I have created a simple circuit at IBM Quantum Composer.
Diagramm of the circuit:
Id C Id
H X H (barrier) X
quantum-computing.ibm.com/composer/files/new?initial=N4IgdghgtgpiBcIBCEBOqCWNUgDQgBMYBnAY0wAcAXDAezARDxAEcJipGB5ABQFEAcgEUAggGUAsgAIATADoADAG4AOmAxhSAGwCuRKStYwtGAEYBGORtKHVYNS1QwA5lJYBtGQF075F1NJ3ABYfNQALN3dzUM0AD0iFL1xI6LsIj1S1UzRMbBSY%2BIyfEABfIA
You see, I have inserted one barrier.
When you delete the barrier you can see a change at the phase disk of the second qubit. The phase is with barrier pi and without 0.
https://quantum-computing.ibm.com/composer/docs/iqx/visualizations#phase-disk
I think the phase of the second qubit without barrier is right.
I think its an error when the phase changes if the barrier is inserted.
Thank you Christian