  We present an abstract model of quantum computation, the "Pauli Fusion"
model, whose primitive operations correspond closely to generators of the ZX
calculus (a formal graphical language for quantum computing). The fundamental
operations of Pauli Fusion are also straightforward abstractions of basic
processes in some leading proposed quantum technologies. These operations have
non-deterministic heralded effects, similarly to measurement-based quantum
computation. We describe sufficient conditions for Pauli Fusion procedures to
be deterministically realisable, so that it performs a given transformation
independently of its non-deterministic outcomes. This provides an operational
model to realise ZX terms beyond the circuit model.
