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A Simplified Stabilizer ZX-calculus

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.
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https://hal.inria.fr/hal-01404591
Contributor : Simon Perdrix <>
Submitted on : Tuesday, November 29, 2016 - 12:04:13 AM
Last modification on : Tuesday, December 18, 2018 - 4:48:02 PM

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

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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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