def v2rdm_hubbard_open_shell():
import openfermion as of
e_fci = []
e_rdm = []
for U in [1]: # range(1, 11):
sites = 5
hubbard = of.hamiltonians.fermi_hubbard(1,
sites,
tunneling=1,
coulomb=U,
chemical_potential=0,
magnetic_field=0,
periodic=True,
spinless=False)
hamiltonian = of.get_interaction_operator(hubbard)
op_mat = of.get_number_preserving_sparse_operator(
hubbard, 2 * sites, sites, spin_preserving=True).toarray()
sz_mat = of.get_number_preserving_sparse_operator(
of.sz_operator(sites), 2 * sites, sites,
spin_preserving=True).toarray()
s2_mat = of.get_number_preserving_sparse_operator(
of.s_squared_operator(sites),
2 * sites,
sites,
spin_preserving=True).toarray()
w, v = np.linalg.eigh(op_mat)
sz_exp = []
s2_exp = []
for ii in range(len(w)):
sz_exp.append((v[:, [ii]].conj().T @ sz_mat @ v[:, [ii]])[0,
0].real)
s2_exp.append((v[:, [ii]].conj().T @ s2_mat @ v[:, [ii]])[0,
0].real)
print(sz_exp[:10])
print(s2_exp[:10])
print(w[:10])
gs_e = w[0]
print(gs_e)
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 = sites
print('n_electrons', n_electrons)
Na = 1 + (n_electrons // 2)
Nb = n_electrons // 2
spatial_basis_rank = sites
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.real,
one_body_ints.real)
v2ab_mat = np.zeros_like(v2ab.data)
for i in range(spatial_basis_rank):
# ia^ j^b j^b ia
idx = bij_bas_ab.rev((i, i))
v2ab_mat[idx, idx] = U
v2ab = Tensor(v2ab_mat, basis=v2ab.basis, name=v2ab.name)
dual_basis = sz_adapted_linear_constraints(
spatial_basis_rank,
Na,
Nb, ['ck', 'cckk', 'kkcc', 'ckck'],
S=0.5,
M=0.5)
print("constructed dual basis")
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 * spatial_basis_rank,
spatial_basis_rank * spatial_basis_rank)),
name='ckck_ab',
basis=bij_bas_ab)
cphdm_ba = Tensor(np.zeros((spatial_basis_rank * spatial_basis_rank,
spatial_basis_rank * spatial_basis_rank)),
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
])
ctensor.dual_basis = dual_basis
A, _, b = ctensor.synthesize_dual_basis()
print("size of dual basis", len(dual_basis.elements))
nc, nv = A.shape
nnz = A.nnz
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 = 0.5e-5
sdp.epsilon = float(epsilon)
sdp.epsilon_inner = float(epsilon)
sdp.disp = True
sdp.iter_max = 50000
sdp.inner_iter_max = 1
sdp.inner_solve = 'CG'
sdp_data = solve_bpsdp(sdp)
print(sdp.primal.T @ sdp.cvec, gs_e)
def sdp_nrep_sz_reconstruction(corrupted_tpdm_aa,
corrupted_tpdm_bb,
corrupted_tpdm_ab,
num_alpha,
num_beta,
disp=False,
inner_iter_type='EXACT',
epsilon=1.0E-8,
max_iter=5000):
if np.ndim(corrupted_tpdm_aa) != 2:
raise TypeError("corrupted_tpdm_aa must be a 2-tensor")
if np.ndim(corrupted_tpdm_bb) != 2:
raise TypeError("corrupted_tpdm_bb must be a 2-tensor")
if np.ndim(corrupted_tpdm_ab) != 2:
raise TypeError("corrupted_tpdm_ab must be a 2-tensor")
if num_alpha != num_beta:
raise ValueError(
"right now we are not supporting differing spin numbers")
spatial_basis_rank = int(np.sqrt(corrupted_tpdm_ab.shape[0]))
# get basis bijection
bij_bas_aa, bij_bas_ab = geminal_spin_basis(spatial_basis_rank)
# build basis look up table
bas_aa = {}
bas_ab = {}
cnt_aa = 0
cnt_ab = 0
# iterate over spatial orbital indices
for p, q in product(range(spatial_basis_rank), repeat=2):
if q > p:
bas_aa[(p, q)] = cnt_aa
cnt_aa += 1
bas_ab[(p, q)] = cnt_ab
cnt_ab += 1
dual_basis = sz_adapted_linear_constraints(spatial_basis_rank, num_alpha,
num_beta,
['ck', 'cckk', 'kkcc', 'ckck'])
dual_basis += d2_e2_mapping(spatial_basis_rank, bas_aa, bas_ab,
corrupted_tpdm_aa, corrupted_tpdm_bb,
corrupted_tpdm_ab)
c_cckk_me_aa = spin_orbital_marginal_norm_min(corrupted_tpdm_aa.shape[0],
tensor_name='cckk_me_aa')
c_cckk_me_bb = spin_orbital_marginal_norm_min(corrupted_tpdm_bb.shape[0],
tensor_name='cckk_me_bb')
c_cckk_me_ab = spin_orbital_marginal_norm_min(corrupted_tpdm_ab.shape[0],
tensor_name='cckk_me_ab')
copdm_a = Tensor(np.zeros((spatial_basis_rank, spatial_basis_rank)),
name='ck_a')
copdm_b = Tensor(np.zeros((spatial_basis_rank, spatial_basis_rank)),
name='ck_b')
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 = Tensor(np.zeros_like(corrupted_tpdm_aa),
name='cckk_aa',
basis=bij_bas_aa)
ctpdm_bb = Tensor(np.zeros_like(corrupted_tpdm_bb),
name='cckk_bb',
basis=bij_bas_aa)
ctpdm_ab = Tensor(np.zeros_like(corrupted_tpdm_ab),
name='cckk_ab',
basis=bij_bas_ab)
ctqdm_aa = Tensor(np.zeros_like(corrupted_tpdm_aa),
name='kkcc_aa',
basis=bij_bas_aa)
ctqdm_bb = Tensor(np.zeros_like(corrupted_tpdm_bb),
name='kkcc_bb',
basis=bij_bas_aa)
ctqdm_ab = Tensor(np.zeros_like(corrupted_tpdm_ab),
name='kkcc_ab',
basis=bij_bas_ab)
cphdm_ab = Tensor(np.zeros((spatial_basis_rank, spatial_basis_rank,
spatial_basis_rank, spatial_basis_rank)),
name='ckck_ab')
cphdm_ba = Tensor(np.zeros((spatial_basis_rank, spatial_basis_rank,
spatial_basis_rank, spatial_basis_rank)),
name='ckck_ba')
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,
c_cckk_me_aa, c_cckk_me_bb, c_cckk_me_ab
])
ctensor.dual_basis = dual_basis
A, _, b = ctensor.synthesize_dual_basis()
nc, nv = A.shape
nnz = A.nnz
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()
sdp.epsilon = float(epsilon)
sdp.epsilon_inner = float(epsilon)
sdp.inner_solve = inner_iter_type
sdp.disp = disp
sdp.iter_max = max_iter
solve_bpsdp(sdp)
rdms_solution = vec2block(sdp.blockstruct, sdp.primal)
return rdms_solution[4], rdms_solution[5], rdms_solution[6]
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)
def sdp_nrep_reconstruction(corrupted_tpdm, num_alpha, num_beta):
"""
Reconstruct a 2-RDm that looks like the input corrupted tpdm
This reconstruction scheme uses the spin-orbital reconstruction code which is not the optimal size SDP
:param corrupted_tpdm: measured 2-RDM from the device
:param num_alpha: number of alpha spin electrons
:param num_beta: number of beta spin electrons
:return: purified 2-RDM
"""
if np.ndim(corrupted_tpdm) != 4:
raise TypeError("corrupted_tpdm must be a 4-tensor")
if num_alpha != num_beta:
raise ValueError(
"right now we are not supporting differing spin numbers")
sp_dim = corrupted_tpdm.shape[0] # single-particle rank
opdm = np.zeros((sp_dim, sp_dim), dtype=int)
oqdm = np.zeros((sp_dim, sp_dim), dtype=int)
tpdm = np.zeros_like(corrupted_tpdm)
tqdm = np.zeros_like(corrupted_tpdm)
tgdm = np.zeros_like(corrupted_tpdm)
opdm = Tensor(tensor=opdm, name='ck')
oqdm = Tensor(tensor=oqdm, name='kc')
tpdm = Tensor(tensor=tpdm, name='cckk')
tqdm = Tensor(tensor=tqdm, name='kkcc')
tgdm = Tensor(tensor=tgdm, name='ckck')
error_matrix = spin_orbital_marginal_norm_min(sp_dim**2,
tensor_name='cckk_me')
rdms = MultiTensor([opdm, oqdm, tpdm, tqdm, tgdm, error_matrix])
db = spin_orbital_linear_constraints(sp_dim, num_alpha + num_beta,
['ck', 'cckk', 'kkcc', 'ckck'])
db += d2_e2_mapping_spinorbital(sp_dim, corrupted_tpdm)
rdms.dual_basis = db
A, _, c = rdms.synthesize_dual_basis()
nv = A.shape[1]
nc = A.shape[0]
nnz = A.nnz
blocklist = [
sp_dim, sp_dim, sp_dim**2, sp_dim**2, sp_dim**2, 2 * sp_dim**2
]
nb = len(blocklist)
sdp = SDP()
sdp.nc = nc
sdp.nv = nv
sdp.nnz = nnz
sdp.blockstruct = blocklist
sdp.nb = nb
sdp.Amat = A.real
sdp.bvec = c.todense().real
sdp.cvec = rdms.vectorize_tensors().real
sdp.Initialize()
sdp.epsilon = float(1.0E-8)
sdp.inner_solve = "EXACT"
sdp.disp = True
solve_bpsdp(sdp)
solution_rdms = vec2block(blocklist, sdp.primal)
tpdm_reconstructed = np.zeros_like(corrupted_tpdm)
for p, q, r, s in product(range(sp_dim), repeat=4):
tpdm_reconstructed[p, q, r, s] = solution_rdms[2][p * sp_dim + q,
r * sp_dim + s]
return tpdm_reconstructed