def test_d2_spin_rep_hubbard():
n_density, rdm_generator = system_hubbard()
density = AntiSymmOrbitalDensity(n_density, 8)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
bas_aa, bas_ab = geminal_spin_basis(4)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
rdms = MultiTensor([tpdm_ab])
dim = int(np.sqrt(tpdm_ab.data.shape[0]))
s_rep_dual_constant = 0
for i, j in product(range(dim), repeat=2):
s_rep_dual_constant += tpdm_ab.data[bas_ab.rev((i, j)),
bas_ab.rev((j, i))]
N = 4
M = 0
S = 0
db = DualBasis()
db += s_representability_d2ab(dim, N, M, S)
rdms.dual_basis = db
xvec = rdms.vectorize_tensors()
A, _, b = rdms.synthesize_dual_basis()
assert np.allclose(A.dot(xvec) - b, 0.0)
assert np.allclose(A.dot(xvec), s_rep_dual_constant)
def test_d2_spin_sz_rep():
n_density, rdm_generator, transform, molecule = system()
assert np.isclose(molecule.fci_energy, -2.84383506834)
density = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
opdm_a, opdm_b = density.construct_opdm()
bas_aa, bas_ab = geminal_spin_basis(molecule.n_orbitals)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
rdms = MultiTensor([opdm_a, opdm_b, tpdm_ab])
dim = int(np.sqrt(tpdm_ab.data.shape[0]))
sz_rep_value = 0
for i in range(dim):
sz_rep_value += 0.5 * (opdm_a.data[i, i] - opdm_b.data[i, i])
N = molecule.n_electrons
M = 0
S = 0
db = DualBasis()
db += s_representability_d2ab(dim, N, M, S)
db += sz_representability(dim, M)
rdms.dual_basis = db
xvec = rdms.vectorize_tensors()
A, _, b = rdms.synthesize_dual_basis()
assert np.allclose(A.dot(xvec) - b, 0.0)
def test_d2_spin_rep():
n_density, rdm_generator, transform, molecule = system()
assert np.isclose(molecule.fci_energy, -2.84383506834)
density = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
bas_aa, bas_ab = geminal_spin_basis(molecule.n_orbitals)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
rdms = MultiTensor([tpdm_ab])
dim = int(np.sqrt(tpdm_ab.data.shape[0]))
s_rep_dual_constant = 0
for i, j in product(range(dim), repeat=2):
s_rep_dual_constant += tpdm_ab.data[bas_ab.rev((i, j)),
bas_ab.rev((j, i))]
N = molecule.n_electrons
M = 0
S = 0
db = DualBasis()
db += s_representability_d2ab(dim, N, M, S)
rdms.dual_basis = db
xvec = rdms.vectorize_tensors()
A, _, b = rdms.synthesize_dual_basis()
assert np.allclose(A.dot(xvec) - b, 0.0)
assert np.allclose(A.dot(xvec), s_rep_dual_constant)