Experimental demonstration of quantum optimal control via the alternating control–evolution protocol

As a crucial component of quantum technologies, quantum optimal control enables the high-fidelity engineering of desired quantum states and operations. Conventional approaches, such as the widely used gradient ascent pulse engineering (GRAPE) algorithm, typically rely on dense pulse sequences with a large number of control parameters, leading to inefficient optimization and increased sensitivity to experimental imperfections. In this work, we propose the alternating control–evolution (ACE) protocol, a flexible framework that constructs quantum operations by interleaving elementary control operations with tunable free evolutions, thereby enabling the design of sparse pulse sequences that exploit intrinsic system dynamics. This design substantially reduces the number of control parameters while retaining high expressibility and control fidelity. Numerical simulations on nuclear magnetic resonance systems show that the ACE protocol achieves more than a 20-fold reduction in the number of control parameters compared to GRAPE, with comparable fidelity in state preparation tasks. We further experimentally validate the ACE protocol on a four-qubit NMR platform by preparing a Greenberger–Horne–Zeilinger (GHZ) state with a fidelity of 99.52%. These results demonstrate that the ACE protocol provides an efficient and experimentally robust strategy for quantum optimal control, particularly suitable for the noisy intermediate-scale quantum (NISQ) era.