Quantum optimal control of two-qubit gates in Rydberg atoms

Quantum computers promise to outperform conventional computational processes by taking advantage of exclusive quantum properties, such as superposition and entanglement. In the last years, several breakthroughs have demonstrated Rydberg atoms as a promising scalable quantum computing platform. Rydberg atoms are excited atoms that show exaggerated properties, where two different internal states encode a qubit with long coherence times. The progress in manipulating individual Rydberg atoms has allowed the experimental realization of single and two-qubit gate protocols. This has motivated a widespread theoretical interest in improving gate fidelity and finding alternative protocols. After reviewing the physics of Rydberg atoms and the most up-to-date gate protocols, in this Thesis we simulate one and two qubits gates, then we apply optimal control techniques, as implemented in the open-source optimal control suite QuOCS, to optimize the laser pulse shapes for the realization of controlled-phase gate.