  Recently, cat states have been used to heuristically improve the runtime of a
classical simulator of quantum circuits based on the diagrammatic ZX-calculus.
Here we investigate the use of cat-state injection within the quantum circuit
model. We explore a family of cat states, $\left| \mathrm{cat}_m^* \right>$,
and describe circuit gadgets using them to concurrently inject
non-stabilizerness (also known as magic) and entanglement into any quantum
circuit. We provide numerical evidence that cat-state injection does not lead
to speed-up in classical simulation. On the other hand, we show that our
gadgets can be used to widen the scope of compelling applications of cat
states. Specifically, we show how to leverage them to achieve savings in the
number of injected qubits, and also to induce scrambling dynamics in otherwise
non-entangling Clifford circuits in a controlled manner.
