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Phase readout of a charge qubit

Christoph Kreisbeck, Franz J. Kaiser, Sigmund Kohler

Published Apr 17, 2009• 0 citations
OpenAlex

Abstract

Abstract.- We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit. Quantum algorithms usually terminate with qubit readout, i.e., a measurement of the quantum register’s state. Generally, the laws of quantum mechanics inhibit one to directly and fully determine the wave function of the qubit from a single measurement. With repeated projective measurements, it is only possible to sample the probability that the qubit is in the one or the other of two orthogonal states. Such destructive measurements can nevertheless be used to demonstrate coherent oscillations by repeating

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Abstract.- We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit. Quantum algorithms usually terminate with qubit readout, i.e., a measurement of the quantum register’s state. Generally, the laws of quantum mechanics inhibit one to directly and fully determine the wave function of the qubit from a single measurement. With repeated projective measurements, it is only possible to sample the probability that the qubit is in the one or the other of two orthogonal states. Such destructive measurements can nevertheless be used to demonstrate coherent oscillations by repeating
We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit with sufficient resolution.
We present a proposal for a qubit charge meter (detector) based on a linear wire of quantum dots placed between two electron reservoirs. A qubit formed by an excess electron in a double quantum dot is coupled electrostatically with a single wire site and the dynamics of this system is studied using the equation of motion for appropriate correlation functions and the evolution operator method. For the qubit-wire system, depending on the qubit position on the wire the readout current oscillates over a long time or the current oscillations decrease very rapidly. This effect cannot be explained in terms of different charges of the wire sites (the same occupancies of all sites are considered). We have found that the qubit's decoherence strongly depends on the structure of the local density of states of the site which is coupled with the qubit. Additionally, the period of the readout current oscillations changes with the wire-qubit electrostatic coupling.
Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot charge qubit strongly coupled to a frequency-tunable high-impedance resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state-dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation, and Hahn-echo measurements and find significantly reduced decoherence rates down to γ_{2}/2π∼3 MHz corresponding to coherence times of up to T_{2}∼50 ns for charge states in gate-defined quantum dot qubits. We realize Rabi π pulses of width down to σ∼0.25 ns.
We investigate the electronic transport through two parallel double quantum dots coupled both capacitively and via a perpendicularly aligned charge qubit. The presence of the qubit leads to a modification of the coherent tunnel amplitudes of each double quantum dot. We study the influence of the qubit on the electronic steady-state currents through the system, the entanglement between the transport double quantum dots, and the back-action on the charge qubit. We use a Born-Markov secular quantum master equation for the system. The obtained currents show signatures of the qubit. The stationary qubit state may be tuned and even rendered pure by applying suitable voltages. In the Coulomb diamonds, it is also possible to stabilize pure entangled states of the transport double quantum dots.
We present a theoretical analysis of the capacitance of a double quantum dot in the charge and spin qubit configurations probed at high frequencies. We find that, in general, the total capacitance of the system consists of two state-dependent terms: the quantum capacitance arising from adiabatic charge motion and the tunneling capacitance that appears when repopulation occurs at a rate comparable or faster than the probing frequency. The analysis of the capacitance lineshape as a function of externally controllable variables offers a way to characterize the qubits' charge and spin state as well as relevant system parameters such as charge and spin relaxation rates, tunnel coupling, electron temperature, and electron ggg factor. Overall, our analysis provides a formalism to understand dispersive qubit-resonator interactions which can be applied to high-sensitivity and noninvasive quantum-state readout.