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ABSTRACT: We present a theoretical analysis of the selective darkening method for
implementing quantum controlled-NOT (CNOT) gates. This method, which we
recently proposed and demonstrated, consists of driving two
transversely-coupled quantum bits (qubits) with a driving field that is
resonant with one of the two qubits. For specific relative amplitudes and
phases of the driving field felt by the two qubits, one of the two transitions
in the degenerate pair is darkened, or in other words, becomes forbidden by
effective selection rules. At these driving conditions, the evolution of the
two-qubit state realizes a CNOT gate. The gate speed is found to be limited
only by the coupling energy J, which is the fundamental speed limit for any
entangling gate. Numerical simulations show that at gate speeds corresponding
to 0.48J and 0.07J, the gate fidelity is 99% and 99.99%, respectively, and
increases further for lower gate speeds. In addition, the effect of
higher-lying energy levels and weak anharmonicity is studied, as well as the
scalability of the method to systems of multiple qubits. We conclude that in
all these respects this method is competitive with existing schemes for
creating entanglement, with the added advantages of being applicable for qubits
operating at fixed frequencies (either by design or for exploitation of
coherence sweet-spots) and having the simplicity of microwave-only operation.
01/2012;
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ABSTRACT: The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with basis states having persistent currents of 1 μA carried by a million pairs of electrons. By tuning the tunnel barrier between these states we see a crossover from quantum to classical. Released from nonequilibrium, the system exhibits spontaneous coherent oscillations. For high barriers the lifetime of the states increases dramatically while the tunneling period approaches the phase coherence time and the oscillations fade away.
Physical Review Letters 04/2011; 106(17):170404. · 7.37 Impact Factor
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[show abstract]
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ABSTRACT: The boundary between the classical and quantum worlds has been intensely
studied. It remains fascinating to explore how far the quantum concept can
reach with use of specially fabricated elements. Here we employ a tunable flux
qubit with basis states having persistent currents of 1$ \mu$A carried by a
billion electrons. By tuning the tunnel barrier between these states we see a
cross-over from quantum to classical. Released from non-equilibrium, the system
exhibits spontaneous coherent oscillations. For high barriers the lifetime of
the states increases dramatically while the tunneling period approaches the
phase coherence time and the classical regime is reached.
12/2010;
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ABSTRACT: We measure the dispersive energy-level shift of an LC resonator magnetically coupled to a superconducting qubit, which clearly shows that our system operates in the ultrastrong coupling regime. The large mutual kinetic inductance provides a coupling energy of ≈ 0.82 GHz, requiring the addition of counter-rotating-wave terms in the description of the Jaynes-Cummings model. We find a 50 MHz Bloch-Siegert shift when the qubit is in its symmetry point, fully consistent with our analytical model.
Physical Review Letters 12/2010; 105(23):237001. · 7.37 Impact Factor
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ABSTRACT: A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit of which the gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-oscillator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency ν(osc) we find the largest vacuum Rabi splitting of ∼0.1 ν(osc). Here being at resonance coincides with the optimal coherence of the symmetry point.
Physical Review Letters 08/2010; 105(6):060503. · 7.37 Impact Factor
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ABSTRACT: Controlled manipulation of quantum states is central to studying natural and
artificial quantum systems. If a quantum system consists of interacting
sub-units, the nature of the coupling may lead to quantum levels with
degenerate energy differences. This degeneracy makes frequency-selective
quantum operations impossible. For the prominent group of transversely coupled
two-level systems, i.e. qubits, we introduce a method to selectively suppress
one transition of a degenerate pair while coherently exciting the other,
effectively creating artificial selection rules. It requires driving two qubits
simultaneously with the same frequency and specified relative amplitude and
phase. We demonstrate our method on a pair of superconducting flux qubits. It
can directly be applied to the other superconducting qubits, and to any other
qubit type that allows for individual driving. Our results provide a
single-pulse controlled-NOT gate for the class of transversely coupled qubits.
08/2010;
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ABSTRACT: Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong backaction. We show that the backaction of a dc-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum nondemolition character, with a QND fidelity of 75%.
Physical Review Letters 07/2010; 105(4):040506. · 7.37 Impact Factor
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ABSTRACT: Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong back-action. We show that the back-action of a DC-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum non-demolition character, with a QND fidelity of 75 %. Comment: submitted to PRL
07/2010;
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ABSTRACT: We present experimental results on the crosstalk between two ac-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning of the phase the measured crosstalk is 0.1% and the correlation between the measurement outcomes is less than 0.05%. These results show that bifurcative readout provides a reliable and generic approach for multipartite correlation experiments.
Applied Physics Letters 03/2010; 96(12):123508-123508-3. · 3.84 Impact Factor
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ABSTRACT: We experimentally demonstrate the in situ tunability of the minimum energy splitting (gap) of a superconducting flux qubit by means of an additional flux loop. Pulses applied via a local control line allow us to tune the gap over a range of several GHz on a nanosecond time scale. The strong flux sensitivity of the gap (up to approximately 0.7 GHz/mPhi0) opens up the possibility to create different types of tunable couplings that are effective at the degeneracy point of the qubit. We investigate the dependence of the relaxation time and the Rabi frequency on the qubit gap.
Physical Review Letters 04/2009; 102(9):090501. · 7.37 Impact Factor
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ABSTRACT: We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum nondemolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model for characterizing the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.
Phys. Rev. B. 10/2008; 78(13).
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ABSTRACT: We observed the dynamics of a superconducting flux qubit coupled to an extrinsic quantum system (EQS). The presence of the EQS is revealed by an anticrossing in the spectroscopy of the qubit. The excitation of a two-photon transition to the third excited state of the qubit-EQS system allows us to extract detailed information about the energy level structure and the coupling of the EQS. We deduce that the EQS is a two-level system, with a transverse coupling to the qubit. The transition frequency and the coupling of the EQS changed during experiments, which supports the idea that the EQS is a two-level system of microscopic origin. Comment: accepted in Physical Review B
10/2008;
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ABSTRACT: The magnetoresistance of a quasi-ballistic Aharonov–Bohm (AB) ring defined in the two-dimensional electron gas (2DEG) of an InP/In0.8Ga0.2As quantum well is studied. The ring is connected to an Al contact on one side and to a 2DEG reservoir at the other side. Two distinct magnetic field regimes can be identified. At magnetic field values where time-reversal symmetry (TRS) is broken, AB oscillations are observed. Besides oscillations with h/e periodicity, we also observe higher harmonics with h/2e and h/3e periods. In the low-magnetic field range, where TRS is preserved, the AB oscillations are alternately dominated by the h/e or h/2e component, depending on the bias voltage. Although Al is superconducting at these low magnetic fields, no evidence is found that the observed AB oscillations are related to the proximity of the superconductor. The bias voltage dependence is qualitatively described in terms of a 1D scattering model.
New Journal of Physics 07/2008; 10(7):073031. · 4.18 Impact Factor
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ABSTRACT: Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantum-mechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1/2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwave-spectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
Physics-Uspekhi 10/2007; 44(10S):117. · 2.15 Impact Factor
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ABSTRACT: We have studied single electron charging effects in lateral quantum dots, defined by metal gates in the two dimensional electron
gas of a GaAs/AlGaAs heterostructure. The charging effects cause periodic oscillations in the conductance versus gate voltage,
where each period corresponds to a change of one electron in the dot. A study of the dependence of these Coulomb oscillations
on the barrier conductances shows that charging effects become visible precisely when the barrier conductances become smaller
than the quantized conductance value 2e2/h. The amplitude of the Coulomb oscillations increases gradually upon reducing the barrier conductances to a value much smaller
than 2e2/h. We determine experimentally the total capacitance involved, and thereby the corresponding charging energy.
09/2007: pages 329-340;
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ABSTRACT: Quantum computation requires quantum logic gates that use the interaction within pairs of quantum bits (qubits) to perform conditional operations. Superconducting qubits may offer an attractive route towards scalable quantum computing. In previous experiments on coupled superconducting qubits, conditional gate behaviour and entanglement were demonstrated. Here we demonstrate selective execution of the complete set of four different controlled-NOT (CNOT) quantum logic gates, by applying microwave pulses of appropriate frequency to a single pair of coupled flux qubits. All two-qubit computational basis states and their superpositions are used as input, while two independent single-shot SQUID detectors measure the output state, including qubit-qubit correlations. We determined the gate's truth table by directly measuring the state transfer amplitudes and by acquiring the relevant quantum phase shift using a Ramsey-like interference experiment. The four conditional gates result from the symmetry of the qubits in the pair: either qubit can assume the role of control or target, and the gate action can be conditioned on either the 0-state or the 1-state. These gates are now sufficiently characterized to be used in quantum algorithms, and together form an efficient set of versatile building blocks.
Nature 07/2007; 447(7146):836-9. · 36.28 Impact Factor
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ABSTRACT: In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system - detector interaction which preserves the eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement. We present experiments in which we perform two consecutive measurements on a quantum two -level system, a superconducting flux qubit, by probing the hysteretic behaviour of a coupled nonlinear resonator. The large correlation between the results of the two measurements demonstrates the QND nature of the readout method. The fact that a QND measurement is possible for superconducting qubits strengthens the notion that these fabricated mesoscopic systems are to be regarded as fundamental quantum objects. Our results are also relevant for quantum information processing, where projective measurements are used for protocols like state preparation and error correction.
12/2006;
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ABSTRACT: The authors have studied low-frequency resistance fluctuations in shadow-evaporated Al/AlOx/Al tunnel junctions. Between 300 and 5 K the spectral density follows a 1/f law. Below 5 K, individual defects distort the 1/f shape of the spectrum. The spectral density decreases linearly with temperature between 150 and 1 K and saturates below 0.8 K. At 4.2 K, it is about two orders of magnitude lower than expected from a recent survey [
D. J. Van Harlingen et al., Phys. Rev. B 70, 064510 (2004)
]. Due to saturation below 0.8 K the estimated qubit dephasing times at 100 mK are only about two times longer than calculated by Van Harlingen et al.
Applied Physics Letters 09/2006; 89(12):122516-122516-3. · 3.84 Impact Factor
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ABSTRACT: We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87%; of the missing 13%, only 3% of the loss of contrast is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by the first measurement.
Physical Review Letters 04/2006; 96(12):127003. · 7.37 Impact Factor
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ABSTRACT: We have studied the dephasing of a superconducting flux qubit coupled to a dc-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spin-echo decay time of .
Physical Review Letters 01/2006; 95(25):257002. · 7.37 Impact Factor
