Switch to stabilizer simulator for Clifford-only circuits

[jon-wurtz]

There is a large time overhead for compilation that is independent of the fact that the circuit is Clifford or not. However, for Clifford-only, we could switch to a stabilizer simulator (such as stim) that runs much faster. Would it be possible to test if the circuit is Clifford, and if so, switch to a fast stabilizer simulator to speed up simulations?

p.s. I have stated this is a bit of an XY problem, I'm sorry:

• X: "I want my simulations and samplers (time-to-bitstring) to be as fast as possible."
• Y: "Check if the circuit is Clifford and choose the backend appropriately."