  Quantum computers provide a promising method to study the dynamics of
many-body systems beyond classical simulation. On the other hand, the
analytical methods developed and results obtained from the integrable systems
provide deep insights on the many-body system. Quantum simulation of the
integrable system not only provides a valid benchmark for quantum computers but
is also the first step in studying integrable-breaking systems. The building
block for the simulation of an integrable system is the Yang-Baxter gate. It is
vital to know how to optimally realize the Yang-Baxter gates on quantum
computers. Based on the geometric picture of the Yang-Baxter gates, we present
the optimal realizations of two types of Yang-Baxter gates with a minimal
number of CNOT or $R_{zz}$ gates. We also show how to systematically realize
the Yang-Baxter gates via the pulse control. We test and compare the different
realizations on IBM quantum computers. We find that the pulse realizations of
the Yang-Baxter gates always have a higher gate fidelity compared to the
optimal CNOT or $R_{zz}$ realizations. On the basis of the above optimal
realizations, we demonstrate the simulation of the Yang-Baxter equation on
quantum computers. Our results provide a guideline and standard for further
experimental studies based on the Yang-Baxter gate.
