order to formalise the usage of the "dots" to denote any number of wires, such as used in the spider fusion rule, this software uses bang-box notation to implement rewrite rules where the spiders can have any number of inputs or outputs. A more recent project to handle ZX-diagrams is PyZX, which is primarily focused on circuit optimisation. A LaTeX package zx-calculus] can be used to typeset ZX-diagrams. Related graphical languages The ZX-calculus is only one of several graphical languages for describing linear maps between qubits. The ZW-calculus was developed alongside the ZX-calculus, and can naturally describe the W-state and Fermionic quantum computing. It was the first graphical language which had a complete rule-set for an approximately universal set of linear maps between qubits, and the early completeness results of the ZX-calculus use a reduction to the ZW-calculus. A more recent language is the ZH-calculus. This adds the H-box as a generator, that generalizes the Hadamard gate from the ZX-calculus. It can naturally describe quantum circuits involving Toffoli gates. Related algebraic concepts Phaseless spiders in the ZX calculus satisfy the axioms of a Hopf algebra with the trivial map as antipode. This can be checked by observing that it is isomorphic to the group algebra of . See also Categorical quantum mechanics Applied category theory String diagram References External links zxcalculus.com Quantomatic Quantum computing