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World Congress on Intelligent Control and Automation

Lyapunov-based control of a double quantum-dot qubit

Shuang Cong, Ming-yong Gao

Published Jun 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1109/wcica.2016.7578626

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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 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.
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.
We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.
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.
The coherent time evolution of electrons in double quantum dots (DQDs) induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven DQDs are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation, we obtain the energy- and time-resolved electron transfer through the device that resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots.
In double quantum dot singlet–triplet qubits, the exchange interaction is used in both quantum gate operation and the measurement of the state of the qubit. The exchange can be controlled electronically by applying gate voltage pulses. We simulate the exchange induced charge state transitions in one and two singlet–triplet qubit systems using the exact diagonalization method. We find that fast detuning pulses may result in leakage between different singlet charge states. The leakage could cause measurement errors and hinder quantum gate operation for example in the case of the two-qubit Coulomb gate.