  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.

Mesoscale and Nanoscale Physics