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

Graph.density_matrix_expectation_value : Expectation value of an operator with respect to a density matrix.

Graph.expectation_value : Expectation value of an operator with respect to a pure state.

Graph.inner_product : Inner product of two vectors.

Graph.trace : Trace of an object.

Notes

The outer product of two complex vectors x\mathbf{x} and y\mathbf{y}

(x⊗y)ij=xiyj∗. (\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 = bo.execute_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="outer2")
<Tensor: name="outer2", operation_name="outer_product", shape=(3, 2, 2, 2)>
>>> result = bo.execute_graph(graph=graph, output_node_names="outer2")
>>> result["output"]["outer2"]["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]]])

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