A Non-Anyonic Qudit
ZW-calculus

Natural Language Processing

ZW-calculus is a graphical language whose structure was motivated by multi-qubit entanglement classification and is also suitable for reasoning about photonic and fermionic quantum computing.

This work introduces a different version of the ZW-calculus for qudits which enables a translation to the recently introduced algebraic qudit ZX-calculus. These graphical calculi can express arbitrary linear maps acting on d-dimensional systems.

Finally, this translation leads to the qufinite ZW-calculus, which inherits from the qufinite ZX-calculus the ability to handle interacting systems of different dimensions. These results set the stage for a proof of completeness for these calculi, which will enable the structural study of complex classical and quantum many-body systems beyond what current qubit-specific methods can reach.