Pauli Fusion: a computational model to realise quantum transformations from ZX terms - Niel de Beaudrap

The ZX calculus is an abstract mathematical tool to represent — and importantly to calculate with — tensors of a sort that are common in quantum computational theory. We present an abstract model of quantum computation, the Pauli Fusion model, whose primitive operations correspond closely to generators of the ZX calculus (and are also straightforward abstractions of basic operations in some leading proposed quantum technologies). These operations have non-deterministic heralded effects, similarly to measurement-based quantum com- putation. 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.