Entanglement entropy

PennyLane Help
1

I want to calculate entanglement entropy of a quantum circuit (6 qubits) , please help with the code

@CatalinaAlbornoz

2

Hi @VQX,

You can use qml.math.vn_entropy to compute the Von Neumann entropy from a state vector or density matrix on a given subsystem.

You can also use qml.qinfo.transforms.vn_entropy to compute the Von Neumann entropy from a QNode returning a state().

I’m not sure whether or not this calculates what you need so please make sure to check the documentation for each function in detail to make sure.

1 Like
3

Hello,
Make follow from here: How make compute Fidelity, Entangling power and Expresibility? · Issue #4182 · PennyLaneAI/pennylane · GitHub
How can make entropy value when returning expectation values?
Thanks you!

4

Hey @wing_chen! Welcome to the forum :muscle:

How can make entropy value when returning expectation values?

You can calculate the entropy of a subsystem from transforming a QNode returning a state:

import pennylane as qml

dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit(x):
    qml.IsingXX(x, wires=[0, 1])
    return qml.state()

print(qml.qinfo.vn_entropy(circuit, wires=[0])(np.pi/2))
# 0.6931472
5

But I return expectation value during training, want to save entropy value with the PQC parameters when training terminates.

6

In that case, you can create separate QNodes that evaluate both like this:

import pennylane as qml

def circuit(x):
    qml.IsingXX(x, wires=[0, 1])

dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit_state(x):
    circuit(x)
    return qml.state()

@qml.qnode(dev)
def circuit_expval(x):
    circuit(x)
    return qml.expval(qml.PauliZ(0))

vn = lambda x, wires : qml.qinfo.vn_entropy(circuit_state, wires=wires)(x)

print(circuit_state(0.1))
print(circuit_expval(0.1))
print(vn(0.1, [0]))

'''
[0.99875026+0.j         0.        +0.j         0.        +0.j
 0.        -0.04997917j]
0.9950041652780258
0.017463060045757477
'''
7

So I need to run two circuit during QNN training? I really do not understand.

8

HI @wing_chen! Yes as Isaac pointed out above, you’ll need two versions of the same circuit if you also want the expectation values. The reason is that qml.qinfo.vn_entropy can only act on circuits that return qml.state, but you can’t return the state and the expectation value at the same time in a single circuit. Feel free to give us more details on what you’re trying to do so we can help you further!

9

I want make record of entropy during training of circle in the transfer learning model for differenr ciruits.

10

Hi @wing_chen,

I’m not sure whether this will work or not but maybe you can try taking a snapshot right before the measurement. This way you will have the state and you can use qml.math.vn_entropy().

I recommend that you try this for a tiny example first. Let me know if it works!