embed_operators

Graph.embed_operators(operators, dimensions, *, name=None)

Embed operators into a larger Hilbert space.

The size of the Hilbert space is defined by the dimensions argument.

Parameters

operators (list[tuple[np.ndarray or Tensor, int]] or tuple[np.ndarray or Tensor, int]) – A tuple or a list of tuples that contain pairs of the operators to be embedded and their corresponding positions in the full space. The positions must be non-negative integers less than the length of the dimensions list. The operators must be at least 2D and can contain leading batch dimensions.
dimensions (list[int]) – The dimensions of each subspace.
name (str, optional) – The name of the node.

Returns

The operators embedded into the full Hilbert space. The dimension of the Hilbert space of the output is equal to the product of the elements of the dimensions list.

Return type

Tensor

See also

kron: Kronecker product between two objects.
kronecker_product_list: Kronecker product of a list of operators.
pauli_kronecker_product: Embed Pauli matrices into a larger Hilbert space.

Examples

Embed a single operator.

>>> sigma_z = graph.pauli_matrix("Z")
>>> graph.embed_operators((sigma_z, 0), [2, 3], name="Z0")
<Tensor: name="Z0", operation_name="embed_operators", shape=(6, 6)>
>>> result = qctrl.functions.calculate_graph(
...     graph=graph, output_node_names=["Z0"]
... )
>>> result.output["Z0"]["value"]
array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])

Embed multiple operators.

>>> number_op = graph.number_operator(2)
>>> sigma_x = graph.pauli_matrix("X")
>>> graph.embed_operators([(number_op, 0), (sigma_x, 2)], [2, 2, 2], name="N0X2")
<Tensor: name="N0X2", operation_name="embed_operators", shape=(8, 8)>
>>> result = qctrl.functions.calculate_graph(
...     graph=graph, output_node_names=["N0X2"]
... )
>>> result.output["N0X2"]["value"]
array([[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j]])