Add Hamiltonian Modeler

[Jacomichi]

Change

• Add Hamiltonian modeler qamomile.core.modeler
• Currently, only support Hamiltonian consisting only of Pauli operators

Usage

The simple example is

    E = jm.Placeholder("E", ndim=2)
    e = jm.Element("e", belong_to=E)
    Z = qm_m.PauliExpr.z(shape=3)
    expr = jm.sum(e, Z[e[0]] * Z[e[1]])
    
    hamiltonian_expr = qm_m.HamiltonianExpr(expr, name="test")
    
    E = [[0, 1], [1, 2], [2, 0]]
    
    builder = qm_m.HamiltonianBuilder(hamiltonian_expr, {"E": E})
    op = builder.build()

    expected_hamiltonian = qm_o.Hamiltonian()
    for i,j in E:
        expected_hamiltonian += qm_o.Z(i) * qm_o.Z(j)

    assert op == expected_hamiltonian

We can also see your HamiltonianExpr (algebraic expression of Hamiltonian) as LaTex in jupyter-notebook.
Some example is in the notebook.

Concern

• Whan kind of type should I expect as input of PauliExpr (

  Qamomile/qamomile/core/modeler/pauli_expr.py

  Line 5 in f322fe3

  def x(shape: int | jm.Placeholder | tuple[int, ...]) -> jm.BinaryVar:

  )

[Jacomichi]

New Change

• Add tutorial and docstrings
• add to_latex method in Hamiltonian