Complete ZX-calculi for the stabiliser fragment in odd prime dimensions - Archive ouverte HAL Access content directly
Conference Papers Year : 2022

Complete ZX-calculi for the stabiliser fragment in odd prime dimensions

Abstract

We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which were lost in previous proposals for higher-dimensional systems. We then prove that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations. Adding a discard construction, we obtain a calculus complete for mixed state stabiliser quantum mechanics in odd prime dimensions, and this furthermore gives a complete axiomatisation for the related diagrammatic language for affine co-isotropic relations.

Dates and versions

hal-03655398 , version 1 (29-04-2022)

Identifiers

Cite

Robert Booth, Titouan Carette. Complete ZX-calculi for the stabiliser fragment in odd prime dimensions. 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Aug 2022, Vienna, Austria. pp.24:1--24:15, ⟨10.4230/LIPIcs.MFCS.2022.24⟩. ⟨hal-03655398⟩
42 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More