Quantum optimal control on many-body states in a Jaynes-Cummings lattice

The quantum optimal control technique is a powerful tool for efficiently implementing high-fidelity quantum operations and generating desirable quantum states. Here we use this technique to study the robust generation of quantum many-body states in a Jaynes Cummings (JC) lattice near quantum critical regions. The chopped random basis (CRAB) algorithm is employed to optimize the time dependence of the light-matter coupling constant and the photon hopping rate of the JC lattice, where these parameters are expanded into a Fourier basis with optimizable Fourier coefficients and frequencies. Our numerical simulation demonstrates that this approach can significantly improve the fidelity of the prepared many-body ground states in comparison with the adiabatic evolution approach. We also analyze the energy gap along the optimized evolution trajectory and the lower bound of the evolution time in relation to the quantum speed limit.
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2. P. Parajuli and L. Tian, in preparation.