Effects of decoherence on diabatic errors in Majorana braiding

Zhen-Tao Zhang, Feng Mei, Xiang-Guo Meng, Bao-Long Liang, and Zhen-Shan Yang
Phys. Rev. A 100, 012324 – Published 16 July 2019

Abstract

The braiding of two non-Abelian Majorana modes is important for realizing topological quantum computation. It can be achieved through tuning the coupling between the two Majorana modes to be exchanged and two ancillary Majorana modes. However, this coupling also makes the braiding subject to environment-induced decoherence. Here, we study the effects of decoherence on the diabatic errors in the braiding process for a set of time-dependent Hamiltonians with finite smoothness. To this end, we employ the master equation to calculate the diabatic excitation population for three kinds of decoherence processes. (1) Only pure dehasing: the scaling of the excitation population changed from T2k2 to T1 (k is the number of the Hamiltonian's time derivatives vanishing at the initial and final times) as the braiding duration T exceeds a certain value. (2) Only relaxation: the scaling transforms from T2k2 to T2 for k=0 and to Ta (a>3) for k>0. (3) Pure dephasing and relaxation: the original scaling switches to T1 first and then evolves to T2 in the adiabatic limit. Interestingly, the third scaling-varying style holds even when the expectation of pure dephasing rate is much smaller than that of the relaxation rate, which is attributed to the vanishing relaxation at the turning points of the braiding.

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  • Received 15 February 2019
  • Revised 20 June 2019

DOI:https://doi.org/10.1103/PhysRevA.100.012324

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhen-Tao Zhang1,*, Feng Mei2,3,†, Xiang-Guo Meng1, Bao-Long Liang1, and Zhen-Shan Yang1

  • 1School of Physics Science and Information Technology, Shandong Key Laboratory of Optical Communication Science and Technology, Liaocheng University, Liaocheng 252059, People's Republic of China
  • 2State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China
  • 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China

  • *zhzhentao@163.com
  • meifeng@sxu.edu.cn

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Vol. 100, Iss. 1 — July 2019

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