# Why and how is quantum noise predictable?

I have been learning about quantum error correction using the zero-noise extrapolation method from this paper and have been pleased with the results. This method takes advantage of the fact that the quantum gate noise is predictable as seen, for example, in the plot below. Here, I have taken a simple 2-qubit circuit given by qc.x(0), qc.h(0), qc.cx(0,1), qc.x(0) and added noise to it in the form of pairs of CNOT gates (a noisey identity matrix). I am plotting the $$|01\rangle$$ solution for this circuit as a function of the number of CNOT pairs that I used. This is done using the qiskit noise model with the IBMQ-montreal gate error rates. Note that the real solution is 0.5.

Clearly, the noise follows a very predictable relationship which to me is unexpected. Instead, what I expected was the noise to be scattered evenly across the real solution (0.5) with the amount of scatter being proportional to the number of gates, as shown in the made up plot below.

My question is, why does the noise follow the predictable curve instead of a random scattering about the real solution? And a follow up question, for an arbitrary circuit, how can I predict what the curve will look like?

Update: I ran my noisy circuits on the real IBMQ-athens machine to see if it is anywhere close to the simulated results. The plot is below is meant to be the same as the first plot (except the maximum depth is a less because I could not exceed 900).

Clearly the noise is no where near as organized as in the simulated version. What I don't know is if that was a failure on my part to simulate the noise correctly, or if it is a problem of the qiskit noise simulator itself.

• Is the first plot coming from actual hardware or is it from using a noise model? Nov 7 '20 at 23:47
• The first plot is from the qiskit noise model where I used the function NoiseModel.from_backend. Nov 8 '20 at 0:33
• I think that although the noise model does try to mimic the behavior of the hardware, it is still kinda fixed... what I mean by that is that on real hardware, the noise fluctuates from run to run somewhat. The gate fidelity changes from run to run rather than stay fixed like it would have with the noise model. Nov 8 '20 at 0:37
• Follow up question, why is the noise model so different compared with the noise from a real QC (plot 1 with my plot 3 respectively). Nov 9 '20 at 18:05
• The noise on the hardware fluctuates randomly within certain range from run to run. The noise model is only meant to represent the hardware noise model in a simple sense. Now, what you can do is to do more shots... This will smoothen out the curve you have more. IBM has max number of shots of 8192 set on their device to make sure people don't take up all the time, but you can submit many jobs and average out the results. Nov 9 '20 at 19:22