Experimental Realization of Shortcuts to Adiabaticity in a Nonintegrable Spin Chain by Local Counterdiabatic Driving

Counterdiabatic driving (CD) offers a fast and robust strategy to manipulate and prepare the quantum state in multibody systems. However, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form for higher-dimensional complex systems. Recently, Sels and Polkovnikov [Proc. Natl. Acad. Sci. U. S. A. 114, E3909 (2017)] proposed a variational method to optimally approximate the CD term with no need for the full spectral information of the original Hamiltonian. Using a nuclear-magnetic-resonance setup, here we report an experimental demonstration of this method to construct available shortcuts to adiabaticity in a nonintegrable spin-$1/2$ chain via only local controls. In this process, the ground state of such a system is rapidly prepared and the final state fidelity is significantly increased compared with the traditional adiabatic method. Our experiments prove the feasibility of this variational method to design CD in practice, and thus it is a promising strategy for fast, high-fidelity quantum-state manipulation in complex and noisy quantum systems.