outer_product

Graph.outer_product(x, y, *, name=None)

Calculate the outer product of two vectors.

The vectors can have different last dimensions but must have broadcastable batch dimensions.

Parameters:

x (np.ndarray or Tensor) – The left multiplicand. It must be a vector of shape (..., M).
y (np.ndarray or Tensor) – The right multiplicand. It must be a vector of shape (..., N).
name (str or None, optional) – The name of the node.

Returns:

The outer product of two vectors of shape (..., M, N).

Return type:

Tensor

See also

density_matrix_expectation_value: Expectation value of an operator with respect to a density matrix.
expectation_value: Expectation value of an operator with respect to a pure state.
inner_product: Inner product of two vectors.
trace: Trace of an object.

Notes

The outer product of two complex vectors \(\mathbf{x}\) and \(\mathbf{y}\) is defined as

\[(\mathbf{x} \otimes \mathbf{y})_{ij} = x_{i} y^\ast_{j}.\]

For more information about the outer product, see outer product on Wikipedia.

Examples

>>> graph.outer_product(np.array([1j, 1j]), np.array([1j, -1j]), name="outer")
<Tensor: name="outer", operation_name="outer_product", shape=(2, 2)>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["outer"])
>>> result.output["outer"]["value"]
array([[1.+0.j, -1.+0.j], [1.+0.j, -1.+0.j]])

>>> graph.outer_product(np.ones((3,1,2), np.ones(2,2), name="outer")
<Tensor: name="outer", operation_name="outer_product", shape=(3, 2, 2, 2)>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["outer"])
>>> result.output["outer"]["value"]
array([[[[1, 1], [1, 1]], [[1, 1], [1, 1]]],
    [[[1, 1], [1, 1]], [[1, 1], [1, 1]]],
    [[[1, 1], [1, 1]], [[1, 1], [1, 1]]])