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Physical Review A

Quantum wire as a charge-qubit detector

T. Kwapiński, Ryszard Taranko

Published Nov 30, 2012• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.052338

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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.
A GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs based two-qubit quantum device that allows the controlled generation and straightforward detection of entanglement by measuring a stationary current-voltage characteristics is proposed. We have developed a two-particle Green's function method of open systems and calculate the properties of three-dimensional interacting entangled systems nonperturbatively. We present concrete device designs and detailed charge-self-consistent predictions. One of the qubits is an all-electric Mach-Zehnder interferometer that consists of two electrostatically defined quantum wires with coupling windows, whereas the second qubit is an electrostatically defined double quantum dot located in a second two-dimensional electron gas beneath the quantum wires. We find that the entanglement of the device can be controlled externally by tuning the tunneling coupling between the two quantum dots.
Lateral semiconductor quantum dot structures have been proposed as an effective quantum bit (qubit) for quantum computation. A single excess electron with the freedom to move between two capacitively coupled quantum dots creates a `pseudo'-spin system with the same qubit behavior as the more natural two level system of a single electron spin. The excess electron in the double dot system is restricted to one of the two dots, thereby creating two separate and distinct states (usually referred to as |L> and |R>). The benefit of these charge qubits lie in the relative ease with which they can be manipulated and created. Experiments have been performed in this area and have shown controllable coherent oscillations and thus efficient single-qubit operations. However, the decoherence rates observed in the experiments is still quite high, making double dot charge qubits not very appealing for large-scale implementations. The following work describes the effect of the electromagnetic (EM) environment of the double quantum dot system on the decoherence of the charge state. Sources of decoherence in similar systems have been extensively investigated before and this paper follows a close theoretical framework to previous work done in the area. The effect of the EM environment can been seen in the calculations discussed below, although it is clear that the decoherence seen in experiments cannot be fully explained by the voltage fluctuations as they are investigated here. The limitations of the calculations are discussed and improvements are suggested.
The decoherence dynamics of two charge qubits in a double quantum dot is investigated theoretically. We consider the quantum dynamics of two interacting electrons in a vertically coupled quantum dot driven by an external electric field. We derive the equations of motion for the density matrix, in which the presence of an electron confined in the double dot represents one qubit. A Markovian approach to the dynamical evolution of the reduced density matrix is adopted. We evaluate the concurrence of two qubits in order to study the effect of acoustic phonons on the entanglement. We also show that the disentanglement effect depends on the double dot parameters and increases with the temperature.
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
A solid-state-based charge qubit is presented. The system consists of a one-dimensional wire with a pair of qubits embedded at its center. It is shown that the system supports collective states localized in the left and right sides of the wire and therefore, as a whole, performs as a single qubit. The couplings between the ground and excited states of the two central qubits are inversely proportional making them fully asynchronized and allowing for coherent manipulation and gate operations. Initialization and measurement devices, such as leads and charge detectors, connected to the edges of the wire are modeled by a continuum of energy states. The coupling to the continuum is discussed using the effective non-Hermitian Hamiltonian. At weak continuum coupling, all internal states uniformly acquire small decay widths. This changes dramatically as the coupling strength increases: the width distribution undergoes a sharp restructuring and is no longer uniformly divided among the eigenstates. Two broad resonances localized at the ends of the wire are formed. These superradiant states (analogous to Dicke states in quantum optics) effectively protect the remaining internal states from decaying into the continuum and hence increase the lifetime of the qubit. Environmental noise is introduced by considering random Gaussian fluctuations of electronic energies. The interplay between decoherence and superradiance is studied by solving the stochastic Liouville equation. In addition to increasing the lifetime, the emergence of the superradiant states increases the qubit coherence.
We discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes. Two distinct quantum dot configurations are studied: (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate voltages. Compared to a previous proposal involving a linear three-dot spin qubit, the three-dot charge qubit allows for less overhead on two-qubit operations. For small interdot tunnel amplitudes, the three-dot qubits have QQQ factors much higher than those obtained for double-dot systems. The high-multipole dot configurations also show a substantial decrease in decoherence at low operation frequencies when compared to the double-dot qubit.