Understanding realistic effects in braiding poor man's Majoranas in linear arrays of quantum dots

By coupling quantum dots through electron co-tunneling and crossed-Andreev reflection processes, one can create effective Kitaev chains with, so called, poor man's Majoranas at the edges.

Recently, experimental teams have been succesful in creating these Kitaev chains, showing conductance measurements indicative for the presence of poor man's Majoranas.

To however conclude whether the observed results are truly consistent with Majoranas, one needs to perform braiding experiments.

We analyse a minimal tuning protocol to braid poor man's Majoranas in linear arrays of quantum dots.

By coupling two poor man's Majorana chains through a normal quantum dot, we can perform braid operations by fine tuning chemical potentials and barrier voltages only.

We analyze the possible sources of errors in experimental settings, and propose methods to correct the errors to raitain a faithful braiding opertion.

We give ways to diagnose the necessary parameter changes by experimental means only, without requiring detail knowledge of the system parameters.

Finally, we give an expectation for the fidelity of the braid when the system is known up to a variance.