Assessing three closed-loop learning algorithms by searching for high-quality quantum control pulses

TL;DR

This paper compares three closed-loop learning algorithms—GRAPE, NMplus, and DE—for optimizing quantum control pulses to reliably prepare high-fidelity Bell states, analyzing their performance in experimental and uncertain conditions.

Contribution

It provides a comprehensive experimental and numerical comparison of three key algorithms for quantum control pulse optimization under realistic uncertainties.

Findings

All three algorithms successfully prepared high-fidelity Bell states.

Convergence speeds varied among algorithms.

Performance differences emerged under significant uncertainties.

Abstract

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.