Quantum Optimal Control at Finite Temperature in Rydberg Atoms Platform

One of the potential candidates for programmable quantum devices is reconfigurable arrays of identical neutral atoms trapped in optical tweezers. As they are neutral, they can be easily packed together, which enables the system to be well-scalable to several hundreds of qubits. By exploiting the Rydberg states, large electric dipole moments among atoms display strong, controllable interactions, and a longer coherence time is obtained. Loading atoms into arrays is a stochastic process, and in order to create a system suitable for quantum computing, a rearrangement among atoms must be made. After obtaining the quantum register, a second application of the rearrangement occurs during algorithms and the implementation of quantum gates to modify the connectivity of the whole device. By precisely controlling the optical tweezers, it is possible to transfer atoms from one lattice site to another. A challenging aspect of the experiment is preventing the loss and heating of atoms during transmission. In this thesis, several numerical techniques are employed to simulate optical trap, laser pulse, and wave functions for a single atom in an one dimensional array. Optimal control techniques such as dCRAB algorithm is applied and developed at finite temperature for moving a single atom in a trap with the aim of maximizing the fidelity among the started stated and the final state after movement. Quantum speed limit of this process is investigated as well to maximize the number of quantum operations for a given decoherence time.