  Transfer of data in linear quantum registers can be significantly simplified
with pre-engineered but not dynamically controlled inter-qubit couplings. We
show how to implement a mirror inversion of the state of the register in each
excitation subspace with respect to the centre of the register. Our
construction is especially appealing as it requires no dynamical control over
individual inter-qubit interactions. If, however, individual control of the
interactions is available then the mirror inversion operation can be performed
on any substring of qubits in the register. In this case a sequence of mirror
inversions can generate any permutation of a quantum state of the involved
qubits.
