qml.kernels.kernel_matrix

kernel_matrix(X1, X2, kernel)

Computes the matrix of pairwise kernel values for two given datasets.

Parameters:

• X1 (list[datapoint]) – List of datapoints (first argument)

• X2 (list[datapoint]) – List of datapoints (second argument)

• kernel ((datapoint, datapoint) -> float) – Kernel function that maps datapoints to kernel value.

Returns:

The matrix of kernel values.

Return type:

array[float]

Example:

Consider a simple kernel function based on AngleEmbedding:

dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(x1, x2):
    qml.templates.AngleEmbedding(x1, wires=dev.wires)
    qml.adjoint(qml.templates.AngleEmbedding)(x2, wires=dev.wires)
    return qml.probs(wires=dev.wires)

kernel = lambda x1, x2: circuit(x1, x2)[0]

With this method we can systematically evaluate the kernel function kernel on pairs of datapoints, where the points stem from different datasets, like a training and a test dataset.

>>> rng = np.random.default_rng(seed=1234)
>>> X_train = rng.random((4,2))
>>> X_test = rng.random((3,2))
>>> qml.kernels.kernel_matrix(X_train, X_test, kernel)
array([[0.99656842, 0.91774724, 0.93966202],
       [0.99958227, 0.91468777, 0.91127346],
       [0.89479886, 0.937256  , 0.80459952],
       [0.87448042, 0.96924743, 0.84069076]])

As we can see, for \(n\) and \(m\) datapoints in the first and second dataset respectively, the output matrix has the shape \(n\times m\).

code/api/pennylane.kernels.kernel_matrix

 

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