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_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_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 spin_adapted_interaction_tensor(two_body_int, one_body_int):
"""
Construct the cost operator in symmetric and antisymmetric basis
The spin-orbital integrals are in the spin-less fermion basis.
Spin-full fermions are index by even/odd
:param two_body_int:
:param one_body_int:
:return:
"""
sp_dim = int(one_body_int.shape[0] / 2)
one_body_spatial_int = np.zeros((sp_dim, sp_dim), dtype=float)
even_set = one_body_int[::2, ::2].copy()
for p, q in product(range(sp_dim), repeat=2):
one_body_spatial_int[p, q] = one_body_int[2 * p, 2 * q]
assert np.allclose(even_set, one_body_spatial_int)
opdm_a_interaction = Tensor(one_body_spatial_int, name='ck_a')
opdm_b_interaction = Tensor(one_body_spatial_int, name='ck_b')
aa_dim = int(sp_dim * (sp_dim - 1) / 2)
ab_dim = int(sp_dim**2)
v2aa = np.zeros((aa_dim, aa_dim))
v2bb = np.zeros_like(v2aa)
v2ab = np.zeros((ab_dim, ab_dim))
b_aa_dict = {}
b_ab_dict = {}
cnt, cnt2 = 0, 0
for i, j in product(range(sp_dim), repeat=2):
if i < j:
b_aa_dict[(i, j)] = cnt
cnt += 1
b_ab_dict[(i, j)] = cnt2
cnt2 += 1
for p, q, r, s in product(range(sp_dim), repeat=4):
if p < q and r < s:
# 0.5 still there because antisymmetric basis becomes <ij|kl> -
# <ij|lk>. The 0.5 for coulomb interaction counting is still
# needed to avoid double counting
v2aa[b_aa_dict[(p, q)], b_aa_dict[(
r, s)]] = 0.5 * (two_body_int[2 * p, 2 * q, 2 * r, 2 * s] -
two_body_int[2 * p, 2 * q, 2 * s, 2 * r])
v2bb[b_aa_dict[(p, q)], b_aa_dict[(r, s)]] = 0.5 * (
two_body_int[2 * p + 1, 2 * q + 1, 2 * r + 1, 2 * s + 1] -
two_body_int[2 * p + 1, 2 * q + 1, 2 * s + 1, 2 * r + 1])
v2ab[b_ab_dict[(p, q)],
b_ab_dict[(r, s)]] = two_body_int[2 * p, 2 * q + 1, 2 * r,
2 * s + 1]
bas_aa, bas_ab = geminal_spin_basis(sp_dim)
v2ab = Tensor(v2ab, basis=bas_ab, name='cckk_ab')
v2bb = Tensor(v2bb, basis=bas_aa, name='cckk_bb')
v2aa = Tensor(v2aa, basis=bas_aa, name='cckk_aa')
return opdm_a_interaction, opdm_b_interaction, v2aa, v2bb, v2ab
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():
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_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 make_sz_spin_adapted_hamiltonian(oei, tei):
"""
Make the sz spin-adapted Hamiltonian tensors
tei = <i, j, k, l> corresponds to i(1)* j(2)* k(2) l(1)
To derive
x, y are spin-variable index
0.5 * sum{pqrs}V_{pqrs} sum_{x, y} (px)^ (qy)^ (ry) (sx)
:param oei: spatial one-electron integrals
:param tei: spatial two-electron integrals
"""
sdim = oei.shape[0]
bas_aa = {}
bas_ab = {}
cnt_aa = 0
cnt_ab = 0
for p, q in product(range(sdim), repeat=2):
if p < q:
bas_aa[(p, q)] = cnt_aa
cnt_aa += 1
bas_ab[(p, q)] = cnt_ab
cnt_ab += 1
v2aa = np.zeros((sdim * (sdim - 1) // 2, sdim * (sdim - 1) // 2))
v2ab = np.zeros((sdim * sdim, sdim * sdim))
rev_bas_aa = dict(zip(bas_aa.values(), bas_aa.keys()))
rev_bas_ab = dict(zip(bas_ab.values(), bas_ab.keys()))
for r, s in product(range(len(bas_aa)), repeat=2):
i, j = rev_bas_aa[r]
k, l = rev_bas_aa[s]
v2aa[r, s] = 0.5 * (tei[i, j, l, k] - tei[j, i, l, k] -
tei[i, j, k, l] + tei[j, i, k, l])
for r, s in product(range(len(bas_ab)), repeat=2):
i, j = rev_bas_ab[r]
k, l = rev_bas_ab[s]
# we don't multiply by 0.5 because we count alpha-beta and beta-alpha
v2ab[r, s] = tei[i, j, l, k]
opdm_a = Tensor(oei, name='ck_a')
opdm_b = Tensor(oei, name='ck_b')
bas_aa, bas_ab = geminal_spin_basis(sdim)
v2ab = Tensor(v2ab, basis=bas_ab, name='cckk_ab')
v2bb = Tensor(v2aa, basis=bas_aa, name='cckk_bb')
v2aa = Tensor(v2aa, basis=bas_aa, name='cckk_aa')
return opdm_a, opdm_b, v2aa, v2bb, v2ab
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_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_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)
def v2rdm_hubbard():
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
import openfermion as of
e_fci = []
e_rdm = []
for U in [4]: # 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)
# op_mat = of.get_sparse_operator(hubbard).toarray()
# # op_mat = of.get_number_preserving_sparse_operator(hubbard, sites * 2, sites-1).toarray()
# w, v = np.linalg.eigh(op_mat)
# # w_idx = 5 # N4U4
# # w_idx = 25 # N6 U4
# w_idx = 4
# n_density = v[:, [w_idx]] @ v[:, [w_idx]].conj().T
# from representability.fermions.density.antisymm_sz_density import AntiSymmOrbitalDensity
# density = AntiSymmOrbitalDensity(n_density, sites * 2)
# tpdm_aa, tpdm_bb, tpdm_ab, [bas_aa, bas_ab] = density.construct_tpdm()
# rev_bas_aa = dict(zip(bas_aa.values(), bas_aa.keys()))
# rev_bas_ab = dict(zip(bas_ab.values(), bas_ab.keys()))
# for r, s in product(range(sites), repeat=2):
# i, j = rev_bas_ab[r]
# k, l = rev_bas_ab[s]
# 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(sites)
# opdm_a = Tensor(opdm_a, name='ck_a')
# opdm_b = Tensor(opdm_b, name='ck_b')
# oqdm_a = Tensor(np.eye(4) - opdm_a.data, name='kc_a')
# oqdm_b = Tensor(np.eye(4) - opdm_b.data, name='kc_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')
# rdms = 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])
# rdmvec = rdms.vectorize_tensors()
hamiltonian = of.get_interaction_operator(hubbard)
op_mat = of.get_number_preserving_sparse_operator(
hubbard, 2 * sites, sites - 1, spin_preserving=False).toarray()
w, _ = np.linalg.eigh(op_mat)
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 - 1
print('n_electrons', n_electrons)
Na = n_electrons // 2
Nb = n_electrons // 2
dim = one_body_ints.shape[0]
spatial_basis_rank = sites
sdim = spatial_basis_rank
mm = dim**2
bij_bas_aa, bij_bas_ab = geminal_spin_basis(spatial_basis_rank)
# h1, v2 = spin_orbital_interaction_tensor(two_body_ints, one_body_ints)
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'])
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))
# print(tpdm_ab.data.trace())
# print(ctensor.vectorize_tensors().T @ rdmvec)
# print(b.shape)
# print("FCI Residual ", np.linalg.norm(A @ rdmvec - b))
# exit()
nc, nv = A.shape
# A.eliminate_zeros()
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
Amat = A.toarray()
# print(A.shape)
# # DQ num vars: 4, 4, 4, 4, 6, 6, 16, 6, 6 16
# print("D2 size ", sum([x**2 for x in [6, 6, 16]]))
# print("D1Q1 size ", sum([x**2 for x in [4, 4, 4, 4]]))
# print("Spin constraint ", 16**2)
# print(sum([x**2 for x in [4, 4, 4, 4, 6, 6, 16, 16]]))
sm = sdim * (sdim - 1) // 2
uadapt = gen_trans_2rdm(sdim**2, sdim)
# spin_adapted_d2ab = uadapt.T @ tpdm_ab.data @ uadapt
# d2ab_sa_a = spin_adapted_d2ab[:sm, :sm]
# d2ab_sa_s = spin_adapted_d2ab[sm:, sm:]
# for r, s in product(range(sdim * (sdim - 1) // 2), repeat=2):
# i, j = bas_aa.fwd(r)
# k, l = bas_aa.fwd(s)
# # print((i, j, k, l), d2ab_sa_a[bas_aa.rev((i, j)), bas_aa.rev((k, l))],
# # uadapt[:, r].T @ tpdm_ab.data @ uadapt[:, s]
# # )
# assert np.isclose(d2ab_sa_a[bas_aa.rev((i, j)), bas_aa.rev((k, l))], uadapt[:, [r]].T @ tpdm_ab.data @ uadapt[:, [s]])
# assert np.isclose(d2ab_sa_a[bas_aa.rev((i, j)), bas_aa.rev((k, l))], np.trace(tpdm_ab.data @ (uadapt[:, [s]] @ uadapt[:, [r]].T)))
# assert np.isclose(d2ab_sa_a[bas_aa.rev((i, j)), bas_aa.rev((k, l))], np.einsum('ij,ij', tpdm_ab.data, (uadapt[:, [s]] @ uadapt[:, [r]].T)))
# assert np.isclose(tpdm_aa.data[r, s] + tpdm_aa.data[s, r], uadapt[:, [r]].T @ tpdm_ab.data @ uadapt[:, [s]] + uadapt[:, [s]].T @ tpdm_ab.data @ uadapt[:, [r]])
# assert np.isclose(tpdm_bb.data[r, s] + tpdm_bb.data[s, r], uadapt[:, [r]].T @ tpdm_ab.data @ uadapt[:, [s]] + uadapt[:, [s]].T @ tpdm_ab.data @ uadapt[:, [r]])
print("AA Dim: ", sdim * (sdim - 1) / 2, sm * (sm + 1) / 2)
for ii in range(Amat.shape[0]):
amats = vec2block(sdp.blockstruct, Amat[ii, :])
for aa in amats:
assert of.is_hermitian(aa)
sdp.Initialize()
epsilon = 1.0E-6
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'
write_sdpfile("new_hubbardN{}U{}_DQG.sdp".format(sites, U), sdp.nc,
sdp.nv, sdp.nnz, sdp.nb, sdp.Amat, sdp.bvec, sdp.cvec,
sdp.blockstruct)
# sdp_data = solve_bpsdp(sdp)
# sdp_data.primal_vector = rdmvec
# sdp.iter_max = 5000
# sdp_data = solve_bpsdp(sdp)
solve_rrsdp(sdp)
print(sdp.primal.T @ sdp.cvec, gs_e)
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 v2rdm_cvvxpy(one_body_ints, two_body_ints, Na, Nb):
"""
Generate a cvxpy Problem corresponding the variational 2-RDM method
Note: if you are using with integrals generated from OpenFermion
you need to reorder the 2-body ints before passing to this function.
this can be accomplished by changing the integrals using einsum
np.einsum('ijkl->ijlk', two_body_ints). the integrals can be found after
grabbing the hamiltonian from molecule.get_molecular_hamiltonian() and calling
the attribute `two_body_tensor`.
This routine returns a cvx problem corresponding to the v2-RDM DQG sdp.
This can be solved by calling cvx.Problem.solve(). We recommend using
the SCS solver.
:param one_body_ints: spinless Fermion one-body integrals
:param two_body_ints: spinless Fermion basis two-body integrals
:param Int Na: number of Fermions with alpha-spin
:param Int Nb: number of Fermions with beta-spin
:return: cvxpy Problem object, variable dictionary
:rtype: cvx.Problem
"""
dim = one_body_ints.shape[0] // 2
mm = dim**2
mn = dim * (dim - 1) // 2
h1a, h1b, v2aa, v2bb, v2ab = spin_adapted_interaction_tensor_rdm_consistent(
two_body_ints, one_body_ints)
print("constructing dual basis")
dual_basis = sz_adapted_linear_constraints(dim, Na, Nb,
['ck', 'cckk', 'kkcc', 'ckck'])
print("dual basis constructed")
bas_aa, bas_ab = geminal_spin_basis(dim)
v2ab.data *= 2.0
copdm_a = h1a
copdm_b = h1b
coqdm_a = Tensor(np.zeros((dim, dim)), name='kc_a')
coqdm_b = Tensor(np.zeros((dim, dim)), name='kc_b')
ctpdm_aa = v2aa
ctpdm_bb = v2bb
ctpdm_ab = v2ab
ctqdm_aa = Tensor(np.zeros((mn, mn)), name='kkcc_aa', basis=bas_aa)
ctqdm_bb = Tensor(np.zeros((mn, mn)), name='kkcc_bb', basis=bas_aa)
ctqdm_ab = Tensor(np.zeros((mm, mm)), name='kkcc_ab', basis=bas_ab)
cphdm_ab = Tensor(np.zeros((dim, dim, dim, dim)), name='ckck_ab')
cphdm_ba = Tensor(np.zeros((dim, dim, dim, dim)), name='ckck_ba')
cphdm_aabb = Tensor(np.zeros((2 * mm, 2 * mm)), 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
print('synthesizing dual basis')
# A, _, b = ctensor.synthesize_dual_basis()
print("dual basis synthesized")
# 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)
# vec_idx = ctensor.tensors[tname].index_vectorized(*v_elements)
# dim = int(np.sqrt(ctensor.tensors[tname].size))
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")
# construct the problem variable for cvx
objective = cvx.Minimize(
cvx.trace(copdm_a.data * variable_dictionary['ck_a']) +
cvx.trace(copdm_b.data * variable_dictionary['ck_b']) +
cvx.trace(v2aa.data * variable_dictionary['cckk_aa']) +
cvx.trace(v2bb.data * variable_dictionary['cckk_bb']) +
cvx.trace(v2ab.data * variable_dictionary['cckk_ab']))
cvx_problem = cvx.Problem(objective, constraints=constraints)
print('problem constructed')
return cvx_problem, variable_dictionary
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_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 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]
