Incorrect expectation values for the identity observable about prototype-zne HOT 2 CLOSED

• Update extrapolator(s) to handle zero variance smoothly, introducing support for the identity observable.

I would prioritize this step over the other two. The rest sounds good to me.

from prototype-zne.

Thanks for reporting this @mberna, read below for my initial assessment (c.c. @1ucian0).

Observations

1. Due to the observable being the trivial one (i.e. identity III...) the expectation value is always 1.0 with variance 0.0 regardless of the circuit, (level of) noise, or anything else. Because of such null variance, the scipy.curvefit extrapolation fails while trying to compute the induced error bar —a feature that came out in version 1.1.0.

2. Real world cases where the variance is zero are highly unlikely to occur —if they ever do— since they arise in scenarios where the computation is fully deterministic: a condition that is rarely met for expectation value calculations via sampling even in the absence of noise (i.e. only if the state is an eigenstate of the observable and measurement takes place in an eigenbasis).

3. In the following line you are requesting to amplify the noise only on two-qubit gates:

   zne_strategy = ZNEStrategy(noise_factors=[1, 3, 5], noise_amplifier=TwoQubitAmplifier())

   Since there are no such gates in your circuit (before decomposition), the noise amplification fails with a warning:

   UserWarning: Noise amplification is not performed since none of the gates are folded.

4. TwoQubitAmplifier is the default behavior if no explicit amplifier is passed since version 1.0.0rc0 —improving upon the previous default CxAmplifier which only addresses CNOT gates. This is especially intended for use with already transpiled circuits, where all gates are going to be either one or two-qubit gates. For this particular case, something like the vanilla LocalFoldingAmplifier or GlobalFoldingAmplifier would be more suited.

Next steps

• Update extrapolator(s) to handle zero variance smoothly, introducing support for the identity observable.
• Build a new MultiQubitAmplifier which will amplify noise in all gates with num_qubits > 1.
• Set such MultiQubitAmplifier as the new default in ZNEStrategy.

Please, let me know if you agree to this and I will proceed.

from prototype-zne.