Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
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DOI：
10.1103/physrevb.102.205101
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发表时间：
2020-04
影响因子：
3.7
通讯作者：
Chuanchang Zeng;G. Sharma;T. Stanescu;S. Tewari
中科院分区：
文献类型：
--
作者：
Chuanchang Zeng;G. Sharma;T. Stanescu;S. Tewari
我们讨论了半导体-超导体(SM-SC)异质结在所谓的准Majorana区基于测量编织的可行性，这是由部分分离的Andreev束束态(PS-ABS)引起的拓扑平凡区。与由导线长度分隔的Majorana零模(MZM)相比，这些低能ABS由空间上以小于系统长度的长度尺度隔开的分量Majorana束缚态(准Majorana模)组成。在准Majorana区，只要PS-ABS的能量分裂小于低能电导峰的典型宽度$ew，ZBCP对各种扰动表现出较强的抗扰性。然而，基于测量的编织的可行性取决于不同的能量尺度$em$。在这篇文章中，我们证明了在准Majorana区中制备能量分裂低于e_m$阈值的SM-SC系统是可能的，因此基于测量的编织在原则上是可能的。从能量低于$em$的PS-ABS开始，我们确定了不同类型微扰的最大振幅，它们与不超过$em$极限的微扰引起的能量分裂是一致的。我们认为，在准Majorana区的SM-SC异质结中，测量产生的微扰大于阈值幅度，不能实现基于测量的编织。我们发现，如果可能的话，在准Majorana体系中使用基于测量的编织的量子计算将受到测量过程本身引入的误差的困扰，而在涉及拓扑MZM的方案中，这种误差的可能性要小得多。
We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime $-$ the topologically-trivial regime due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs), which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width $\e_w$ of the low-energy conductance peaks $\e_w$. However, the feasibility of measurement-based braiding depends on a different energy scale $\e_m$. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the $\e_m$ threshold, so that measurement-based braiding is possible in principle. Starting with ps-ABSs with energy below $\e_m$, we identify the maximum amplitudes of different types of perturbations that are consistent with perturbation-induced energy splittings not exceeding the $\e_m$ limit. We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for $\e_m$ cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs.