# A Simplified Stabilizer ZX-calculus

2 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : The stabilizer ZX-calculus is a rigorous graphical language for reasoning about stabilizer quantum mechanics. This language has been proved to be complete in two steps: first in a setting where scalars (diagrams with no inputs or outputs) are ignored and then in a more general setting where a new symbol and three additional rules have been added to keep track of scalars. Here, we introduce a simplified version of the stabilizer ZX-calculus: we give a smaller set of axioms and prove that meta-rules like only the topology matters', colour symmetry' and `upside-down symmetry', which were considered as axioms in previous versions of the stabilizer ZX-calculus, can in fact be derived. In particular, we show that the additional symbol and one of the rules introduced for proving the completeness of the scalar stabilizer ZX-calculus are not necessary. We furthermore show that the remaining two rules dedicated to scalars cannot be derived from the other rules, i.e. they are necessary.
Document type :
Conference papers
Domain :

https://hal.inria.fr/hal-01404591
Contributor : Simon Perdrix Connect in order to contact the contributor
Submitted on : Tuesday, November 29, 2016 - 12:04:13 AM
Last modification on : Saturday, October 16, 2021 - 11:26:08 AM

### Identifiers

• HAL Id : hal-01404591, version 1
• ARXIV : 1602.04744

### Citation

Miriam Backens, Simon Perdrix, Quanlong Wang. A Simplified Stabilizer ZX-calculus. 13th International Conference on Quantum Physics and Logic , Jun 2016, Glasgow, United Kingdom. ⟨hal-01404591⟩

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