I'm playing around with the IBM Q to demonstrate the qunatum Zeno effect.
If we prepare a qubit in the $|0\rangle$ state and apply 5 consecutive $R_y(\pi/5)$ gates, we should end up in state $|1\rangle $ with 100% probability since $R_y(\pi/5)^5=R_y(\pi)$.
This gives output 00100, as expected.
If we now add couplings between each of these gates and measure them (using deferred measurement), then after the first $\pi/4$ rotation we collapse the q qubit into either $|0\rangle $ with probability $\cos^2(\pi/8)=0.905$ or into $|1\rangle $ with probability $\sin^2(\pi/8)=0.095$.
What happens after all 5 have been applied, with measurements after each rotation?
My intuition tels me to create a probability tree such as
which gives us a total probability of 67.4% chance of ending up with a |0> state.
The IBM Q simulator gives a 66.3% chance of measuring $|0\rangle $. Is this just statistical error or is there something wrong with my circuit?
My circuit is available at https://quantumexperience.ng.bluemix.net/share/code/5c3890a72f408b005a0d9f06