In the field of quantum computing, topological quantum computing is an important branch with a series of advantages such as high fault tolerance. Topological quantum computation relies heavily on the non-Abelian weaving of quantum states, which is a quantum statistical property closely related to the nonlocality of quantum states. In the past twenty years, many researchers have studied a strange particle-Mayorana Fermion, which can realize non-Abelian weaving in superconducting ordered parameter system, and a special case of this particle-majorana zero mode at zero energy.

Recently, the team of Professor Xie Xincheng of Peking University Quantum Materials Science Center cooperated with Anjiao University and other units to explain a new way to realize non-Abelian weaving, that is, to realize non-Abelian weaving by using Jackiw-Rebbi zero mode widely existing in topological insulators.

The concept of Jackiw-Rebbi zero mode first appeared in the field of high-energy physics, and then extended to the field of condensed matter physics, which is used to refer to the topological protection zero-energy mode at the edge of topological insulators. Compared with majorana zero mode, Jackiw-Rebbi zero mode has no self-yoke property, so it can appear in non-superconducting systems without particle hole symmetry protection.

In this work, the researchers constructed Jackiw-Rebbi zero mode in quantum spin Hall insulator, and confirmed that this zero mode will lead to frequency doubling Aharonov-Bohm effect, which can show non-Abelian weaving characteristics without superconductivity, while majorana zero mode can be regarded as a special case of Jackiw-Rebbi zero mode with particle hole symmetry.

(a) realizing the zero-mode non-Abelian braided cross nanowire structure of Jackiw-Rebbi; The numerical results of wave function evolution show the non-Abelian weaving characteristics of Jackiw-Rebbi zero mode.

The researchers also found that when the degeneracy is destroyed, Jackiw-Rebbi zero module will show non-Abelian weaving properties that Mayorana zero module fusion rules do not have. This tunable property, which is independent of superconductivity and large energy gap, may provide a new idea for topological quantum computing.

The related results were published in National Science Review (NSR), titled "Dual-frequency Aharonov-Bohm Effect and Non-Abelian Weaving Properties of jackiw-rebbi Zero Mode". Wu Yijia, Ph.D. student of Peking University Quantum Materials Science Center, is the first author, Professor Xie Xincheng and Associate Professor Liu Jie of Xi Jiaotong University are the corresponding authors, and other collaborators include Liu Haiwen of Beijing Normal University and Professor Jiang Hua of Suzhou University.