ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity

  title={ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity},
  author={Miriam Backens and Aleks Kissinger},
  journal={Electronic Proceedings in Theoretical Computer Science},
We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ circuits. The diagrammatic language is generated by two kinds of nodes: the so-called `spider' associated with the computational basis, as well as a new arity-$N$ generalisation of the Hadamard gate, which satisfies a variation of the spider fusion law. Unlike… 

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