  We analyse the control of Majorana zero-energy states by mapping the
fermionic system onto a chain of Ising spins. Although the topological
protection is lost for the Ising system, the mapping provides additional
insight into the nature of the quantum states. By controlling the local
magnetic field, one can separate the Ising chain into ferromagnetic and
paramagnetic phases, corresponding to topological and non-topological sections
of the fermionic system. In this paper we propose (topologically non-protected)
protocols performing the braiding operation, and in fact also more general
rotations. We first consider a T-junction geometry, but we also propose a
protocol for a purely one-dimensional system. Both setups rely on an extra
spin-1/2 coupler. By including the extra spin in the T-junction geometry, we
overcome limitations due to the 1D character of the Jordan-Wigner
transformation. In the 1D geometry the coupler, which controls one of the Ising
links, should be manipulated once the ferromagnetic (topological) section of
the chain is moved far away. We also propose experimental implementations of
our scheme. One is based on a chain of flux qubits which allows for all needed
control fields. We also describe how to translate our scheme for the 1D setup
to a chain of superconducting wires hosting each a pair of Majorana edge
states.
