qat.fermion.transforms.transform_to_bk_basis

qat.fermion.transforms.transform_to_bk_basis(fermion_hamiltonian: Union[FermionHamiltonian, ElectronicStructureHamiltonian]) → SpinHamiltonian

Transform to Bravyi-Kitaev (BK) basis.

Parameters

fermion_hamiltonian (Union[FermionHamiltonian, ElectronicStructureHamiltonian]) – The fermionic hamiltonian.

Returns

Hamiltonian in BK spin representation.

Return type

SpinHamiltonian

Examples:

from qat.core import Term
from qat.fermion import FermionHamiltonian
from qat.fermion.transforms import transform_to_bk_basis

hamiltonian = FermionHamiltonian(
    2, [Term(0.3, "Cc", [0, 1]), Term(1.4, "CcCc", [0, 1, 1, 0])])

spin_hamiltonian = transform_to_bk_basis(hamiltonian)

print(f"H = {hamiltonian} \n")
print(f"H(spin) = {spin_hamiltonian}")

H = 0.3 * (Cc|[0, 1]) +
1.4 * (Cc|[0, 0]) +
1.4 * (CCcc|[0, 1, 0, 1]) 

H(spin) = (0.35+0j) * I^2 +
-0.075j * (Y|[0]) +
(-0.075+0j) * (XZ|[0, 1]) +
(0.075+0j) * (X|[0]) +
0.075j * (YZ|[0, 1]) +
(-0.35+0j) * (Z|[1]) +
(-0.35+0j) * (Z|[0]) +
(0.35+0j) * (ZZ|[0, 1])