How to Calculate Fidelity in PennyLane with Finite Shots?

PennyLane Help
1

Hi everyone,

I would like to ask for help with calculating fidelity in PennyLane when using a device with finite shots, for example:

dev = qml.device("lightning.qubit", wires=n_qubits, shots=10000)

My goal is to prepare the ground state of the Ising model using Quantum Natural Gradient. How can fidelity be calculated effectively in this scenario?

I am very grateful for your help and insights!

2

Hi @QuantumH , welcome to the Forum!

You could try getting the expectation value of a Hermitian operator rho to obtain the fidelity between rho and the state of your circuit.
Here’s a code example.

import numpy as np
import pennylane as qml

dev = qml.device("lightning.qubit", wires=2, shots=10)

y=np.array([[1,0],[0,-1]])

@qml.qnode(dev)
def circuit(param):
    qml.RX(param, wires=0)
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.Hermitian(y, wires=[1]))

print("Result: ", circuit(0.123))

You can see another example that does the same in our data-reuploading classifier demo.

If you just want to compute the fidelity for two states you can use qml.math.fidelity without needing to create a circuit.

Let me know if this is what you were looking for!

3

Thank you @CatalinaAlbornoz for your help! This is very useful.

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