  Recent developments in classical simulation of quantum circuits make use of
clever decompositions of chunks of magic states into sums of efficiently
simulable stabiliser states. We show here how, by considering certain
non-stabiliser entangled states which have more favourable decompositions, we
can speed up these simulations. This is made possible by using the ZX-calculus,
which allows us to easily find instances of these entangled states in the
simplified diagram representing the quantum circuit to be simulated. We
additionally find a new technique of partial stabiliser decompositions that
allow us to trade magic states for stabiliser terms. With this technique we
require only $2^{\alpha t}$ stabiliser terms, where $\alpha\approx 0.396$, to
simulate a circuit with T-count $t$. This matches the $\alpha$ found by Qassim
et al., but whereas they only get this scaling in the asymptotic limit, ours
applies for a circuit of any size. Our method builds upon a recently proposed
scheme for simulation combining stabiliser decompositions and optimisation
strategies implemented in the software QuiZX. With our techniques we manage to
reliably simulate 50-qubit 1400 T-count hidden shift circuits in a couple of
minutes on a consumer laptop.
