ZX Calculus – how Dirac notation was converted into a 2-D tool to unlock quantum computing

This paper is a ‘spiritual child’ of the 2005 lecture notes Kindergarten Quantum Mechanics, which showed how a simple, pictorial extension of Dirac notation allowed several quantum features to be easily expressed and derived, using language even a kindergartner can understand. Central to that approach was the use of pictures and pictorial transformation rules to understand and derive features of quantum theory and computation. However, this approach left many wondering ‘where’s the beef?’ In other words, was this new approach capable of producing new results, or was it simply an aesthetically pleasing way to restate stuff we already know?

Bob Coecke, Dominic Horsman, Aleks Kissinger, Quanlong Wang

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