✨ Improved circuit decomposition for heuristic Clifford synthesis

[pehamTom]

What's the problem this feature will solve?

The current implementation only allows for vertical splitting of circuits. Other decomposition schemes (like horizontal decompositions) have to be done manually before calling the solver several times. It would be an interesting direction to look at improved decomposition schemes.

Describe the solution you'd like

One way to provide maximal flexibility is to be able to specify a maximal depth and a maximal number of qubits that limit the kind of decompositions that are possible. Since parallelism of decomposed circuit is traded off with depth, an even more advanced way would be to figure the "optimal" parameters out without user input. Something like an analysis of the connectivity of the unoptimized input circuit could provide key insights.