State Preparation in a Jaynes-Cummings Lattice with Quantum Optimal Control: Threshold Time and Quantum Speed Limit.

We develop a quantum optimal control (QOC) algorithm to study state preparation in a finite-sized Jaynes-Cummings (JC) lattice with unit fillings. In our previous study [1], we showed that desired many-body states can be generated with high fidelity when the evolution time is beyond a threshold time that depends on the bounds of the system parameters. In this work, we improve the QOC algorithm to achieve a better understanding of the relation between the threshold time and the quantum speed limit (QSL). With the current algorithm, the infidelity of the prepared states can be lowered to below 10^-5. We also calculate energy fluctuations and entanglement of the prepared states during the time evolution, which lead to more insights on the threshold time.



[1] Parajuli et.al. State Preparation in a Jaynes-Cummings Lattice with Quantum Optimal Control, arXiv: 2306.11968