Entanglement generation through the interplay of harmonic driving and interaction in coupled superconducting qubits

We study the manipulation of quantum entanglement by periodic external fields. As an entanglement measure we compute numerically the concurrence of two coupled superconducting qubits both driven by a dc + ac external control parameter. We show that when the driving term of the Hamiltonian commutes with the qubit–qubit interaction term, it is possible to create or destroy entanglement in a controlled way by tuning the system at or near multiphoton resonances. On the other hand, when the driving does not commute with the qubit–qubit interaction, the control and generation of entanglement induced by the driving field is more robust and extended in parameter space, beyond the multiphoton resonances.     

Controlling qubit transitions through quantum interference during nonadiabatic rapid passage

We provide a further exploration of a type of nonadiabatic rapid passage known as twisted rapid passage (TRP). This class of rapid passage pulses allows a qubit to be driven through resonance multiple times during a single TRP sweep. The multiple resonances give rise to controllable quantum interference effects that provide direct control over qubit transitions so that transitions can be greatly enhanced or suppressed. These quantum interference effects have recently been observed experimentally. We examine here a number of new TRP pulse profiles and show that they can be used to implement a quantum NOT gate that operates both nonadiabatically and with sufficient reliability to surpass the accuracy threshold needed for the gate to be used as part of a fault-tolerant scheme of quantum computation. These new TRP pulse profiles are shown to provide performance advantages over TRP pulses previously considered in the literature.     

Parametric control of a superconducting flux qubit

Parametric control of a superconducting flux qubit has been achieved by using two-frequency microwave pulses. We have observed Rabi oscillations stemming from parametric transitions between the qubit states when the sum of the two microwave frequencies or the difference between them matches the qubit Larmor frequency. We have also observed multiphoton Rabi oscillations corresponding to one- to four-photon resonances by applying single-frequency microwave pulses. The parametric control demonstrated in this work widens the frequency range of microwaves for controlling the qubit and offers a high quality testing ground for exploring nonlinear quantum phenomena of macroscopically distinct states.     

Quantum jumps in Landau-Zener transitions in the dissipative dynamics of a superconducting qubit

The effect of noise on the populations of the levels of a qubit in individual experimental implementations has been studied by the quantum trajectory method. A transition to the average dynamics obtained by means of multiple measurements of the state of the qubit is analyzed. The developed method is applied to investigate the effect of noise on the interference pattern appearing in the amplitude spectroscopy of the qubit in a strong variable field owing to Landau-Zener transitions. The effect of the number of repeated measurements and the fluctuation of the phase of a pump pulse on the formation of the response of the qubit to the external field has been analyzed. This makes it possible to interpret recent experiments in terms of individual implementations and averaged dynamics.     

Fast qubit initialization in a superconducting circuit

We demonstrate an active reset protocol in a superconducting quantum circuit. The thermal population on the excited state of a transmon qubit is reduced through driving the transitions between the qubit and an ancillary qubit. Furthermore,we investigate the efficiency of this approach at different temperatures. The result shows that population in the first excited state can be dropped from 7% to 2.55% in 27 ns at 30 m K. The efficiency improves as the temperature increases. Compared to other schemes, our proposal alleviates the requirements for measurement procedure and equipment. With the increase of qubit integration, the fast reset technique holds the promise of improving the fidelity of quantum control.     

Spectroscopy of a driven solid-state qubit coupled to a structured environment

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the n-photon resonance scales with the nth Bessel function of the driving strength in the weak-damping regime.     

Macroscopic resonant tunneling in an rf-SQUID flux qubit under a single-cycle sinusoidal driving

We experimentally demonstrate the observation of macroscopic resonant tunneling(MRT) phenomenon of the macroscopic distinct flux states in a radio frequency superconducting quantum interference device(rf-SQUID) under a singlecycle sinusoidal driving.The population of the qubit exhibits interference patterns corresponding to resonant tunneling peaks between states in the adjacent potential wells.The dynamics of the qubit depends significantly on the amplitude,frequency,and initial phase of the driving signal.We do the numerical simulations considering the intra-well and interwell relaxation mechanism,which agree well with the experimental results.This approach provides an effective way to manipulate the qubit population by adjusting the parameters of the external driving field.     

Landau-Zener interferometry for qubits

One may probe coherence of a qubit by periodically sweeping its control parameter. The qubit is then excited by the Landau-Zener (LZ) mechanism. The interference between multiple LZ transitions leads to an oscillatory dependence of the energy absorption rate on the sweeping amplitude and on the period. This interference pattern allows to determine the decoherence time of the qubit. We introduce a simple phenomenological model describing this interferometer, and find the form of the interference pattern.Received: 21 October 2003, Published online: 8 December 2003PACS: 03.67.-a Quantum information - 85.25.Dq Superconducting quantum interference devicesD.A. Ivanov: Present address: Paul Scherrer Institute, 5232 Villigen PSI, Switzerland     

Nonlinear resonances in the absorption spectrum of the three-level atomic V system in strong polyharmonic and weak biharmonic fields

A three-level atomic system with a strong three-mode field and a probing biharmonic field at transitions 1→2 and 1?3 (1 is a common lower level), respectively, is studied theoretically by numerical simulation and an analysis of the mathematical expressions derived for the particular case of a symmetric arrangement of the strong field components relative to the transition frequency ω₂₁. The absorption spectrum of the probing field components contains parametric supernarrow resonances against the background of resonances of the nonlinear interference effect. The ratios of the differences in the frequencies of the strong and probing fields, at which the supernarrow resonances appear, are found analytically. The results coincide with those obtained from numerical simulation.     

Optimizing a phase gate using quantum interference

A controlled interference is proposed to reduce, by two orders of magnitude, the decoherence of a quantum gate for which the gate fidelity is limited by coupling to states other than the /0> and /1> qubit states. This phenomenon is demonstrated in an ultracold neutral atom implementation of a phase gate using qubits based on motional states in individual wells of an optical lattice.     

Quantum computation with a one-dimensional optical lattice

We present an economical dynamical control scheme to perform quantum computation on a one-dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the lattice. They can be activated by external laser beams resulting in a two-qubit phase gate or in an exchange interaction. A realization of the Toffoli gate is presented, which requires only a single laser pulse and no individual atom addressing.     

Interaction-Induced Chiral Quantum States of the Ultracold Polar Molecules

The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving field. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chiral states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.     

Interaction-Induced Chiral Quantum States of the Ultracold Polar Molecules

The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving field. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chiral states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.     

Improved Superconducting Qubit State Readout by Path Interference

High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. We demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined with other qubit readout methods based on the discrimination of cavity photon states to further improve the qubit state readout.     

The initial decoherence of the mesoscopic Josephson junction flux qubit

For a mesoscopic radio frequency superconducting quantum interference device (rfSQUID), at a degeneracy point, the system reduces to a quantum two-state system which can be used as a flux qubit. When the noise environment is equivalent to a harmonic oscillators bath, by virtue of an operator-norm measure for the short time decoherence, this paper investigates the initial decoherence of the flux qubit operating in the ohmic noise environment and illustrates its property by means of the numerical evaluation.     

Mesoscopic fluctuations of the population of a qubit in a strong alternating field

Fluctuations of the population of a Josephson qubit in an alternating field, which is a superposition of electromagnetic pulses with large amplitudes, are studied. It is shown that the relative phase of pulses is responsible for the rate of Landau–Zener transitions and, correspondingly, for the frequency of transitions between adiabatic states. The durations of pulses incident on the qubit are controlled with an accuracy of the field period, which results in strong mesoscopic fluctuations of the population of the qubit. Similar to the magnetic field in mesoscopic physics, the relative phase of pulses can destroy the interference pattern of the population of the qubit. The influence of the duration of the pulse and noise on the revealed fluctuation effects is studied.     

Nondestructive readout for a superconducting flux qubit

We present a new readout method for a superconducting flux qubit, based on the measurement of the Josephson inductance of a superconducting quantum interference device that is inductively coupled to the qubit. The intrinsic flux detection efficiency and backaction are suitable for a fast and nondestructive determination of the quantum state of the qubit, as needed for readout of multiple qubits in a quantum computer. We performed spectroscopy of a flux qubit and we measured relaxation times of the order of 80 micros.     

Quantum trajectories of superconducting qubits

In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurement process, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.     

An analytical study on absorptive lineshape of a driven N-type open four-level system: Quantum interference effects

An open four-level system of having two pairs of closely spaced levels (N-type configuration) is driven by a single electromagnetic field and tuned resonant with the average frequency of four dipole allowed transitions. Under the Doppler free condition and by using a semiclassical formulation of atom-field interaction for four dipole allowed transitions, we derive the optical Bloch equations for the said four-level system coupled to the driving field. In order to obtain the field induced polarization and hence the absorptive lineshapes, we use the usual perturbation method for getting the approximate analytical solution to the coupled optical Bloch equations for the density matrix elements. Through the off-diagonal complex density matrix elements, we introduce the field dependent phase angles arising out of the quantum interference between the levels participating in dipole allowed transitions. The difference between the field dependent and field independent phases are pointed out. In particular, we investigate the effects of Rabi frequencies and the field dependent phases on the absorptive lineshape. The analytical expressions for the effective linewidths, effective detunings and the induced polarization clearly indicate the role of quantum interference.     

Measurements of a periodically driving qubit using a quantum point contact

Using the method developed by Gurvitz [1996 Phys. Rev. B 53 15932], we obtained the Bloch-type rate equations describing the entire system of a periodically driving qubit monitored by a quantum point contact detector. The results demonstrate that the isolated qubit can be kept in its initial state with a large driving frequency due to more difficult electron tunneling in qubit, and this initial state can always be measured at a small measurement-induced decoherence rate during a short time.