kernel_matrix(X1, X2, kernel)[source]

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

  • 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.


The square matrix of kernel values.

Return type



Consider a simple kernel function based on AngleEmbedding:

dev = qml.device('default.qubit', wires=2, shots=None)
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.

>>> X_train = np.random.random((4,2))
>>> X_test = np.random.random((3,2))
>>> qml.kernels.kernel_matrix(X_train, X_test, kernel)
tensor([[0.88875298, 0.90655175, 0.89926447],
        [0.93762197, 0.98163781, 0.93076383],
        [0.91977339, 0.9799841 , 0.91582698],
        [0.80376818, 0.98720925, 0.79349212]], requires_grad=True)

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