Proposal of detecting topological transition of quantum braiding in three-fold degenerate eigen subspace

• URL: http://arxiv.org/abs/2401.01703v1
• Date: Wed, 3 Jan 2024 12:13:08 GMT
• Title: Proposal of detecting topological transition of quantum braiding in three-fold degenerate eigen subspace
• Authors: Zhi-Wei Han, Jia-Hao Liang, Zhao-Xin Fu, Hong-Zhi Liu, Zi-Yuan Chen, Meng Wang, Ze-Rui He, Jia-Yi Huang, Qing-Xian Lv, Kai-Yu Liao, and Yan-Xiong Du
• Abstract summary: The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. We show that a three-fold eigen subspace can be degenerated in a four-level Hamiltonian which is the minimal physical system.
• Score: 10.625176985333017
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once that the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally-feasible system provides a platform to investigate braiding dynamics, the SU(3) physics and the qutrit gates.

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