  The ZX-calculus is a graphical language for suitably represented tensor
networks, called ZX-diagrams. Calculations are performed by transforming
ZX-diagrams with rewrite rules. The ZX-calculus has found applications in
reasoning about quantum circuits, condensed matter systems, quantum algorithms,
quantum error correcting codes, and counting problems. A key notion is the
stabiliser fragment of the ZX-calculus, a subfamily of ZX-diagrams for which
rewriting can be done efficiently in terms of derived simplifying rewrites.
Recently, higher dimensional qudits - in particular, qutrits - have gained
prominence within quantum computing research. The main contribution of this
work is the derivation of efficient rewrite strategies for the stabiliser
fragment of the qutrit ZX-calculus. Notably, this constitutes a first
non-trivial step towards the simplification of qutrit quantum circuits. We then
give further unexpected areas in which these rewrite strategies provide
complexity-theoretic insight; namely, we reinterpret known results about
evaluating the Jones polynomial, an important link invariant in knot theory,
and counting graph colourings.
