[rfc] larger scale compilation, optimization and (resource) analysis

[alexandrupaler]

The complete compilation of quantum algorithms will generate circuits with billions/millions of gates and the current software tools do not scale to these requirements. The bloqs of Qualtran are mitigating this scalability issue up to some abstraction level. However, when it comes to the complete compilation and analysis of complete bloqs (or subcircuits), or to the full QIR/Qasm compilation, then there might exist scalability issues.

We are developing a tool that can easily handle extremely large circuits, and would like to interface it to Qualtran. This issue is to initiate the discussion about:

• would a tool that can handle extremely large circuits be useful to Qualtran?
• when it comes to circuit analysis, which non-obvious cost metrics would be of interest? (e.g. average number of CNOT gates between pairs of T gates)
• should Qualtran interface with such a tool through Cirq? (we already have such an interface that can handle gates of at most three qubits)