  The ZX-calculus is a universal graphical language for qubit quantum
computation, meaning that every linear map between qubits can be expressed in
the ZX-calculus. Furthermore, it is a complete graphical rewrite system: any
equation involving linear maps that is derivable in the Hilbert space formalism
for quantum theory can also be derived in the calculus by rewriting. It has
widespread usage within quantum industry and academia for a variety of tasks
such as quantum circuit optimisation, error-correction, and education.
  The ZW-calculus is an alternative universal graphical language that is also
complete for qubit quantum computing. In fact, its completeness was used to
prove that the ZX-calculus is universally complete. This calculus has advanced
how quantum circuits are compiled into photonic hardware architectures in the
industry.
  Recently, by combining these two calculi, a new calculus has emerged for
qubit quantum computation, the ZXW-calculus. Using this calculus,
graphical-differentiation, -integration, and -exponentiation were made
possible, thus enabling the development of novel techniques in the domains of
quantum machine learning and quantum chemistry.
  Here, we generalise the ZXW-calculus to arbitrary finite dimensions, that is,
to qudits. Moreover, we prove that this graphical rewrite system is complete
for any finite dimension. This is the first completeness result for any
universal graphical language beyond qubits.
