Quantum optimal control on many-body ground state preparation in Jaynes-Cummings lattices

The ability to engineer the desired quantum many-body state and dynamics is essential for quantum computing. However, due to noises and significant control errors in quantum devices, achieving this goal is extremely challenging. Robust algorithms like adiabatic algorithms often require a long evolution time to maintain a quantum system in a desired many-body state. But long evolution time increases the interaction time between the system and the environment, which leads to decoherence and errors in the system. To overcome this limitation, quantum optimal control (QOC) theory has been developed. QOC is a numerical technique to design fast and robust control pulses to drive the quantum system to the target state under a given set of constraints. Here we use QOC with Chopped-Random Basis (CRAB) algorithm to prepare quantum many-body ground states in Jaynes-Cummings lattices. Our study shows that a high-fidelity many-body ground state can be prepared in a significantly shorter time using the CRAB algorithm than using the adiabatic algorithm. We find the minimal evolution time for achieving fidelity above 0.99 under various parameter constraints. We also analyze the effect of Gaussian noise in the control parameters on the fidelity of prepared states at the optimal evolution time. This study provides insight into the development of fast and efficient quantum algorithms for the many-body ground state preparation in quantum devices.