnetic flux threading...flux-qubit and the cantilever. An additional magnetic flux threading through...flux-qubit and the mechanical degrees of freedom of the cantilever are...superconducting-loop-oscillator when the intrinsic frequency is 10 kHz...flux-qubit-cantilever turns out to be an entangled quantum state, where...flux-qubit-cantilever without a Josephson junction, is also discussed....oscillator is proposed, which consists of a flux-qubit in the form of ...flux-qubit-cantilever. A part of the flux-qubit (larger loop) is projected...superconducting-loop-oscillator with its axis of rotation along the z-axis...qubit...frequency (E/h) is ∼3.9×1011 Hz....frequency (E/h) is ∼4×1011 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: 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...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...qubit in different conditions (different oscillation frequencies) by changing...frequency noise contributions, and discuss the experimental results and...qubit, indicated as double SQUID qubit, can be manipulated by rapidly ...qubit manipulation, changing the potential from the two-well “W” case ...qubit manipulated by fast pulses: experimental observation of distinct...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

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 circuit produces a magnetic moment, which is measured by the inductively...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...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 ...qubit (Fig. 2 in  ). The dependence of the frequency of these oscillations...qubit, and I q t the current circulating in the qubit. The persistent ...oscillations is in the different scale of the resonance frequency. To ... 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: Serban, I., Solano, E., Wilhelm, F. K.

Date: 2007-02-28

qubit initially in the state 1 / 2 | ↑ + | ↓ the probability distribution...qubit. The dephasing rate is also expected to diverge. The peaks at Ω ...qubit split already during the transient motion of p ̂ t , much faster...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...qubit quadratically coupled to its detector, a damped harmonic oscillator...qubit and oscillator. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and ℏ ν / k...qubit and oscillator. We also show that the pointer becomes measurable...qubit drawn in the single junction version, the surrounding SQUID loop...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...qubit as a two-level system. The qubit used in the actual experiment contains...qubits...oscillator has the frequency Ω because it has not yet "seen" the qubit ... 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....qubit. In the phase regime, the manipulation of the energy states is realized...oscillation of the retrapping probability in one of the wells has a frequency...qubit, where the coherent evolution between the two flux states is induced...oscillation frequency versus the normalized amplitude of the microwave...frequency of the Larmor oscillations, the microwave-free qubit manipulation...oscillation and microwave-driven Rabi oscillation are rather similar. ...qubit by applying microwave pulses at 19 GHz. The oscillation frequency...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: Yoshihara, Fumiki, Nakamura, Yasunobu, Yan, Fei, Gustavsson, Simon, Bylander, Jonas, Oliver, William D., Tsai, Jaw-Shen

Date: 2014-02-06

oscillation, $1/f$ noise...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...qubit’s energy eigenbasis; this component is not averaged out when Ω R...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...qubit followed by a readout pulse, and P s w as a function of the microwave...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...qubit by studying the decay of Rabi oscillations under strong driving ...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 ...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.

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...qubit-resonator or qubit-qubit spectrum. They are typically ver...frequency associated to the operating point φ i . This frequency is illustrated...two-qubit operations in circuit QED. ϵ is the strength of the drive used...qubit. The fidelity is extracted by injecting these unitaries in Eq. (...qubit-qubit entangled states. The parameters of every pulses entering ...qubit relaxation and dephasing is similar....qubit-resonator and qubit-qubit interactions. We discuss in detail how...qubit (see Section  sec:SB)....qubits and microwave resonators. Up to now, these transitions have been...qubit or the resonator, with the significant disadvantage that such implementations...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 ...oscillations of the qubit frequency using a flux-bias line. Not only can...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...oscillations in the Rabi oscillations that reduce the fidelity. These ...qubit transition frequencies in and out of resonance without crossing ...qubit frequency modulation...oscillators (see Section  sec:Duffing) with E J 1 = 25 GHz, E J 2 = 35...qubit at the red sideband frequency assuming the second qubit is in its...qubit is excited. Blue dashed line: population transfer error 1 - P t ...qubits have frequencies separated enough that they do not overlap during...qubit splitting is modulated at a frequency that lies exactly between ... 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: 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). We explicitly account for the back action of a tank circuit and...oscillations with lower frequency. Deterministic case (a) together with...qubit levels. The resulting Rabi oscillations of supercurrent in the qubit...qubit coupled to a dissipative tank circuit Q T = 100 , λ = 2.5 × 10 -...qubit to microscopic degrees of freedom in the solid. Fortunately this...qubit. The external source, typically in GHz range, induces transitions...qubit coupled to a dissipative tank circuit. The voltage across the tank...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...oscillating with Rabi frequency, while B (C) decays to zero. (Note: to...qubit coupled to a tank circuit....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 ...qubit evolution as the coupling between the qubit and the tank is increased...qubit coupled to a loss-free tank circuit. Oscillations of A. Deterministic...qubit as having definite wave function. However, if the interaction is...qubit without dissipation....qubit coupled to a loss-free tank circuit. Oscillations of A. Deterministic...frequency. Deterministic case (a) together with one realization (b) are...oscillations in MHz range can be detected using conventional NMR pulse...qubit. Here we present the results of detailed computer simulations of...oscillations between quantum states in mesoscopic superconducting systems ... 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: Grajcar, M., Izmalkov, A., Il'ichev, E., Wagner, Th., Oukhanski, N., Huebner, U., May, T., Zhilyaev, I., Hoenig, H. E., Greenberg, Ya. S.

Date: 2003-03-31

frequency  ω T . Then both amplitude v and phase shift χ (with respect...qubit, inductively coupled to a Nb LC tank circuit. The resonant properties...qubit, which changes drastically as its flux states pass through degeneracy...oscillator are sensitive to the effective susceptibility (or inductance...qubit’s quantum properties, without using spectroscopy. In a range 50 ...qubit states. Thus, the tank both applies the probing field to the qubit...qubit inductance by the tank flux, and (B) losses caused by field-induced...frequency due to the change of the effective qubit inductance by the tank...qubit...qubit vs external flux. The dashed lines represent the classical potential...qubit....qubit temperature at 30 mK. (c) Full dip width at half the maximum amplitude...qubit loop is inductively coupled to a parallel resonant tank circuit ...qubit coupled to a tank circuit. ... We have observed signatures of resonant tunneling in an Al three-junction qubit, inductively coupled to a Nb LC tank circuit. The resonant properties of the tank oscillator are sensitive to the effective susceptibility (or inductance) of the qubit, which changes drastically as its flux states pass through degeneracy. The tunneling amplitude is estimated from the data. We find good agreement with the theoretical predictions in the regime of their validity.

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

Date: 2004-07-30

qubit) junctions have a critical current of 4.2 (0.45)  μ A. The device...oscillator. We achieve generation and control of the entangled state by...Qubit - SQUID device and spectroscopy a, Atomic force micrograph of the...qubit - oscillator system for some given bias point. The blue and red ...qubit area away from the qubit symmetry point. Inset, energy levels of...frequencies are shown by the filled squares in b). b, Rabi frequency, ...oscillations: after a π pulse on the qubit resonance ( | 00 → | 10 ) we...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 (a two-level system) and a superconducting quantum interference ...oscillator, as demonstrated in ion/atom-trap experiments or cavity quantum...qubit (the smallest loop closed by three junctions); the qubit to SQUID...qubits. Single-qubit operations, direct coupling between two qubits, and...qubit coupled to a harmonic oscillator ... 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.