Implementing Noise in Pennylane (using qiskit.aer)

Question

I want to implement noise in Pennylane using qiskit as a plug-in. I found this tutorial from Pennylane. But, when testing it the bit-flip error seems to have no effect at all.

Here, I made some slight modifications: I take the expectation value of PauliX and can choose 0 or 1 is an initial state.

import qiskit.providers.aer.noise as noise

# create a bit flip error with probability p 
p = 0.9
my_bitflip = noise.pauli_error([('X', p), ('I', 1 - p)])

# create an empty noise model
my_noise_model = noise.NoiseModel()
# attach the error to the hadamard gate 'h'
my_noise_model.add_quantum_error(my_bitflip, ['h'], [0])

dev4 = qml.device('qiskit.aer', wires=1, noise_model = my_noise_model)

@qml.qnode(dev4)
def bitflip_circuit_aer():
    qml.BasisState(np.array([1]),wires=[0])
    qml.Hadamard(0)
    return qml.expval(qml.PauliX(0))

print(bitflip_circuit_aer()) 

It does not make any difference whether I choose p=0.0 or p=0.9. I always get +1 for initial state 0 and -1 for initial state 1, as if there was no noise at all.

The tutorial is from May 2021. Did something decisive change since then?

Answer 1

If you are starting with $|0\rangle$ state.

Than after $H$ you are in $|+\rangle=|0\rangle+|1\rangle$ state, which is eigenstate of $X$, with eigenvalue $+1$.

If $X$ will happen (in case of an error in probability $p$), the state will not change at all, and no error will happen:

$$X|+\rangle=X|0\rangle+X|1\rangle=|+\rangle$$

So the error of $X$ and no error is the same thing, and measuring in $X$ base, will always give you the same measurement value since $|+\rangle$ is eigenstate of $X$.

The same thing is happening with $|1\rangle$ initial state. Try the math, I can write it too if you like. The only different thing will be a global phase of minus in case of $X$ error, which is not affecting the measurement result.