  One-dimensional topological superconductors treated at the mean-field level
host zero-energy edge Majorana modes, which encode topological degeneracy of
their ground states. Geometric manipulations (braiding) of multiple wires can
be used to induce topologically robust transformations within the ground state
subspace. The mean-field ground states do not have a definite number of
particles and thus cannot describe an isolated system. Projecting such states
onto fixed particle number gives a very good approximation to the true ground
state of an isolated superconductor. In previous work, we showed that so
projecting the prototypical Kitaev wave function of a single wire retains key
features of the mean-field description, such as the zero-energy single-particle
spectral peaks near the wire edges. Here we consider the case of multiple wires
with conserved total charge. Again, using the projected Kitaev wave functions
as the template, we identify the many-body counterparts of the mean-field
topologically degenerate ground states. We then demonstrate how the quantum
gates equivalent to braiding of Majorana zero modes can be implemented, albeit
with reduced protection from noise and disorder.
