Ancilla-driven quantum computation for qudits and continuous variables

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.