  Reading out Majorana bound states (MBSs) is essential both to verify their
non-Abelian property and to realize topological quantum computation. Here, we
construct a protocol to measure the parity of two MBSs in a Majorana island
coupled to double quantum dot (DQD). The parity information is mapped to the
charge state of the DQD through Landau-Zener transition. The operation needed
is sweeping the bias of the DQD, which is followed by charge sensing. In the
case without fine-tuning, a single run of sweep-and-detection implement a weak
measurement of the parity. We find that in general a sequence of about ten runs
would completely project a superposition state to either parity, and the charge
detection in each run records how the state of MBSs collapses step by step.
Remarkably, this readout protocol is of non-demolition and robust to low
frequency charge fluctuation.
