Work

A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness

Year: 2019

Type: conference-paper

Abstract: Recent completeness results on the ZX-calculus used a third-party language, namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly non-constructive. We address this issue in the following. To do so, we first describe a generic normal form for ZX-diagrams in any fragment that contains Clifford+T quantum mechanics. We give sufficient conditions for an axiomatisation to be complete, and an algorithm to reach the normal form. Finally, we apply these results to the Clifford+T fragment and the general ZX-calculus - for which we already know the completeness-, but also for any fragment of rational angles: we show that the axiomatisation for Clifford+T is also complete for any fragment of dyadic angles, and that a simple new rule (called cancellation) is necessary and sufficient otherwise.

Source: ACM/IEEE Symposium on Logic in Computer Science (LICS)

DOI: 10.1109/lics.2019.8785754

Authors: Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Software-based quantum program and resource optimisation, Validation of near-future quantum technologies