
The Vectorial Lambda Calculus Revisited
We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vec...
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PBScalculus: A Graphical Language for QuantumControlled Computations
We introduce the PBScalculus to represent and reason on quantum computa...
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On a recipe for quantum graphical languages
Different graphical calculi have been proposed to represent quantum comp...
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A HoTT Quantum Equational Theory (Extended Version)
This paper presents an equational theory for the QRAM model of quantum c...
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Towards a Minimal Stabilizer ZXcalculus
The stabilizer ZXcalculus is a rigorous graphical language for reasonin...
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Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZXcalculus)
This paper is a `spiritual child' of the 2005 lecture notes Kindergarten...
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The ZX calculus: A complete graphical calculus for classical circuits using spiders
We give a complete presentation for the fragment, ZX , of the ZXcalcu...
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Completeness of the ZXCalculus
The ZXCalculus 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 all of quantum mechanics. We first improve on the knowntobecomplete presentation or the socalled Clifford fragment of the language  a restriction that is not universal  by adding some axioms. Thanks to a system of backandforth translation between the ZXCalculus and a thirdparty complete graphical language, we prove that the provided axiomatisation is complete for the first approximately universal fragment of the language, namely Clifford+T. We then prove that the expressive power of this presentation, though aimed at achieving completeness for the aforementioned restriction, extends beyond Clifford+T, to a class of diagrams that we call linear with Clifford+T constants. We use another version of the thirdparty language  and an adapted system of backandforth translation  to complete the language for the ZXCalculus as a whole, that is, with no restriction. We briefly discuss the added axioms, and finally, we provide a complete axiomatisation for an altered version of the language which involves an additional generator, making the presentation simpler.
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