Entangling gates for trapped-ion quantum computation and quantum simulation

The trapped-ion system has been a leading platform for practical quantum computation and quantum simulation since the first scheme of a quantum gate was proposed by Cirac and Zoller in 1995. Quantum gates with trapped ions have shown the highest fidelity among all physical platforms. Recently, sophisticated schemes of quantum gates such as amplitude, phase, frequency modulation, or multi-frequency application, have been developed to make the gates fast, robust to many types of imperfections, and applicable to multiple qubits. Here, we review the basic principle and recent development of quantum gates with trapped ions.