When I run this program on ibmqx2 (the backend matters) in IBM Q Experience, the results are interesting. Essentially, the program measures the error rate on $|q_0\rangle$ after fiddling with $|q_1\rangle$.

include "qelib1.inc";
gate nG0 ( param ) q  {
  h q;

qreg q[2];
creg c[1];

ry(pi) q[1];
measure q[0] -> c[0];

Unexpectedly, the value of $|q_0\rangle$ depends on the angle of rotation around y-axis for $|q_1\rangle$. Here are typical runs of 8 192 shots on ibmqx2.

Error rate of q[0] vs ry() rotation of q[1]

ry() q[1]   Error rate q[0]     Expected error rate q[0]
0            0.940%             ~1%
pi/4         9.351%             ~1%
pi/2        30.273%             ~1%     
3pi/4       52.209%             ~1%
pi          60.742%             ~1%     
5pi/4       51.941%             ~1%
3pi/2       30.518%             ~1%
7pi/4        9.509%             ~1%
2pi          0.684%             ~1%

A few notes:

  • For $0$ and $2\pi$ the $Ry$ operations are optimized away in the transpiled code.
  • Don't forget that we're operating on $|q_1\rangle$ and measuring $|q_0\rangle$. These qubits should be completely independent. Changes to $|q_1\rangle$ shouldn't impact $|q_0\rangle$.
  • The error rate is above 50% from $\frac{3}{4}\pi$ to $\frac{5}{4}\pi$. That suggests that application of $Ry$ on $|q_1\rangle$ does not just destabilize the system, it causes that $|q_0\rangle$ favors the $|1\rangle$ state.
  • Changing $Ry$ to $Rx$ also demonstrates the problem. Changing $Ry$ to $Rz$ makes the problem to go away.
  • $\begingroup$ You mentioned that backend matters. What are error rates on other backends? $\endgroup$ Dec 28 '19 at 10:37

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 :-).


This was a readout crosstalk error that has now been resolved.


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