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arXiv:1611.09451 · New Journal of Physics

Entangled states of two quantum dots mediated by Majorana fermions

Zhengang Shi, W Wang, X. X. Yi

Published Jan 29, 2016• 6 citations
arXivHTMLPDF

Abstract

With the assistance of a pair of Majorana fermions, we propose schemes to entangle two quantum dots by Lyapunov control in the charge and spin degrees of freedom. Four different schemes are considered, i.e., the teleportation scheme, the crossed Andreev reflection scheme, the intradot spin flip scheme, and the scheme beyond the intradot spin flip. We demonstrate that the entanglement can be generated by modulating the chemical potential of quantum dots with square pulses, which is easily realized in practice. In contrast to Lyapunov control, the preparation of entangled states by adiabatic passage is also discussed. There are two advantages in the scheme by Lyapunov control, i.e., it is flexible to choose a control Hamiltonian, and the control time is much shorter with respect to the scheme by adiabatic passage. Furthermore, we find that the results are quite different by different adiabatic passages in the scheme beyond the intradot spin flip, which can be understood as an effect of quantum destructive interference.

DOI
10.1088/1367-2630/18/2/023005

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The adiabatic passage of two correlated electrons in three coupled quantum dots is shown to provide a robust and controlled way of distilling, transporting, and detecting spin entanglement, as well as measuring the rate of spin disentanglement. By employing tunable interdot coupling the scheme creates from an unentangled two-electron state, a superposition of spatially separated singlet and triplet states. A single measurement of a dot population (charge) collapses the wave function to either of these states, realizing the entanglement to the charge conversion. The scheme is robust, with the efficiency close to 100%, for a large range of realistic spectral parameters.
Quantum state preparation through external control is fundamental to established methods in quantum information processing and in studies of dynamics. In this respect, excitons in semiconductor quantum dots are of particular interest, since their coupling to light allows them to be driven into a specified state using the coherent interaction with a tuned optical field, such as an external laser pulse. We propose a protocol, based on adiabatic rapid passage, for the creation of entangled states in an ensemble of pairwise coupled two-level systems, such as an ensemble of coupled quantum dots. We show by quantitative analysis using realistic parameters for semiconductor quantum dots that this method is feasible where other approaches are unavailable. Furthermore, this scheme can be generically transferred to some other physical systems, including circuit QED, nuclear and electron spins in solid-state environments, and photonic coupled cavities.
The Lyapunov control theory was used in the manipulation of a single qubit in the two-level double quantum-dot (DQD) system. The proposed control process is composed of three parts: firstly a slope pulse takes the system from a positive detuning adiabatically to the anti-crossing point, which corresponds to the resonance state of the system; then a Lyapunov-based control pulse drives the charge qubit transfer non-adiabatically; finally another slope pulse takes the system away from the anti-crossing point to keep the system stable. The charge state probability P|L〉and the curve of Lyapunov-based control pulse were studied under different control parameters. Simulation results showed that: the designed Lyapunov-based control pulse has a rise time ~100ps, which is in the scope of the Aglient 81134A pulse generator for the implement, and it results in a significant probability 86% for transition from the initial charge state |R〉 to the desired target charge state |L〉. Although our control scheme is designed specific for the DQD system, the technique is independent of the physical architecture and has potential for wider applications.
Abstract Long‐distance transfer of quantum states is an indispensable part of large‐scale quantum information processing. A novel scheme for the transfer of two‐electron entangled states from one edge of a quantum dot array to the other by coherent adiabatic passage is proposed. This protocol is mediated by pulsed tunneling barriers. In a second step, a speed up is sought for by shortcut to adiabaticity techniques. This significantly reduces the operation time and, thus, minimizes the impact of decoherence. For typical parameters of state‐of‐the‐art solid state devices, the accelerated protocol has an operation time in the nanosecond range and terminates before a major coherence loss sets in. The scheme represents a promising candidate for entanglement transfer in solid state quantum information processing.
We propose a scheme for extracting entangled charge qubits from quantum-dot chains that support zero-energy edge modes. The edge mode is composed of Majorana fermions localized at the ends of each chain. The qubit, logically encoded in double quantum dots, can be manipulated through tunneling and pairing interactions between them. The detailed form of the entangled state depends on both the parity measurement (an even or odd number) of the boundary-site electrons in each chain and the teleportation between the chains. The parity measurement is realized through the dispersive coupling of coherent-state microwave photons to the boundary sites, while the teleportation is performed via Bell measurements. Our scheme illustrates localizable entanglement in a fermionic system, which serves feasibly as a quantum repeater under realistic experimental conditions, as it allows for finite temperature effect and is robust against disorders, decoherence and quasi-particle poisoning.
For a two-level double quantum-dot (DQD) system, we proposed an alternative ultrafast manipulation approach, Lyapunov-based control method, to transfer the charge qubit from the initial charge state |R) to the target charge state |L) on the picosecond scale. Better control performance is obtained compared with that via Landau-Zener-Stu̅ckberge-Majorana interference, and the designed control fields can be implemented in the actual experiment facility. The control process is composed of three parts: first, a slope pulse takes the system from a positive detuning adiabatically to the anticrossing point, which corresponds to the resonance state of the system; then, a Lyapunov-based control pulse drives the charge qubit transfer nonadiabatically; finally, another slope pulse takes the system away from the anticrossing point to keep the system stable. The charge qubit transfer performance and the function of Lyapunov-based control pulse were studied under different control parameters. Simulation results showed that the designed Lyapunov-based control pulse has a rise time ~20 ps, which is in the scope of the Tektronix AWG70000A series arbitrary waveform generator and results in a significant probability ~96% for the transition from the initial charge state |R) to the target charge state |L). The fidelity of the control process designed can achieve ~94%. This is the first result directly applicable for a DQD charge qubit transfer using the Lyapunov-based control method.