  Although qubits are the leading candidate for the basic elements in a quantum
computer, there are also a range of reasons to consider using higher
dimensional qudits or quantum continuous variables (QCVs). In this paper we use
a general `quantum variable' formalism to propose a method of quantum
computation in which ancillas are used to mediate gates on a well-isolated
`quantum memory' register and which may be applied to the setting of qubits,
qudits (for $d>2$) or QCVs. More specifically, we present a model in which
universal quantum computation may be implemented on a register using only:
repeated applications of a single fixed two-body ancilla-register interaction
gate, ancillas prepared in a single state, and local measurements of these
ancillas. In order to maintain determinism in the computation, adaptive
measurements via a classical-feedforward of measurement outcomes are used, with
the method similar to that in measurement-based quantum computation (MBQC). We
show that our model has the same hybrid quantum-classical processing advantages
as MBQC, including the power to implement any Clifford circuit in essentially
one layer of quantum computation. In some physical settings, high-quality
measurements of the ancillas may be highly challenging or not possible, and
hence we also present a globally unitary model which replaces the need for
measurements of the ancillas with the requirement for ancillas to be prepared
in states from a fixed orthonormal basis. Finally, we discuss settings in which
these models may be of practical interest.
