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arXiv:1401.2614 · IEEE Journal of Quantum Electronics

Ultrafast Manipulation of a Double Quantum-Dot Charge Qubit Using Lyapunov-Based Control Method

Shuang Cong, Ming-yong Gao, Gang Cao, Guang‐Can Guo, Guo‐Ping Guo

Published Jun 8, 2015• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/jqe.2015.2440783

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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.
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.
For a double quantum dot (DQD) system, we propose a Lyapunov control method to transfer the state from initial state to the target state on the picosecond scale, which open a significant new area of research for the system control theories. The control laws are composed of two-direction components, one is used to eliminate the dissipation in the system, another is used to transfer the state. The Lyapunov stability theorem ensures the system can be transferred to the target state in high probability, and the coefficients in control laws leads very fast convergence. The role of eliminating the dissipation plays the suppression of decoherence effect. Numerical simulation results show that the transfer probability and fidelity can be increased up to 98.79% and 98.97%, respectively. This is the first result directly applicable to a DQD system's state transferring using the Lyapunov control method. We also give specific experimental realization scheme.
A basic requirement for quantum information processing is the ability to universally control the state of a single qubit on timescales much shorter than the coherence time. Although ultrafast optical control of a single spin has been achieved in quantum dots, scaling up such methods remains a challenge. Here we demonstrate complete control of the quantum-dot charge qubit on the picosecond scale [corrected], orders of magnitude faster than the previously measured electrically controlled charge- or spin-based qubits. We observe tunable qubit dynamics in a charge-stability diagram, in a time domain, and in a pulse amplitude space of the driven pulse. The observations are well described by Landau-Zener-Stückelberg interference. These results establish the feasibility of a full set of all-electrical single-qubit operations. Although our experiment is carried out in a solid-state architecture, the technique is independent of the physical encoding of the quantum information and has the potential for wider applications.
We propose an efficient control protocol for charge transfer in a double quantum dot. We consider numerically a two-dimensional model system, where the quantum dots are subjected to time-dependent electric fields corresponding to experimental gate voltages. Our protocol enables navigation in the charge stability diagram from a state to another through controllable variation of the fields. We show that the well-known adiabatic Landau-Zener transition-when supplemented with a time-dependent field tailored with optimal control theory-can remarkably improve the transition speed. The results also lead to a simple control scheme obtained from the experimental charge stability diagram that requires only a single parameter. Eventually, we can achieve the ultrafast performance of the composite pulse protocol that allows the system to be driven at the quantum speed limit.
We demonstrate multipulse quantum control of a single electron charge qubit. The qubit is manipulated by applying nonadiabatic voltage pulses to a surface depletion gate and readout is achieved using a quantum point-contact charge sensor. We observe Ramsey fringes in the excited-state occupation in response to a $\ensuremath{\pi}/2$-$\ensuremath{\pi}/2$ pulse sequence and extract ${T}_{2}^{*}\ensuremath{\sim}60$ ps away from the charge degeneracy point. Simulations suggest these results may be extended to implement a charge echo by reducing the interdot tunnel coupling and pulse rise time, thereby increasing the nonadiabaticity of the pulses.
We report on an optimal single-electron charge qubit for a solid-state double quantum dot (DQD) system and analyse its dynamics under a time-dependent linear detuning, using GPU accelerated numerical solutions to the time-dependent Schrödinger equation. The optimal qubit is found to have basis states defined as the symmetric and antisymmetric linear combinations of the lowest energy bonding and anti-bonding states of the DQD at zero bias. In contrast to charge qubits defined by the two localised ground states of the uncoupled DQD, this choice of the basis causes the resulting dynamics to have a maximal overlap with an idealised two-state model. Our optimal qubit basis states are not localised to a single quantum dot and, as such, initialising the qubit requires a particular sequence of gate pulses to take the system from an initial fiducial state of the DQD to the logical 000 or 111. We determine this sequence using pulses that incorporate the expected experimental finite rise times. We also show how to perform arbitrary single qubit operations on the Bloch sphere using spin-echo type pulsing, allowing us to obtain any qubit state with at most two single pulses. Measurement of the optimal qubits is achieved by determining the probability of finding the electron in one of the dots.