In quantum chemistry calculation, choosing cut-off dimension is important. To make use of limited computation resource, we desire to efficiently represent larger Hilbert space with a small set of basis, which is called downfolding. Here we implement several downfolding strategy. We also test VQE with the downfolded Hamiltonians. The codes are stored in downfolding_methods.py.

genHam.py and solveHam.py are wrappers to make it user friendly.

2

H 0 0 0
H 0 0 0.75

python3 genHam.py --config H2.xyz --strategy HF ccpVDZ sto-3G

where --strategy in the example means using Hatree Fock to downfold ccpVDZ basis into a smaller basis with the same size of sto-3G basis. Here HF can be replaced by B3LYP or EGNN. If we set two same basis like --strategy HF sto-3G sto-3G, the programe will do no downfolding and generate a Hamiltonian on sto-3G molecular orbital (MO) basis. The downfolding strategy is explained in /documents.

We can also use a self defined fock matrix TBD, we provide a EGNN method TBD.

We also provide Quasi Orbital(QO) strategy TBD. (Reference Here, TBD)

python3 genHam.py -JW

python3 solveHam.py --particle fermion --method FCI 

Alternatively, we can set --method ED to solve qubit Hamiltonian with ED; or set --method FCI or --method CCSD to solve fermionic Hamiltonian.

A simple example following this readme file.

In this example, we directly use functions in downfolding_methods.py. WHere we benchmark the energy results of different downfolding strategies, we also benchmark the 1-norm of Pauli coefficient of the Hamiltonian.