Pauli Fusion: a Computational Model to Realise Quantum Transformations from ZX Terms

TL;DR

The paper introduces Pauli Fusion, an abstract quantum computation model based on ZX calculus generators, enabling deterministic realization of quantum transformations beyond traditional circuit models.

Contribution

It proposes a new computational framework that aligns with quantum technologies and provides conditions for deterministic implementation of ZX-based transformations.

Findings

Pauli Fusion operations correspond to ZX calculus generators.

Conditions for deterministic realization of quantum transformations are established.

The model extends quantum computation beyond standard circuit approaches.

Abstract

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.