Why are these circuits not equivalent?

[Geremia]

For these two circuits:

1. qr: randomly-generated Clifford circuit:
   
2. qr_shuffled: previous circuit with gate-order shuffled:
   

Why does

qcec.verify(qr,qr_shuffled)

return <EquivalenceCheckingManager.Results: not_equivalent>?

I thought gate order didn't matter in quantum circuits, as unitary operations are involved here, no?

[burgholzer]

Well, because they are not equivalent.
The order of gates very much matters in quantum circuits, why wouldn't it?
I suggest you take a look into one of the references linked in the readme to read up on how the functionality of a quantum circuit is designed.

[Geremia]

Gate order does matter.
What you seem to want to be testing is whether quantum circuits are reversible.

For example, for this circuit:

Simulating this circuit with its reversed circuit appended:

produces a result of 100% in the $|0001\rangle$ state, proving it's reversible.