qml.qinfo.transforms.mutual_info¶
-
mutual_info(tape, wires0, wires1, base=None, **kwargs)[source]¶ Compute the mutual information from a
QuantumTapereturning astate():\[I(A, B) = S(\rho^A) + S(\rho^B) - S(\rho^{AB})\]where \(S\) is the von Neumann entropy.
The mutual information is a measure of correlation between two subsystems. More specifically, it quantifies the amount of information obtained about one system by measuring the other system.
- Parameters
qnode (QNode or QuantumTape or Callable) – A quantum circuit returning a
state().wires0 (Sequence(int)) – List of wires in the first subsystem.
wires1 (Sequence(int)) – List of wires in the second subsystem.
base (float) – Base for the logarithm. If None, the natural logarithm is used.
- Returns
The transformed circuit as described in
qml.transform. Executing this circuit will provide the mutual information 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 mutual information of two subsystems from a
QNodereturning astate().dev = qml.device("default.qubit", wires=2) @qml.qnode(dev) def circuit(x): qml.IsingXX(x, wires=[0, 1]) return qml.state()
>>> mutual_info_circuit = qinfo.mutual_info(circuit, wires0=[0], wires1=[1]) >>> mutual_info_circuit(np.pi/2) 1.3862943611198906 >>> x = np.array(0.4, requires_grad=True) >>> mutual_info_circuit(x) 0.3325090393262875 >>> qml.grad(mutual_info_circuit)(np.array(0.4, requires_grad=True)) tensor(1.24300677, requires_grad=True)
See also
vn_entropy(),pennylane.math.mutual_info()andpennylane.mutual_info()