[Feature]: Construct embedded operator from levels, embedding, and matrix.

[andgoldschmidt]

Feature Description

Embedded operators interface is not flexible enough to handle generic systems.

This is my current solution to construct from levels and embedding levels:

CZ = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 -1]
levels = [3, 3]
embedding = [1:2, 1:2]
subspace_indices = get_subspace_indices(embedding, levels)
U_goal = EmbeddedOperator(
    embed(CZ, system, subspace=subspace_indices),
    subspace_indices,
    levels
)

Importance

1 (lowest)

What does this feature affect?

• quantum system construction
• problem setup
• problem solution
• problem performance
• solution analysis
• plotting
• documentation
• tests
• other (please specify below)

Other information

No response

[andgoldschmidt]

Desired behavior is that a user always passes the subsystem operator, never the embedded operator:

U_goal = EmbeddedOperator(
    GATES[:CZ],
    system,
    subspace=get_subspace_indices([1:2, 1:2], [3, 3])
)