  Non-Abelian quasiparticles have been predicted to exist in a variety of
condensed matter systems. Their defining property is that an adiabatic braid
between two of them results in a nontrivial change of the quantum state of the
system. To date, no experimental platform has reached the desired control over
non-Abelian quasiparticles to demonstrate this remarkable property. The
simplest non-Abelian quasiparticles -- the Majorana bound states (MBS) -- can
occur in one-dimensional (1D) electronic nano-structures proximity-coupled to a
bulk superconductor -- a platform that is being currently explored in great
depth both theoretically and experimentally. When tuned appropriately, such
nano-wires can localize MBS at their ends, a pair of which forms a two-level
system that is robust to local perturbations. This constitutes a topologically
protected qubit that can serve as the building block for a topological quantum
computer. To implement braiding operations among the MBS, schemes that allow to
move MBS across wire networks have been explored theoretically. Here, we
propose a simpler alternative setup, based on chains of magnetic adatoms on the
surface of a thin-film superconductor, in which the control over an externally
applied magnetic field suffices to create and manipulate MBS. We consider
specific 1D patterns of adatoms, which can be engineered with
scanning-tunneling-microscope based lateral atomic manipulation techniques, and
show that they allow for the creation, annihilation, adiabatic motion, and
braiding of pairs of MBS by varying the magnitude and orientation of the
external magnetic field.
