Summary

Fixed some problems with QuantumCircuit.decompose when dealing with high-level objects (i.e. that can get synthesized by HighLevelSynthesis).

Blocks #13295 and #13301.

Details and comments

Previously, running decompose would first run HighLevelSynthesis (in case no specific gates to decompose are set) and the Decompose. This would end up decomposing high-level objects twice instead of once. In addition, specifying high-level objects by name, could end up not decomposing them at all.

For example

Circuit at hand:
   ┌──────────┐
q: ┤ Clifford ├
   └──────────┘
Expected result when decomposing:
   ┌───┐
q: ┤ H ├
   └───┘
.decompose(['clifford']) gives:
   ┌──────────┐
q: ┤ Clifford ├
   └──────────┘
.decompose() gives:
   ┌─────────┐
q: ┤ U2(0,π) ├
   └─────────┘
where's my H gate? :(

This is now fixed by pulling HLS into Decompose, which iterates over each node and only applies HLS if an operation does not have a definition.