Optimal quantum control applied to quantum dots

Abstract

In the present study, we review the one-qubit dynamics and we offer a new unifying interpretation of the Landau-Zenner and the Rabi dynamics, by indicating the physical elements responsible for the manifestation of one phenomenon or the other, without the need to define them as separate phenomena. Furthermore, we demonstrate the possibility of electrically implementing quantum gates with high fidelity in two different platforms of quantum dots, with the assistance of the two-point boundary-value quantum control paradigm (TBQCP). In the first platform consisting of a double quantum dot (DQD) embedded in a nanowire, we optimized single qubit pulses corresponding to three quantum gates assuring a fidelity for every gate higher than 0,99. Also we compare the dynamical efficiency of the optimized pulses via the TBQCP method, respect to the other dynamical mechanisms (Rabi and Landau-Zener); and we found that TBQCP can provide pulses that can perform tasks in shorter times. For the second platform consisting of an electrostatical DQD, we implement the quantum permutation algorithm (QPA), which requires the quantum superposition of states with well-defined relative phases. Because of the necessity of using at least a three level system in this algorithm, we use hybrid qubits instead of spin qubits. In order to find the optimal AC electric fields that implement the required quantum gates, we apply the TBQCP method. By employing such method, we were able to determine optimal electric pulses that perform the quantum gates with high fidelity and in times faster than decoherence and relaxation time. Our results demonstrate the possibility of achieving all-electrical universal quantum gates in DQDs by means of optimal quantum control.