Thanks for pointing this out! It turns out that this device was mis-calibrated in a way that was leading to that behavior. We just fixed the calibrations, so the problem should be gone now. I apologize for the trouble, and we will try to update our routine calibrations to detect and prevent this problem from coming up in the future :-).
It seems like the skew is indeed high on qubit 0. I ran a single Hadamard followed by measure on this qubit, and see about 13% skew. The other qubits on this device seem fine (less than 2% skew).
This is probably an error on the backend's discriminator (i.e. manifesting as high readout error). To see this, you can try applying readout error mitigation (code ...
Your expectation here is correct. c should be 0 (well, modulo some small readout errors). The difference between backends is just due to a software bug on some of them. This will get fixed, thanks for reporting.
As an aside, it is important to note that on current IBM devices, there is a constraint that all measurements are done simultaneously. So both ...
Of course if we have unitary evolution
$$|\psi_1\rangle = U|\psi_0\rangle$$
$$|\psi_0\rangle = U^\dagger|\psi_1\rangle$$
I did not read the paper, but evidently the authors do something different, based on the following: the Schrödinger equation
changes its form if we substitute $t\rightarrow -t$ to ...
Each quantum processor has specific so-called error rate and a little bit different type of noise caused by specific conditions the processor runs in. Therefore, results produced by same circuits can be different on different quantum processors.
In your case, there is apparently a bias caused by some external factors specific for ibmqx2. You can try to run ...