Gate-level intuition before frameworks
notesQuantum Circuit Designphysicscomputer science
Summary
Simulators hide the part worth learning. Drawing circuits by hand for a week made the entanglement bookkeeping obvious in a way the library never did.
Why by hand
A framework answers the question you typed. Working by hand exposes the questions you did not know to ask — mostly about which qubits actually need to talk to each other.
Where it breaks
Hand analysis stops scaling almost immediately. That limit is useful information: it marks the point where the tool is doing real work rather than hiding it.