qml.qinfo.transforms.vn_entropy¶

vn_entropy(tape, wires, base=None, **kwargs)[source]¶

Compute the Von Neumann entropy from a QuantumTape returning a state().

\[S( \rho ) = -\text{Tr}( \rho \log ( \rho ))\]

Parameters

tape (QNode or QuantumTape or Callable) – A quantum circuit returning a state().
wires (Sequence(int)) – List of wires in the considered subsystem.
base (float) – Base for the logarithm, default is None the natural logarithm is used in this case.

Returns

The transformed circuit as described in qml.transform. Executing this circuit will provide the Von Neumann entropy in the form of a tensor.

Return type

qnode (QNode) or quantum function (Callable) or tuple[List[QuantumTape], function]

Example

It is possible to obtain the entropy of a subsystem from a QNode returning a state().

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

>>> vn_entropy(circuit, wires=[0])(np.pi/2)
0.6931471805599453

The function is differentiable with backpropagation for all interfaces, e.g.:

>>> param = np.array(np.pi/4, requires_grad=True)
>>> qml.grad(vn_entropy(circuit, wires=[0]))(param)
tensor(0.62322524, requires_grad=True)