  Parametrised quantum circuits contain phase gates whose phase is determined
by a classical algorithm prior to running the circuit on a quantum device. Such
circuits are used in variational algorithms like QAOA and VQE. In order for
these algorithms to be as efficient as possible it is important that we use the
fewest number of parameters. We show that, while the general problem of
minimising the number of parameters is NP-hard, when we restrict to circuits
that are Clifford apart from parametrised phase gates and where each parameter
is used just once, we can efficiently find the optimal parameter count. We show
that when parameter transformations are required to be sufficiently
well-behaved that the only rewrites that reduce parameters correspond to simple
'fusions'. Using this we find that a previous circuit optimisation strategy by
some of the authors [Kissinger, van de Wetering. PRA (2019)] finds the optimal
number of parameters. Our proof uses the ZX-calculus. We also prove that the
standard rewrite rules of the ZX-calculus suffice to prove any equality between
parametrised Clifford circuits.
