UC Merced

Robust and high-fidelity preparation of quantum states in many-body systems is crucial for quantum information processing but remains challenging due to the inherent complexity of many-body states. We present several control techniques for the generation of correlated many-body states and multipartite entangled states. The approaches we have employed include quantum shortcuts to adiabaticity (STA), quantum optimal control (QOC), and controlled pulse techniques to overcome the challenges in realistic devices. We study counter-diabatic (CD) driving in finite-sized Jaynes-Cummings (JC) lattices, deriving simplified CD Hamiltonians that suppress diabatic transitions while maintaining local qubit-cavity couplings in specific configurations. Numerical simulations confirm that this approach significantly accelerates state preparation while ensuring robustness against control errors and noise. Extending this framework to a general multisite JC lattice, we construct a local CD Hamiltonian that reproduces the exact nonlocal CD dynamics, enabling efficient multipartite W-state generation. These results demonstrate the feasibility of STA-based state preparation in superconducting quantum circuits and related platforms. We also explore the QOC approach for achieving high-fidelity ground-state preparation in JC lattices using the chopped random basis algorithm and Nelder-Mead optimization. Our results reveal that QOC outperforms adiabatic methods beyond a threshold evolution time, which we show is closely related to the quantum speed limit (QSL). We refine our QOC algorithm to improve fidelity and analyze entanglement dynamics, providing deeper insights into the fundamental constraints of quantum state preparation. Additionally, we develop a scalable method for generating dual-rail continuous-variable cluster states in phononic quantum networks using local phonon-phonon interactions and radiation pressure coupling. We also demonstrate how distant qubits can be entangled via interactions with mechanical resonators, highlighting applications in distributed quantum networks. Overall, this thesis advances state preparation techniques in JC lattices through STA and QOC while introducing a scalable approach for CV cluster state generation in phononic networks, contributing to the development of practical and robust quantum technologies.