qml.qinfo.transforms.purity

purity(tape, wires, **kwargs)

Compute the purity of a QuantumTape returning state().

\[\gamma = \text{Tr}(\rho^2)\]

where \(\rho\) is the density matrix. The purity of a normalized quantum state satisfies \(\frac{1}{d} \leq \gamma \leq 1\), where \(d\) is the dimension of the Hilbert space. A pure state has a purity of 1.

It is possible to compute the purity of a sub-system from a given state. To find the purity of the overall state, include all wires in the wires argument.

Parameters

• tape (QNode or QuantumTape or Callable) – A quantum circuit object returning a state().

• wires (Sequence(int)) – List of wires in the considered subsystem.

Returns

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

Return type

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

Example

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

@qml.qnode(dev)
def noisy_circuit(p):
    qml.Hadamard(wires=0)
    qml.CNOT(wires=[0, 1])
    qml.BitFlip(p, wires=0)
    qml.BitFlip(p, wires=1)
    return qml.state()

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

>>> purity(noisy_circuit, wires=[0, 1])(0.2)
0.5648000000000398
>>> purity(circuit, wires=[0])(np.pi / 2)
0.5
>>> purity(circuit, wires=[0, 1])(np.pi / 2)
1.0

See also

pennylane.math.purity()

code/api/pennylane.qinfo.transforms.purity

 

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