qml.vn_entropy

vn_entropy(wires, log_base=None)

Von Neumann entropy of the system prior to measurement.

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

Parameters

• wires (Sequence[int] or int) – The wires of the subsystem

• log_base (float) – Base for the logarithm.

Returns

Measurement process instance

Return type

VnEntropyMP

Example:

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

@qml.qnode(dev)
def circuit_entropy(x):
    qml.IsingXX(x, wires=[0, 1])
    return qml.vn_entropy(wires=[0])

Executing this QNode:

>>> circuit_entropy(np.pi/2)
0.6931472

It is also possible to get the gradient of the previous QNode:

>>> param = np.array(np.pi/4, requires_grad=True)
>>> qml.grad(circuit_entropy)(param)
tensor(0.62322524, requires_grad=True)

Note

Calculating the derivative of vn_entropy() is currently supported when using the classical backpropagation differentiation method (diff_method="backprop") with a compatible device and finite differences (diff_method="finite-diff").

Note

qml.vn_entropy can also be used to compute the entropy of entanglement between two subsystems by computing the Von Neumann entropy of either of the subsystems.

See also

pennylane.math.vn_entropy(), pennylane.math.vn_entanglement_entropy()

code/api/pennylane.vn_entropy

 

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