def test_solver_via_rdms():
molecule = build_lih_moleculardata()
n_electrons = molecule.n_electrons
sz = 0
oei, tei = molecule.get_integrals()
elec_hamil = fqe.restricted_hamiltonian.RestrictedHamiltonian(
(oei, np.einsum("ijlk", -0.5 * tei)))
soei, stei = spinorb_from_spatial(oei, tei)
astei = np.einsum('ijkl', stei) - np.einsum('ijlk', stei)
molecular_hamiltonian = of.InteractionOperator(0, soei, 0.25 * astei)
reduced_ham = of.chem.make_reduced_hamiltonian(molecular_hamiltonian,
molecule.n_electrons)
fqe_wf = fqe.Wavefunction([[n_electrons, sz, molecule.n_orbitals]])
graph = fqe_wf.sector((n_electrons, sz)).get_fcigraph()
fci_coeffs = np.zeros((graph.lena(), graph.lenb()), dtype=np.complex128)
fci_coeffs[0, 0] = 1.0
fqe_wf.set_wfn(strategy="from_data",
raw_data={(n_electrons, sz): fci_coeffs})
bcsolve = BrillouinCondition(molecule, run_parallel=False)
assert bcsolve.reduced_ham == reduced_ham
for pp, qq in zip(elec_hamil.tensors(), bcsolve.elec_hamil.tensors()):
assert np.allclose(pp, qq)
bcsolve.iter_max = 1
bcsolve.bc_solve_rdms(fqe_wf)
assert np.allclose(bcsolve.acse_energy,
[-8.957417182801088, -8.969256797233033])
def test_get_l_m():
molecule = build_lih_moleculardata()
oei, tei = molecule.get_integrals()
lrt_obj = LowRankTrotter(oei=oei, tei=tei)
num_l, m_list = lrt_obj.get_l_and_m(1.0e-8, 1.0e-8)
assert isinstance(num_l, int)
assert isinstance(m_list, list)
assert len(m_list) == num_l
def test_initialization():
empty = LowRankTrotter()
obj_attributes = ["molecule", "oei", "tei", "icut", "lmax", "mcut", "mmax"]
for oa in obj_attributes:
assert hasattr(empty, oa)
molecule = build_lih_moleculardata()
oei, tei = molecule.get_integrals()
molecule_load = LowRankTrotter(molecule=molecule)
assert np.allclose(molecule_load.oei, oei)
assert np.allclose(molecule_load.tei, tei)
assert np.isclose(molecule_load.icut, 1.0e-8)
assert np.isclose(molecule_load.mcut, 1.0e-8)
def test_second_factorization():
molecule = build_lih_moleculardata()
oei, tei = molecule.get_integrals()
lrt_obj = LowRankTrotter(oei=oei, tei=tei)
eigenvalues, one_body_squares, _ = lrt_obj.first_factorization()
s_rho_rho, basis_changes = lrt_obj.second_factorization(
eigenvalues, one_body_squares)
true_basis_changes = []
for l in range(one_body_squares.shape[0]):
w, v = np.linalg.eigh(one_body_squares[l][::2, ::2])
true_basis_changes.append(v.conj().T)
assert np.allclose(v.conj().T, basis_changes[l])
assert np.allclose(s_rho_rho[l], eigenvalues[l] * np.outer(w, w))
def test_vbc():
molecule = build_lih_moleculardata()
n_electrons = molecule.n_electrons
oei, tei = molecule.get_integrals()
nalpha = molecule.n_electrons // 2
nbeta = nalpha
sz = nalpha - nbeta
fqe_wf = fqe.Wavefunction([[n_electrons, sz, molecule.n_orbitals]])
fqe_wf.set_wfn(strategy='hartree-fock')
adapt = VBC(oei, tei, nalpha, nbeta, iter_max=1, verbose=False)
adapt.vbc(fqe_wf)
assert np.isclose(adapt.energies[0], -8.957417182801091)
assert np.isclose(adapt.energies[-1], -8.97304439380826)
def test_trotter_prep():
times = [0.1, 0.2, 0.3]
molecule = build_lih_moleculardata()
oei, tei = molecule.get_integrals()
lrt_obj = LowRankTrotter(oei=oei, tei=tei)
(
eigenvalues,
one_body_squares,
one_body_correction,
) = lrt_obj.first_factorization()
(
scaled_density_density_matrices,
basis_change_matrices,
) = lrt_obj.second_factorization(eigenvalues, one_body_squares)
for tt in times:
# get values from function to test
test_tbasis, test_srr = lrt_obj.prepare_trotter_sequence(tt)
# compute true values
trotter_basis_change = [
basis_change_matrices[0] @ expm(
-1j * tt * (lrt_obj.oei + one_body_correction[::2, ::2]))
]
time_scaled_rho_rho_matrices = []
for ii in range(len(basis_change_matrices) - 1):
trotter_basis_change.append(basis_change_matrices[ii + 1]
@ basis_change_matrices[ii].conj().T)
time_scaled_rho_rho_matrices.append(
tt * scaled_density_density_matrices[ii])
time_scaled_rho_rho_matrices.append(tt *
scaled_density_density_matrices[-1])
trotter_basis_change.append(basis_change_matrices[ii + 1].conj().T)
assert len(trotter_basis_change) == len(test_tbasis)
assert len(time_scaled_rho_rho_matrices) == len(test_srr)
# check against true values
for t1, t2 in zip(trotter_basis_change, test_tbasis):
assert np.allclose(t1, t2)
assert np.allclose(t1.conj().T @ t1, np.eye(t1.shape[0]))
for t1, t2 in zip(test_srr, time_scaled_rho_rho_matrices):
assert np.allclose(t1, t2)
assert of.is_hermitian(t1)
def test_adapt():
molecule = build_lih_moleculardata()
n_electrons = molecule.n_electrons
oei, tei = molecule.get_integrals()
norbs = molecule.n_orbitals
nalpha = molecule.n_electrons // 2
nbeta = nalpha
sz = nalpha - nbeta
occ = list(range(nalpha))
virt = list(range(nalpha, norbs))
soei, stei = spinorb_from_spatial(oei, tei)
astei = np.einsum('ijkl', stei) - np.einsum('ijlk', stei)
molecular_hamiltonian = of.InteractionOperator(0, soei, 0.25 * astei)
reduced_ham = of.chem.make_reduced_hamiltonian(molecular_hamiltonian,
molecule.n_electrons)
fqe_wf = fqe.Wavefunction([[n_electrons, sz, molecule.n_orbitals]])
fqe_wf.set_wfn(strategy='hartree-fock')
sop = OperatorPool(norbs, occ, virt)
sop.two_body_sz_adapted() # initialize pool
adapt = ADAPT(oei, tei, sop, nalpha, nbeta, iter_max=1, verbose=False)
assert np.isclose(
np.linalg.norm(adapt.reduced_ham.two_body_tensor -
reduced_ham.two_body_tensor), 0)
adapt.adapt_vqe(fqe_wf)
assert np.isclose(adapt.energies[0], -8.957417182801091)
assert np.isclose(adapt.energies[-1], -8.970532463968661)
sop = OperatorPool(norbs, occ, virt)
sop.one_body_sz_adapted()
adapt = ADAPT(oei,
tei,
sop,
nalpha,
nbeta,
iter_max=10,
stopping_epsilon=10,
verbose=True)
adapt.adapt_vqe(fqe_wf)
assert np.isclose(adapt.energies[-1], -8.957417182801091)
assert np.isclose(adapt.energies[0], -8.95741717733075)
def test_first_factorization():
molecule = build_lih_moleculardata()
oei, tei = molecule.get_integrals()
lrt_obj = LowRankTrotter(oei=oei, tei=tei)
(
eigenvalues,
one_body_squares,
one_body_correction,
) = lrt_obj.first_factorization()
# get true op
n_qubits = molecule.n_qubits
fermion_tei = of.FermionOperator()
test_tei_tensor = np.zeros((n_qubits, n_qubits, n_qubits, n_qubits))
for p, q, r, s in product(range(oei.shape[0]), repeat=4):
if np.abs(tei[p, q, r, s]) < EQ_TOLERANCE:
coefficient = 0.0
else:
coefficient = tei[p, q, r, s] / 2.0
for sigma, tau in product(range(2), repeat=2):
if 2 * p + sigma == 2 * q + tau or 2 * r + tau == 2 * s + sigma:
continue
term = (
(2 * p + sigma, 1),
(2 * q + tau, 1),
(2 * r + tau, 0),
(2 * s + sigma, 0),
)
fermion_tei += of.FermionOperator(term, coefficient=coefficient)
test_tei_tensor[2 * p + sigma, 2 * q + tau, 2 * r + tau, 2 * s +
sigma] = coefficient
mol_ham = of.InteractionOperator(
one_body_tensor=np.zeros((n_qubits, n_qubits)),
two_body_tensor=test_tei_tensor,
constant=0,
)
# check induced norm on operator
checked_op = of.FermionOperator()
for (
p,
q,
) in product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = one_body_correction[p, q]
checked_op += of.FermionOperator(term, coefficient)
# Build back two-body component.
for l in range(one_body_squares.shape[0]):
one_body_operator = of.FermionOperator()
for p, q in product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = one_body_squares[l, p, q]
one_body_operator += of.FermionOperator(term, coefficient)
checked_op += eigenvalues[l] * (one_body_operator**2)
true_fop = of.normal_ordered(of.get_fermion_operator(mol_ham))
difference = of.normal_ordered(checked_op - true_fop)
assert np.isclose(0, difference.induced_norm())
def test_generalized_doubles_takagi():
molecule = build_lih_moleculardata()
oei, tei = molecule.get_integrals()
nele = 4
nalpha = 2
nbeta = 2
sz = 0
norbs = oei.shape[0]
nso = 2 * norbs
fqe_wf = fqe.Wavefunction([[nele, sz, norbs]])
fqe_wf.set_wfn(strategy='hartree-fock')
fqe_wf.normalize()
_, tpdm = fqe_wf.sector((nele, sz)).get_openfermion_rdms()
d3 = fqe_wf.sector((nele, sz)).get_three_pdm()
soei, stei = spinorb_from_spatial(oei, tei)
astei = np.einsum('ijkl', stei) - np.einsum('ijlk', stei)
molecular_hamiltonian = of.InteractionOperator(0, soei, 0.25 * astei)
reduced_ham = make_reduced_hamiltonian(molecular_hamiltonian,
nalpha + nbeta)
acse_residual = two_rdo_commutator_symm(reduced_ham.two_body_tensor, tpdm,
d3)
for p, q, r, s in product(range(nso), repeat=4):
if p == q or r == s:
continue
assert np.isclose(acse_residual[p, q, r, s],
-acse_residual[s, r, q, p].conj())
Zlp, Zlm, _, one_body_residual = doubles_factorization_takagi(acse_residual)
test_fop = get_fermion_op(one_body_residual)
# test the first four factors
for ll in range(4):
test_fop += 0.25 * get_fermion_op(Zlp[ll])**2
test_fop += 0.25 * get_fermion_op(Zlm[ll])**2
op1mat = Zlp[ll]
op2mat = Zlm[ll]
w1, v1 = sp.linalg.schur(op1mat)
w1 = np.diagonal(w1)
assert np.allclose(v1 @ np.diag(w1) @ v1.conj().T, op1mat)
v1c = v1.conj()
w2, v2 = sp.linalg.schur(op2mat)
w2 = np.diagonal(w2)
assert np.allclose(v2 @ np.diag(w2) @ v2.conj().T, op2mat)
oww1 = np.outer(w1, w1)
fqe_wf = fqe.Wavefunction([[nele, sz, norbs]])
fqe_wf.set_wfn(strategy='hartree-fock')
fqe_wf.normalize()
nfqe_wf = fqe.get_number_conserving_wavefunction(nele, norbs)
nfqe_wf.sector((nele, sz)).coeff = fqe_wf.sector((nele, sz)).coeff
this_generatory = np.einsum('pi,si,ij,qj,rj->pqrs', v1, v1c, oww1, v1,
v1c)
fop = of.FermionOperator()
for p, q, r, s in product(range(nso), repeat=4):
op = ((p, 1), (s, 0), (q, 1), (r, 0))
fop += of.FermionOperator(op,
coefficient=this_generatory[p, q, r, s])
fqe_fop = build_hamiltonian(1j * fop, norb=norbs, conserve_number=True)
exact_wf = fqe.apply_generated_unitary(nfqe_wf, 1, 'taylor', fqe_fop)
test_wf = fqe.algorithm.low_rank.evolve_fqe_givens_unrestricted(
nfqe_wf,
v1.conj().T)
test_wf = fqe.algorithm.low_rank.evolve_fqe_charge_charge_unrestricted(
test_wf, -oww1.imag)
test_wf = fqe.algorithm.low_rank.evolve_fqe_givens_unrestricted(
test_wf, v1)
assert np.isclose(abs(fqe.vdot(test_wf, exact_wf))**2, 1)