Progress of quantum entanglement in a trapped-ion based quantum computer

In recent years, there have been significant progress toward building a practical quantum computer, demon-strating key ingredients such as single-qubit gates and a two-qubit entangling gate. Among various physical platforms for a potential quantum computing processor, a trapped-ion system has been one of the most promising platforms due to long coherence times, high-fidelity quantum gates, and qubit connectivity. However, scaling up the number of qubits for a practical quantum computing faces a core challenge in operating high-fidelity quantum gates under influence from neighboring qubits. In particular, for the trapped-ion system, unwanted quantum crosstalk between qubits and ions' quantum motional states hinder performing high-fidelity entan-glement as the number of ions increases. In this review, we introduce a trapped-ion system and explain how to perform single-qubit gates and a two-qubit entanglement. Moreover, we mainly address theoretical and exper-imental approaches to achieve high-fidelity and scalable entanglement toward a trapped-ion based quantum computer.