✨ Scalable Clifford (sub-)circuit optimizer

[jannikpflieger]

What's the problem this feature will solve?

Currently, a depth-optimal Clifford synthesis is implemented. Usually, depth-optimal approaches scale poorly and are thus limited by the number of qubits.

A first heuristic is already implemented. However this implementation is not suited to optimize Clifford sub-circuits in a non-Clifford circuit (Issue: #365).

Describe the solution you'd like

To tackle the scaling problem, we can make use of scalable heuristics, such as peephole optimization.

We can do this by identifying blocks of Clifford gates and optimizing each block within a non-Clifford Circuit.
While doing this, we can implement different strategies for performing the (peephole) optimization. Such as horizontal circuit splitting (Issue: #305).