  An incomplete quantum measurement can induce non-trivial dynamics between
degenerate subspaces, a closed sequence of such projections produces a
non-abelian holonomy. We show how to induce unitary evolution on an initial
subspace from such finite discrete sequences and also construct a near
deterministic repeat-until-success protocol. We also prove necessary and
sufficient criteria on the auxiliary Hilbert space dimension required for
inducing isometries between between subspaces.
