Symmetries of Molecular Integrals - Azure Quantum | Microsoft Learn

    // Create a `OrbitalIntegral` instance to store a two-electron molecular
    // orbital integral data.
    var orbitalIntegral = new OrbitalIntegral(new[] { 0, 1, 2, 3 }, 0.123);

    // Create an `OrbitalIntegralHamiltonian` instance to store the orbital integral
    // terms.
    var orbitalIntegralHamiltonian = new OrbitalIntegralHamiltonian();
    orbitalIntegralHamiltonian.Add(orbitalIntegral);

    // Convert the orbital integral representation to a fermion
    // representation. This also requires choosing a convention for
    // mapping spin orbital indices to integer indices.
    var fermionHamiltonian = orbitalIntegralHamiltonian.ToFermionHamiltonian(IndexConvention.UpDown);

    // Alternatively, one can add orbital integrals directly to a fermion Hamiltonian
    // as follows. This automatically enumerates over all symmetries, and then
    // orders the `HermitianFermionTerm` instances in canonical order. We will need to
    // choose an indexing convention as well.
    fermionHamiltonian.AddRange(orbitalIntegral
        .ToHermitianFermionTerms(0, IndexConvention.UpDown)
        .Select(o => (o.Item1, o.Item2.ToDoubleCoeff())));