/// <summary>
/// This approximates the Hamiltonian ground state by a greedy algorithm
/// that minimizes only the PP term energies. If there are no PP terms,
/// states will be occupied in lexicographic order.
/// </summary>
/// <returns>
/// Greedy trial state for minimizing Hamiltonian diagonal one-electron energy.
/// </returns>
internal static SingleCFWavefunction <int> GreedyStatePreparationSCF(this FermionHamiltonian hamiltonian, int nElectrons)
{
if (hamiltonian.Terms.ContainsKey(TermType.Fermion.PP))
{
var hPPTermSortedByCoeff = hamiltonian.Terms[TermType.Fermion.PP];
var spinOrbitalIndices = hPPTermSortedByCoeff.OrderBy(o => o.Value).Select(o => o.Key.Sequence.First().Index).Take((int)nElectrons).ToArray();
return(new SingleCFWavefunction <int>(spinOrbitalIndices));
}
else
{
return(new SingleCFWavefunction <int>(Enumerable.Range(0, nElectrons).ToArray()));
}
}
/// <summary>
/// This approximates the Hamiltonian ground state by a greedy algorithm
/// that minimizes only the PP term energies. If there are no PP terms,
/// states will be occupied in lexicographic order.
/// </summary>
/// <returns>
/// Greedy trial state for minimizing Hamiltonian diagonal one-electron energy.
/// </returns>
public static FermionWavefunction <int> CreateHartreeFockState(this FermionHamiltonian hamiltonian, int nElectrons)
{
SingleCFWavefunction <int> greedyState = hamiltonian.GreedyStatePreparationSCF(nElectrons);
var wavefunction = new FermionWavefunction <int>
{
Energy = 0.0,
Method = StateType.SparseMultiConfigurational,
MCFData = new SparseMultiCFWavefunction <int>()
};
wavefunction.MCFData.Set(greedyState, new System.Numerics.Complex(1.0, 0.0));
return(wavefunction);
}
/// <summary>
/// Method for constructing a Pauli Hamiltonian from a fermion Hamiltonina.
/// </summary>
/// <param name="sourceHamiltonian">Input orbital integral Hamiltonian.</param>
/// <param name="encoding">Identifies how the terms should be encoded on the qubits.</param>
/// <returns>Fermion Hamiltonian constructed from orbital integrals.</returns>
public static PauliHamiltonian ToPauliHamiltonian(
this FermionHamiltonian sourceHamiltonian,
QubitEncoding encoding = QubitEncoding.JordanWigner)
{
var nFermions = sourceHamiltonian.SystemIndices.Max() + 1;
var hamiltonian = new PauliHamiltonian();
Func <FermionTerm, TermType.Fermion, double, IEnumerable <(PauliTerm, PauliTermValue)> > conversion =
(fermionTerm, termType, coeff)
=> (fermionTerm.ToJordanWignerPauliTerms(termType, coeff));
foreach (var termType in sourceHamiltonian.Terms)
{
foreach (var term in termType.Value)
{
hamiltonian.AddRange(conversion(term.Key, termType.Key, term.Value.Value));
}
}
// Create a copy of fermion indices hash set.
hamiltonian.SystemIndices = new HashSet <int>(sourceHamiltonian.SystemIndices.ToList());
return(hamiltonian);
}