  We characterise a model of universal quantum computation where the register
(computational) qubits are controlled by ancillary qubits, using only a single
fixed interaction between register and ancillary qubits. No additional access
is required to the computational register and the dynamics of both the register
and ancilla are unitary. This scheme is inspired by the measurement-based
ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010],
but does not require measurements of the ancillas, and in this respect is
similar to the original gate based model of quantum computation. We consider
what possible forms this ancilla-register interaction can take, with a proof
that the interaction is necessarily locally equivalent to SWAP combined with an
entangling controlled gate. We further show which Hamiltonians can create such
interactions and discuss two examples; the two-qubit XY Hamiltonian and a
particular case of the XXZ Hamiltonian. We then give an example of a simple,
finite and fault tolerant gate set for universal quantum computation in this
model.
