  Designing a high-quality control is crucial for reliable quantum computation.
Among the existing approaches, closed-loop leaning control is an effective
choice. Its efficiency depends on the learning algorithm employed, thus
deserving algorithmic comparisons for its practical applications. Here, we
assess three representative learning algorithms, including GRadient Ascent
Pulse Engineering (GRAPE), improved Nelder-Mead (NMplus) and Differential
Evolution (DE), by searching for high-quality control pulses to prepare the
Bell state. We first implement each algorithm experimentally in a nuclear
magnetic resonance system and then conduct a numerical study considering the
impact of some possible significant experimental uncertainties. The experiments
report the successful preparation of the high-fidelity target state with
different convergence speeds by the three algorithms, and these results
coincide with the numerical simulations when potential uncertainties are
negligible. However, under certain significant uncertainties, these algorithms
possess distinct performance with respect to their resulting precision and
efficiency. This study provides insight to aid in the practical application of
different closed-loop learning algorithms in realistic physical scenarios.

Quantum Physics