Direct Experimental Simulation of Yang-Baxter Equation

Chao Zheng, Shijie Wei

Michio Jimbo

Chao Zheng, Junlin Li, Siyu Song +1 more

Having been introduced in the field of many bodies of statistical mechanics, the Yang–Baxter equation has become an important tool in a variety of fields of physics. In this work, we report the first direct experimental simulation of the Yang–Baxter equation using linear quantum optics. The equality between the two sides of the Yang–Baxter equation in two dimension has been demonstrated directly, and the spectral parameter transformation in the Yang–Baxter equation is explicitly confirmed.

Chao Zheng, Junlin Li, Siyu Song +1 more

Introduced in the field of many-body statistical mechanics, Yang-Baxter equation has become an important tool in a variety of fields of physics. In this work, we report the first direct experimental simulation of the Yang-Baxter equation using linear quantum optics. The equality between the two sides of the Yang-Baxter equation in two dimensions has been demonstrated directly, and the spectral parameter transformation in the Yang-Baxter equation is explicitly confirmed.

Hengyan Wang, Shijie Wei, Chao Zheng +6 more

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.

Rinat Kashaev, Vladimir V. Mangazeev