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_q2_mapping_hubbard():
n_density, rdm_generator = system_hubbard()
density = AntiSymmOrbitalDensity(n_density, 8)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
tqdm_aa, tqdm_bb, tqdm_ab, _ = density.construct_thdm()
opdm_a, opdm_b = density.construct_opdm()
bas_aa, bas_ab = geminal_spin_basis(4)
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
tpdm_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
tqdm_aa = Tensor(tqdm_aa, name='kkcc_aa', basis=bas_aa)
tqdm_bb = Tensor(tqdm_bb, name='kkcc_bb', basis=bas_aa)
tqdm_ab = Tensor(tqdm_ab, name='kkcc_ab', basis=bas_ab)
rdms = MultiTensor(
[opdm_a, opdm_b, tpdm_aa, tpdm_bb, tpdm_ab, tqdm_aa, tqdm_bb, tqdm_ab])
dual_basis = d2_q2_mapping(4)
rdms.dual_basis = dual_basis
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
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)
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_trace():
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_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
rdms = MultiTensor([tpdm_aa, tpdm_bb, tpdm_ab])
dual_basis = trace_d2_aa(molecule.n_orbitals, molecule.n_electrons / 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, b, c = rdms.synthesize_dual_basis()
Amat = A.todense()
bmat = b.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = trace_d2_bb(molecule.n_orbitals, molecule.n_electrons / 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = trace_d2_ab(molecule.n_orbitals, molecule.n_electrons / 2,
molecule.n_electrons / 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
db = DualBasis()
db += trace_d2_aa(molecule.n_orbitals, molecule.n_electrons / 2)
db += trace_d2_ab(molecule.n_orbitals, molecule.n_electrons / 2,
molecule.n_electrons / 2)
db += trace_d2_bb(molecule.n_orbitals, molecule.n_electrons / 2)
rdms.dual_basis = db
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def test_d2_d1_mapping_hubbard():
n_density, rdm_generator = system_hubbard()
density = AntiSymmOrbitalDensity(n_density, 8)
tpdm_aa, tpdm_bb, tpdm_ab, [bas_aa, bas_ab] = density.construct_tpdm()
opdm_a, opdm_b = density.construct_opdm()
from itertools import product
test_opdm = np.zeros_like(opdm_a)
for i, j in product(range(opdm_a.shape[0]), repeat=2):
if i <= j:
for r in range(opdm_a.shape[0]):
if i != r and j != r:
top_gem = tuple(sorted([i, r]))
bot_gem = tuple(sorted([j, r]))
parity = (-1)**(r < i) * (-1)**(r < j)
if i == j:
test_opdm[i, j] += tpdm_aa[bas_aa[top_gem],
bas_aa[bot_gem]] * parity
else:
test_opdm[j,
i] += tpdm_aa[bas_aa[top_gem],
bas_aa[bot_gem]] * parity * 0.5
test_opdm[j,
i] += tpdm_aa[bas_aa[bot_gem],
bas_aa[top_gem]] * parity * 0.5
test_opdm[i,
j] += tpdm_aa[bas_aa[top_gem],
bas_aa[bot_gem]] * parity * 0.5
test_opdm[i,
j] += tpdm_aa[bas_aa[bot_gem],
bas_aa[top_gem]] * parity * 0.5
assert np.allclose(test_opdm, opdm_a)
bas_aa, bas_ab = geminal_spin_basis(4)
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
tpdm_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
rdms = MultiTensor([opdm_a, opdm_b, tpdm_aa, tpdm_bb, tpdm_ab])
# d2ab_d1a test
Na = Nb = 2
dual_basis = d2ab_d1a_mapping(4, Nb)
dual_basis += d2ab_d1b_mapping(4, Na)
dual_basis += d2aa_d1a_mapping(4, Na)
dual_basis += d2bb_d1b_mapping(4, Nb)
rdms.dual_basis = dual_basis
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
w, v = np.linalg.eigh(np.dot(Amat, Amat.T))
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def test_d2_trace_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_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
rdms = MultiTensor([tpdm_aa, tpdm_bb, tpdm_ab])
dual_basis = trace_d2_aa(4, 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, b, c = rdms.synthesize_dual_basis()
Amat = A.todense()
bmat = b.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = trace_d2_bb(4, 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = trace_d2_ab(4, 2, 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
db = DualBasis()
db += trace_d2_aa(4, 2)
db += trace_d2_ab(4, 2, 2)
db += trace_d2_bb(4, 2)
rdms.dual_basis = db
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def system_h4():
print('Running System Setup H4')
basis = 'sto-3g'
multiplicity = 1
charge = 0
r = 0.75
geometry = [('H', [0.0, 0.0, 0.0]), ('H', [0, 0, r]), ('H', [0, 0, 2 * r]),
('H', [0, 0, 3 * r])]
molecule = MolecularData(geometry, basis, multiplicity, charge)
# Run Psi4.
molecule = run_psi4(molecule,
run_scf=True,
run_mp2=False,
run_cisd=False,
run_ccsd=False,
run_fci=True,
delete_input=False)
op_mat = of.get_sparse_operator(
molecule.get_molecular_hamiltonian()).toarray()
w, v = np.linalg.eigh(op_mat)
n_density = v[:, [0]] @ v[:, [0]].conj().T
rdm_generator = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
transform = jordan_wigner
return n_density, rdm_generator, transform, molecule
def system_hubbard():
print('Running System Setup')
import openfermion as of
U = 1
sites = 4
hubbard = of.hamiltonians.fermi_hubbard(1,
sites,
tunneling=1,
coulomb=U,
chemical_potential=0,
magnetic_field=0,
periodic=False,
spinless=False)
# hamiltonian = of.get_interaction_operator(hubbard)
op_mat = of.get_number_preserving_sparse_operator(
hubbard, 8, 4, spin_preserving=False).toarray()
w, v = np.linalg.eigh(op_mat)
gs_e = w[0]
print(gs_e)
op_mat = of.get_sparse_operator(hubbard).toarray()
w, v = np.linalg.eigh(op_mat)
print(w[0])
n_density = v[:, [0]] @ v[:, [0]].conj().T
rdm_generator = AntiSymmOrbitalDensity(n_density, sites * 2)
return n_density, rdm_generator
def test_d1_q1_mapping():
n_density, rdm_generator, transform, molecule = system_h4()
density = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
opdm_a, opdm_b = density.construct_opdm()
oqdm_a, oqdm_b = density.construct_ohdm()
bas_aa, bas_ab = geminal_spin_basis(molecule.n_orbitals)
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
oqdm_a = Tensor(oqdm_a, name='kc_a')
oqdm_b = Tensor(oqdm_b, name='kc_b')
rdms = MultiTensor([opdm_a, opdm_b, oqdm_a, oqdm_b])
dual_basis = d1a_q1a_mapping(molecule.n_orbitals)
rdms.dual_basis = dual_basis
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = d1b_q1b_mapping(molecule.n_orbitals)
rdms.dual_basis = dual_basis
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis_a = d1b_q1b_mapping(molecule.n_orbitals)
dual_basis_b = d1a_q1a_mapping(molecule.n_orbitals)
rdms.dual_basis = dual_basis_a + dual_basis_b
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def test_unspin_adapt_1():
heh_file = os.path.join(DATA_DIRECTORY,
'H1-He1_sto-3g_singlet_1+_0.74.hdf5')
molecule = MolecularData(filename=heh_file)
tpdm_from_of = np.einsum('ijkl->ijlk', molecule.fci_two_rdm)
rho, rdm_generator, transform, mol2 = system()
assert np.allclose(np.conj(rho).T, rho)
dim = molecule.n_qubits
rdm_generator_antisym = AntiSymmOrbitalDensity(rho, molecule.n_qubits)
tpdm_aa, tpdm_bb, tpdm_ab, [bas_aa, bas_ab
] = rdm_generator_antisym.construct_tpdm()
assert np.allclose(opdm, molecule.fci_one_rdm)
assert np.allclose(tpdm, tpdm_from_of)
tpdm_test = unspin_adapt(tpdm_aa, tpdm_bb, tpdm_ab)
# print(np.linalg.norm(tpdm[::2, ::2, ::2, ::2] - tpdm_test[::2, ::2, ::2, ::2]))
np.testing.assert_allclose(tpdm[::2, ::2, ::2, ::2],
tpdm_test[::2, ::2, ::2, ::2])
# print(np.linalg.norm(tpdm[1::2, 1::2, 1::2, 1::2] - tpdm_test[1::2, 1::2, 1::2, 1::2]))
np.testing.assert_allclose(tpdm[1::2, 1::2, 1::2, 1::2],
tpdm_test[1::2, 1::2, 1::2, 1::2])
# print(np.linalg.norm(tpdm[::2, 1::2, ::2, 1::2] - tpdm_test[::2, 1::2, ::2, 1::2]))
np.testing.assert_allclose(tpdm[::2, 1::2, ::2, 1::2],
tpdm_test[::2, 1::2, ::2, 1::2])
# print(np.linalg.norm(tpdm[1::2, ::2, 1::2, ::2] - tpdm_test[1::2, ::2, 1::2, ::2]))
np.testing.assert_allclose(tpdm[1::2, ::2, 1::2, ::2],
tpdm_test[1::2, ::2, 1::2, ::2])
for p, q, r, s in product(range(tpdm.shape[0]), repeat=4):
if not np.isclose(tpdm[p, q, r, s], tpdm_test[p, q, r, s]):
print((p, q, r, s), tpdm[p, q, r, s], tpdm_test[p, q, r, s])
heh_file = os.path.join(DATA_DIRECTORY,
'H1-He1_sto-3g_singlet_1+_0.74.hdf5')
molecule = MolecularData(filename=heh_file)
tpdm_from_of = np.einsum('ijkl->ijlk', molecule.fci_two_rdm)
for p, q, r, s in product(range(tpdm.shape[0]), repeat=4):
if not np.isclose(tpdm_from_of[p, q, r, s], tpdm[p, q, r, s]):
print((p, q, r, s), tpdm_from_of[p, q, r, s], tpdm[p, q, r, s])
t_tpdm_aa, t_tpdm_bb, t_tpdm_ab = get_sz_spin_adapted(tpdm)
assert np.allclose(t_tpdm_ab, tpdm_ab)
def system():
print('Running System Setup')
basis = 'sto-3g'
multiplicity = 1
charge = 1
geometry = [('He', [0.0, 0.0, 0.0]), ('H', [0, 0, 0.740848149])]
molecule = MolecularData(geometry, basis, multiplicity, charge)
# Run Psi4.
molecule = run_psi4(molecule,
run_scf=True,
run_mp2=False,
run_cisd=False,
run_ccsd=False,
run_fci=True,
delete_input=False)
molecule, gs_wf, n_density, eigen_val = get_molecule_openfermion(
molecule, eigen_index=2)
rdm_generator = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
transform = jordan_wigner
return n_density, rdm_generator, transform, molecule
def test_d2_g2_mapping():
n_density, rdm_generator, transform, molecule = system_h4()
density = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
tqdm_aa, tqdm_bb, tqdm_ab, _ = density.construct_thdm()
phdm_ab, phdm_ba, phdm_aabb = density.construct_phdm()
opdm_a, opdm_b = density.construct_opdm()
bas_aa, bas_ab = geminal_spin_basis(molecule.n_orbitals)
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
tpdm_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
tqdm_aa = Tensor(tqdm_aa, name='kkcc_aa', basis=bas_aa)
tqdm_bb = Tensor(tqdm_bb, name='kkcc_bb', basis=bas_aa)
tqdm_ab = Tensor(tqdm_ab, name='kkcc_ab', basis=bas_ab)
phdm_ab = Tensor(phdm_ab, name='ckck_ab')
phdm_ba = Tensor(phdm_ba, name='ckck_ba')
phdm_aabb = Tensor(
phdm_aabb, name='ckck_aabb'
) # What basis do we want to use for super blocks like this?
rdms = MultiTensor([
opdm_a, opdm_b, tpdm_aa, tpdm_bb, tpdm_ab, tqdm_aa, tqdm_bb, tqdm_ab,
phdm_ab, phdm_ba, phdm_aabb
])
dual_basis = d2_g2_mapping(molecule.n_orbitals)
rdms.dual_basis = dual_basis
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def test_d2_e2_constraint():
n_density, rdm_generator, transform, molecule = system()
density = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
tpdm_aa, tpdm_bb, tpdm_ab, [bas_aa, bas_ab] = density.construct_tpdm()
tqdm_aa, tqdm_bb, tqdm_ab, _ = density.construct_thdm()
# generate error tensors
corrupted_tpdm_aa = add_gaussian_noise(tpdm_aa, 1)
corrupted_tpdm_aa = 0.5 * (corrupted_tpdm_aa + corrupted_tpdm_aa.T)
corrupted_tpdm_bb = add_gaussian_noise(tpdm_bb, 1)
corrupted_tpdm_bb = 0.5 * (corrupted_tpdm_bb + corrupted_tpdm_bb.T)
corrupted_tpdm_ab = add_gaussian_noise(tpdm_ab, 1)
corrupted_tpdm_ab = 0.5 * (corrupted_tpdm_ab + corrupted_tpdm_ab.T)
error_aa = corrupted_tpdm_aa - tpdm_aa
error_bb = corrupted_tpdm_bb - tpdm_bb
error_ab = corrupted_tpdm_ab - tpdm_ab
error_matrix_aa = density.construct_tpdm_error_matrix(error_aa)
error_matrix_bb = density.construct_tpdm_error_matrix(error_bb)
error_matrix_ab = density.construct_tpdm_error_matrix(error_ab)
assert error_matrix_aa.shape[0] == 2 * tpdm_aa.shape[0]
assert error_matrix_bb.shape[0] == 2 * tpdm_bb.shape[0]
assert error_matrix_ab.shape[0] == 2 * tpdm_ab.shape[0]
dim_aa = tpdm_aa.shape[0]
dim_bb = tpdm_bb.shape[0]
dim_ab = tpdm_ab.shape[0]
assert np.allclose(error_matrix_aa[:dim_aa, :dim_aa], np.eye(dim_aa))
assert np.allclose(error_matrix_bb[:dim_bb, :dim_bb], np.eye(dim_bb))
assert np.allclose(error_matrix_ab[:dim_ab, :dim_ab], np.eye(dim_ab))
assert np.allclose(error_matrix_aa[:dim_aa, dim_aa:], error_aa)
assert np.allclose(error_matrix_aa[dim_aa:, :dim_aa], error_aa.T)
assert np.allclose(error_matrix_bb[:dim_bb, dim_bb:], error_bb)
assert np.allclose(error_matrix_bb[dim_bb:, :dim_bb], error_bb.T)
assert np.allclose(error_matrix_ab[:dim_ab, dim_ab:], error_ab)
assert np.allclose(error_matrix_ab[dim_ab:, :dim_ab], error_ab.T)
# get basis bijection
bij_bas_aa, bij_bas_ab = geminal_spin_basis(molecule.n_orbitals)
tpdm_aa = Tensor(tensor=tpdm_aa, name='cckk_aa', basis=bij_bas_aa)
error_tensor_aa = Tensor(tensor=error_matrix_aa, name='cckk_me_aa')
tpdm_bb = Tensor(tensor=tpdm_bb, name='cckk_bb', basis=bij_bas_aa)
error_tensor_bb = Tensor(tensor=error_matrix_bb, name='cckk_me_bb')
tpdm_ab = Tensor(tensor=tpdm_ab, name='cckk_ab', basis=bij_bas_ab)
error_tensor_ab = Tensor(tensor=error_matrix_ab, name='cckk_me_ab')
rdms = MultiTensor([
tpdm_aa, tpdm_bb, tpdm_ab, error_tensor_aa, error_tensor_bb,
error_tensor_ab
])
xvec = rdms.vectorize_tensors()
db = d2_e2_mapping(int(np.sqrt(dim_ab)), bas_aa, bas_ab, corrupted_tpdm_aa,
corrupted_tpdm_bb, corrupted_tpdm_ab)
rdms.dual_basis = db
A, _, b = rdms.synthesize_dual_basis()
A = A.todense()
b = b.todense()
w, v = np.linalg.eigh(A.dot(A.T))
assert np.all(w > 0)
assert np.allclose(A.dot(xvec) - b, 0.0)
def test_d2_g2_mapping():
n_density, rdm_generator, transform, molecule = system_h4()
# n_density, rdm_generator = system_hubbard()
# n_density, rdm_generator, transform, molecule = system()
dim = 4
density = AntiSymmOrbitalDensity(n_density, 2 * dim)
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
tqdm_aa, tqdm_bb, tqdm_ab, _ = density.construct_thdm()
phdm_ab, phdm_ba, phdm_aabb = density.construct_phdm()
# for i, j, k, l in product(range(dim), repeat=4):
# fop = ((2 * i, 1), (2 * j + 1, 0), (2 * l + 1, 1), (2 * k, 0))
# fop = of.FermionOperator(fop)
# opmat = of.get_sparse_operator(fop, n_qubits=2 * dim)
# rdm_val = (np.trace(n_density @ opmat))
# # print(rdm_val, phdm_ab[i * dim + j, k * dim + l])
# assert np.isclose(rdm_val, phdm_ab[i * dim + j, k * dim + l])
# for i, j, k, l in product(range(dim), repeat=4):
# fop = ((2 * i + 1, 1), (2 * j, 0), (2 * l, 1), (2 * k + 1, 0))
# fop = of.FermionOperator(fop)
# opmat = of.get_sparse_operator(fop, n_qubits=2 * dim)
# rdm_val = (np.trace(n_density @ opmat))
# assert np.isclose(rdm_val, phdm_ba[i * dim + j, k * dim + l])
# for i, j, k, l in product(range(dim), repeat=4):
# fop = ((2 * i, 1), (2 * j, 0), (2 * k, 1), (2 * l, 0))
# fop = of.FermionOperator(fop)
# opmat = of.get_sparse_operator(of.jordan_wigner(fop), n_qubits=2 * dim)
# rdm_val = (np.trace(n_density @ opmat))
# assert np.isclose(rdm_val, phdm_aabb[i * dim + j, l * dim + k])
# for i, j, k, l in product(range(dim), repeat=4):
# fop = ((2 * i + 1, 1), (2 * j + 1, 0), (2 * k + 1, 1), (2 * l + 1, 0))
# fop = of.FermionOperator(fop)
# opmat = of.get_sparse_operator(of.jordan_wigner(fop), n_qubits=2 * dim)
# rdm_val = (np.trace(n_density @ opmat))
# # print((i, j, k, l), rdm_val, phdm_aabb[i * dim + j + dim**2, l * dim + k + dim**2])
# assert np.isclose(rdm_val, phdm_aabb[i * dim + j + dim**2, l * dim + k + dim**2])
# for i, j, k, l in product(range(dim), repeat=4):
# fop = ((2 * i, 1), (2 * j, 0), (2 * k + 1, 1), (2 * l + 1, 0))
# fop = of.FermionOperator(fop)
# opmat = of.get_sparse_operator(of.jordan_wigner(fop), n_qubits=2 * dim)
# rdm_val = (np.trace(n_density @ opmat))
# assert np.isclose(rdm_val, phdm_aabb[i * dim + j, l * dim + k + dim**2])
# for i, j, k, l in product(range(dim), repeat=4):
# fop = ((2 * i + 1, 1), (2 * j + 1, 0), (2 * l, 1), (2 * k, 0))
# fop = of.FermionOperator(fop)
# opmat = of.get_sparse_operator(of.jordan_wigner(fop), n_qubits=2 * dim)
# rdm_val = (np.trace(n_density @ opmat))
# # print((i, j, k, l), rdm_val, phdm_aabb[i * dim + j + dim**2, k * dim + l])
# assert np.isclose(rdm_val, phdm_aabb[i * dim + j + dim**2, k * dim + l])
# for i, j, k, l in product(range(dim), repeat=4):
# assert np.isclose(phdm_aabb[i * dim + j + dim**2, k * dim + l],
# phdm_aabb[k * dim + l, i * dim + j + dim**2]
# )
assert of.is_hermitian(phdm_ab)
assert of.is_hermitian(phdm_ba)
assert of.is_hermitian(phdm_aabb)
w, v = np.linalg.eigh(phdm_ab)
assert np.all(w > -1.0E-14)
w, v = np.linalg.eigh(phdm_ba)
assert np.all(w > -1.0E-14)
w, v = np.linalg.eigh(phdm_aabb)
assert np.all(w > -1.0E-14)
opdm_a, opdm_b = density.construct_opdm()
bas_aa, bas_ab = geminal_spin_basis(dim)
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
tpdm_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
tqdm_aa = Tensor(tqdm_aa, name='kkcc_aa', basis=bas_aa)
tqdm_bb = Tensor(tqdm_bb, name='kkcc_bb', basis=bas_aa)
tqdm_ab = Tensor(tqdm_ab, name='kkcc_ab', basis=bas_ab)
phdm_ab = Tensor(phdm_ab, name='ckck_ab', basis=bas_ab)
phdm_ba = Tensor(phdm_ba, name='ckck_ba', basis=bas_ab)
phdm_aabb = Tensor(
phdm_aabb, name='ckck_aabb'
) # What basis do we want to use for super blocks like this?
rdms = MultiTensor([
opdm_a, opdm_b, tpdm_aa, tpdm_bb, tpdm_ab, tqdm_aa, tqdm_bb, tqdm_ab,
phdm_ab, phdm_ba, phdm_aabb
])
dual_basis = d2_g2_mapping(dim)
rdms.dual_basis = dual_basis
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def test_d2_trace_h4():
n_density, rdm_generator, transform, molecule = system_h4()
density = AntiSymmOrbitalDensity(n_density, molecule.n_qubits)
dim = molecule.n_orbitals
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
Na, Nb = 2, 2
trace_ab = 0
for i, j in product(range(molecule.n_orbitals), repeat=2):
trace_ab += tpdm_ab[i * dim + j, i * dim + j]
assert np.isclose(trace_ab, Na, Nb)
assert np.isclose(np.trace(tpdm_aa), Na * (Na - 1) / 2)
assert np.isclose(np.trace(tpdm_bb), Nb * (Nb - 1) / 2)
bas_aa, bas_ab = geminal_spin_basis(molecule.n_orbitals)
tpdm_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bas_ab)
rdms = MultiTensor([tpdm_aa, tpdm_bb, tpdm_ab])
dual_basis = trace_d2_aa(molecule.n_orbitals, molecule.n_electrons / 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, b, c = rdms.synthesize_dual_basis()
Amat = A.todense()
bmat = b.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = trace_d2_bb(molecule.n_orbitals, molecule.n_electrons / 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
dual_basis = trace_d2_ab(molecule.n_orbitals, molecule.n_electrons / 2,
molecule.n_electrons / 2)
rdms.dual_basis = DualBasis(elements=[dual_basis])
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
db = DualBasis()
db += trace_d2_aa(molecule.n_orbitals, molecule.n_electrons / 2)
db += trace_d2_ab(molecule.n_orbitals, molecule.n_electrons / 2,
molecule.n_electrons / 2)
db += trace_d2_bb(molecule.n_orbitals, molecule.n_electrons / 2)
rdms.dual_basis = db
A, _, c = rdms.synthesize_dual_basis()
Amat = A.todense()
cmat = c.todense()
primal_vec = rdms.vectorize_tensors()
residual = Amat.dot(primal_vec) - cmat
assert np.allclose(residual, np.zeros_like(residual))
def dqg_run_bpsdp():
import sys
from openfermion.hamiltonians import MolecularData
from openfermionpsi4 import run_psi4
from openfermionpyscf import run_pyscf
from openfermion.utils import map_one_pdm_to_one_hole_dm, \
map_two_pdm_to_two_hole_dm, map_two_pdm_to_particle_hole_dm
print('Running System Setup')
basis = 'sto-6g'
# basis = '6-31g'
multiplicity = 1
# charge = 0
# geometry = [('H', [0.0, 0.0, 0.0]), ('H', [0, 0, 0.75])]
# charge = 1
# geometry = [('H', [0.0, 0.0, 0.0]), ('He', [0, 0, 0.75])]
charge = 0
bd = 1.2
# geometry = [('H', [0.0, 0.0, 0.0]), ('H', [0, 0, bd]),
# ('H', [0.0, 0.0, 2 * bd]), ('H', [0, 0, 3 * bd])]
# geometry = [['H', [0, 0, 0]], ['H', [1.2, 0, 0]],
# ['H', [0, 1.2, 0]], ['H', [1.2, 1.2, 0]]]
# geometry = [['He', [0, 0, 0]], ['H', [0, 0, 1.2]]]
# geometry = [['Be' [0, 0, 0]], [['B', [1.2, 0, 0]]]]
geometry = [['N', [0, 0, 0]], ['N', [0, 0, 1.1]]]
molecule = MolecularData(geometry, basis, multiplicity, charge)
# Run Psi4.
# molecule = run_psi4(molecule,
# run_scf=True,
# run_mp2=False,
# run_cisd=False,
# run_ccsd=False,
# run_fci=True,
# delete_input=True)
molecule = run_pyscf(molecule,
run_scf=True,
run_mp2=False,
run_cisd=False,
run_ccsd=False,
run_fci=True)
print('nuclear_repulsion', molecule.nuclear_repulsion)
print('gs energy ', molecule.fci_energy)
print("hf energy ", molecule.hf_energy)
nuclear_repulsion = molecule.nuclear_repulsion
gs_energy = molecule.fci_energy
import openfermion as of
hamiltonian = molecule.get_molecular_hamiltonian(
occupied_indices=[0], active_indices=[1, 2, 3, 4])
print(type(hamiltonian))
print(hamiltonian)
nuclear_repulsion = hamiltonian.constant
hamiltonian.constant = 0
ham = of.get_sparse_operator(hamiltonian).toarray()
w, v = np.linalg.eigh(ham)
idx = 0
gs_energy = w[idx]
n_density = v[:, [idx]] @ v[:, [idx]].conj().T
from representability.fermions.density.antisymm_sz_density import AntiSymmOrbitalDensity
density = AntiSymmOrbitalDensity(n_density, 8)
opdm_a, opdm_b = density.construct_opdm()
tpdm_aa, tpdm_bb, tpdm_ab, _ = density.construct_tpdm()
true_tpdm = density.get_tpdm(density.rho, density.dim)
true_tpdm = true_tpdm.transpose(0, 1, 3, 2)
test_tpdm = unspin_adapt(tpdm_aa, tpdm_bb, tpdm_ab)
assert np.allclose(true_tpdm, test_tpdm)
tqdm_aa, tqdm_bb, tqdm_ab, _ = density.construct_thdm()
phdm_ab, phdm_ba, phdm_aabb = density.construct_phdm()
Na = np.round(opdm_a.trace()).real
Nb = np.round(opdm_b.trace()).real
one_body_ints, two_body_ints = hamiltonian.one_body_tensor, hamiltonian.two_body_tensor
two_body_ints = np.einsum('ijkl->ijlk', two_body_ints)
n_electrons = Na + Nb
print('n_electrons', n_electrons)
dim = one_body_ints.shape[0]
spatial_basis_rank = dim // 2
bij_bas_aa, bij_bas_ab = geminal_spin_basis(spatial_basis_rank)
opdm_a_interaction, opdm_b_interaction, v2aa, v2bb, v2ab = \
spin_adapted_interaction_tensor_rdm_consistent(two_body_ints,
one_body_ints)
dual_basis = sz_adapted_linear_constraints(
spatial_basis_rank,
Na,
Nb, ['ck', 'kc', 'cckk', 'ckck', 'kkcc'],
S=1,
M=-1)
print("constructed dual basis")
opdm_a = Tensor(opdm_a, name='ck_a')
opdm_b = Tensor(opdm_b, name='ck_b')
oqdm_a = Tensor(np.eye(dim // 2) - opdm_a.data, name='kc_a')
oqdm_b = Tensor(np.eye(dim // 2) - opdm_b.data, name='kc_b')
tpdm_aa = Tensor(tpdm_aa, name='cckk_aa', basis=bij_bas_aa)
tpdm_bb = Tensor(tpdm_bb, name='cckk_bb', basis=bij_bas_aa)
tpdm_ab = Tensor(tpdm_ab, name='cckk_ab', basis=bij_bas_ab)
tqdm_aa = Tensor(tqdm_aa, name='kkcc_aa', basis=bij_bas_aa)
tqdm_bb = Tensor(tqdm_bb, name='kkcc_bb', basis=bij_bas_aa)
tqdm_ab = Tensor(tqdm_ab, name='kkcc_ab', basis=bij_bas_ab)
phdm_ab = Tensor(phdm_ab, name='ckck_ab', basis=bij_bas_ab)
phdm_ba = Tensor(phdm_ba, name='ckck_ba', basis=bij_bas_ab)
phdm_aabb = Tensor(phdm_aabb, name='ckck_aabb')
dtensor = MultiTensor([
opdm_a, opdm_b, oqdm_a, oqdm_b, tpdm_aa, tpdm_bb, tpdm_ab, tqdm_aa,
tqdm_bb, tqdm_ab, phdm_ab, phdm_ba, phdm_aabb
])
copdm_a = opdm_a_interaction
copdm_b = opdm_b_interaction
coqdm_a = Tensor(np.zeros((spatial_basis_rank, spatial_basis_rank)),
name='kc_a')
coqdm_b = Tensor(np.zeros((spatial_basis_rank, spatial_basis_rank)),
name='kc_b')
ctpdm_aa = v2aa
ctpdm_bb = v2bb
ctpdm_ab = v2ab
ctqdm_aa = Tensor(np.zeros_like(v2aa.data),
name='kkcc_aa',
basis=bij_bas_aa)
ctqdm_bb = Tensor(np.zeros_like(v2bb.data),
name='kkcc_bb',
basis=bij_bas_aa)
ctqdm_ab = Tensor(np.zeros_like(v2ab.data),
name='kkcc_ab',
basis=bij_bas_ab)
cphdm_ab = Tensor(np.zeros((spatial_basis_rank**2, spatial_basis_rank**2)),
name='ckck_ab',
basis=bij_bas_ab)
cphdm_ba = Tensor(np.zeros((spatial_basis_rank**2, spatial_basis_rank**2)),
name='ckck_ba',
basis=bij_bas_ab)
cphdm_aabb = Tensor(np.zeros(
(2 * spatial_basis_rank**2, 2 * spatial_basis_rank**2)),
name='ckck_aabb')
ctensor = MultiTensor([
copdm_a, copdm_b, coqdm_a, coqdm_b, ctpdm_aa, ctpdm_bb, ctpdm_ab,
ctqdm_aa, ctqdm_bb, ctqdm_ab, cphdm_ab, cphdm_ba, cphdm_aabb
])
print(
(ctensor.vectorize_tensors().T @ dtensor.vectorize_tensors())[0,
0].real)
print(gs_energy)
ctensor.dual_basis = dual_basis
A, _, b = ctensor.synthesize_dual_basis()
print("size of dual basis", len(dual_basis.elements))
print(A @ dtensor.vectorize_tensors() - b)
nc, nv = A.shape
A.eliminate_zeros()
nnz = A.nnz
from sdpsolve.sdp import SDP
from sdpsolve.solvers.bpsdp import solve_bpsdp
from sdpsolve.solvers.bpsdp.bpsdp_old import solve_bpsdp
from sdpsolve.utils.matreshape import vec2block
sdp = SDP()
sdp.nc = nc
sdp.nv = nv
sdp.nnz = nnz
sdp.blockstruct = list(map(lambda x: int(np.sqrt(x.size)),
ctensor.tensors))
sdp.nb = len(sdp.blockstruct)
sdp.Amat = A.real
sdp.bvec = b.todense().real
sdp.cvec = ctensor.vectorize_tensors().real
sdp.Initialize()
epsilon = 1.0E-7
sdp.epsilon = float(epsilon)
sdp.epsilon_inner = float(epsilon) / 100
sdp.disp = True
sdp.iter_max = 70000
sdp.inner_solve = 'CG'
sdp.inner_iter_max = 2
# # sdp_data = solve_bpsdp(sdp)
solve_bpsdp(sdp)
# # create all the psd-matrices for the
# variable_dictionary = {}
# for tensor in ctensor.tensors:
# linear_dim = int(np.sqrt(tensor.size))
# variable_dictionary[tensor.name] = cvx.Variable(shape=(linear_dim, linear_dim), PSD=True, name=tensor.name)
# print("constructing constraints")
# constraints = []
# for dbe in dual_basis:
# single_constraint = []
# for tname, v_elements, p_coeffs in dbe:
# active_indices = get_var_indices(ctensor.tensors[tname], v_elements)
# single_constraint.append(variable_dictionary[tname][active_indices] * p_coeffs)
# constraints.append(cvx.sum(single_constraint) == dbe.dual_scalar)
# print('constraints constructed')
# print("constructing the problem")
# objective = cvx.Minimize(
# cvx.trace(copdm_a.data @ variable_dictionary['ck_a']) +
# cvx.trace(copdm_b.data @ variable_dictionary['ck_b']) +
# cvx.trace(ctpdm_aa.data @ variable_dictionary['cckk_aa']) +
# cvx.trace(ctpdm_bb.data @ variable_dictionary['cckk_bb']) +
# cvx.trace(ctpdm_ab.data @ variable_dictionary['cckk_ab']))
# cvx_problem = cvx.Problem(objective, constraints=constraints)
# print('problem constructed')
# cvx_problem.solve(solver=cvx.SCS, verbose=True, eps=0.5E-5, max_iters=100000)
# rdms_solution = vec2block(sdp.blockstruct, sdp.primal)
print(gs_energy)
# print(cvx_problem.value + nuclear_repulsion)
# print(sdp_data.primal_value() + nuclear_repulsion)
print(sdp.primal.T @ sdp.cvec)
print(nuclear_repulsion)
rdms = vec2block(sdp.blockstruct, sdp.primal)
tpdm = unspin_adapt(rdms[4], rdms[5], rdms[6])
print(np.einsum('ijij', tpdm))
tpdm = np.einsum('ijkl->ijlk', tpdm)