The Yang-Baxter equation (YBE) has created many applications in the integrable models of the statistical mechanics. It is recently shown that the YBE can be further applied in quantum information processing. Conversely, quantum simulation also provides novel approaches for effectively checking the YBE in quantum devices. Here, we adopted the method inspired by the previous work to experimentally perform the simulation of the YBE on a four-qubit nuclear magnetic resonance quantum processor. Whether the YBE is satisfied or not can be preliminarily determined by measuring the ancillary qubit without the assistance of quantum state tomography, and two hand sides of the YBE are concurrently simulated, not in separate forms involved in the existing protocols. The experimental result shows that the discrimination accuracy is over 98.1% when the condition of YBE is satisfied. The global and local entanglements in the YBE system are also studied by the numerical simulation and experiments. It is found that the YBE is not only a tool to yield the global entanglement but also the symptom when the local entanglement is equal to each other.

中文翻译：

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自旋量子模拟器上四维Yang-Baxter方程的实验模拟

Yang-Baxter方程（YBE）在统计力学的可积模型中创建了许多应用程序。最近显示YBE可以进一步应用于量子信息处理。相反，量子模拟也提供了新颖的方法来有效地检查量子器件中的YBE。在这里，我们采用了先前工作的启发方法，在四量子位核磁共振量子处理器上实验性地进行了YBE的仿真。可以通过测量辅助量子位来初步确定是否满足YBE，而无需借助量子态层析成像技术，并且可以同时模拟YBE的两只手，而不是以现有协议中涉及的单独形式进行模拟。实验结果表明，该算法的判别精度达到98以上。满足YBE的条件时为1％。通过数值模拟和实验研究了YBE系统中的整体和局部纠缠。发现YBE不仅是产生全局纠缠的工具，而且还是局部纠缠彼此相等时的症状。