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Environment and classical channels in categorical quantum mechanics

Bob Coecke ; Simon Perdrix.

We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to define classical channels, quantum measurements and&nbsp;[&hellip;]

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Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus

Ali Assaf ; Alejandro Díaz-Caro ; Simon Perdrix ; Christine Tasson ; Benoî t Valiron.

We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic: each one is equipped with an additive and a&nbsp;[&hellip;]

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Completeness of the ZX-Calculus

Emmanuel Jeandel ; Simon Perdrix ; Renaud Vilmart.

The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics and quantum information theory. It comes equipped with an equational presentation. We focus here on a very important property of the language: completeness, which roughly ensures the equational theory captures&nbsp;[&hellip;]

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Towards a Minimal Stabilizer ZX-calculus

Miriam Backens ; Simon Perdrix ; Quanlong Wang.

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only if these two diagrams represent the same quantum evolution&nbsp;[&hellip;]

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Addition and Differentiation of ZX-diagrams

Emmanuel Jeandel ; Simon Perdrix ; Margarita Veshchezerova.

The ZX-calculus is a powerful framework for reasoning in quantum computing. It provides in particular a compact representation of matrices of interests. A peculiar property of the ZX-calculus is the absence of a formal sum allowing the linear combinations of arbitrary ZX-diagrams. The universality&nbsp;[&hellip;]

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