def evolve_fqe_givens_unrestricted(wfn: Wavefunction,
u: np.ndarray) -> Wavefunction:
"""Evolve a wavefunction by u generated from a 1-body Hamiltonian.
Args:
wfn: 2^{n} x 1 vector.
u: (n x n) unitary matrix.
Returns:
New evolved wfn object.
"""
rotations, diagonal = givens_decomposition_square(u.copy())
# Iterate through each layer and time evolve by the appropriate
# fermion operators
for layer in rotations:
for givens in layer:
i, j, theta, phi = givens
if not np.isclose(phi, 0):
op = of.FermionOperator(((j, 1), (j, 0)), coefficient=-phi)
wfn = wfn.time_evolve(1.0, op)
if not np.isclose(theta, 0):
op = of.FermionOperator(
((i, 1),
(j, 0)), coefficient=-1j * theta) + of.FermionOperator(
((j, 1), (i, 0)), coefficient=1j * theta)
wfn = wfn.time_evolve(1.0, op)
# evolve the last diagonal phases
for idx, final_phase in enumerate(diagonal):
if not np.isclose(final_phase, 1.0):
op = of.FermionOperator(((idx, 1), (idx, 0)),
-np.angle(final_phase))
wfn = wfn.time_evolve(1.0, op)
return wfn
def evolve_fqe_givens_sector(wfn: Wavefunction, u: np.ndarray,
sector='alpha') -> Wavefunction:
"""Evolve a wavefunction by u generated from a 1-body Hamiltonian.
Args:
wfn: FQE Wavefunction on n-orbitals
u: (n x n) unitary matrix.
sector: Optional either 'alpha' or 'beta' indicating which sector
to rotate
Returns:
New evolved wfn object.
"""
if sector == 'alpha':
sigma = 0
elif sector == 'beta':
sigma = 1
else:
raise ValueError("Bad section variable. Either (alpha) or (beta)")
if not np.isclose(u.shape[0], wfn.norb()):
raise ValueError(
"unitary is not specified for the correct number of orbitals")
rotations, diagonal = givens_decomposition_square(u.copy())
# Iterate through each layer and time evolve by the appropriate
# fermion operators
for layer in rotations:
for givens in layer:
i, j, theta, phi = givens
if not np.isclose(phi, 0):
op = of.FermionOperator(
((2 * j + sigma, 1), (2 * j + sigma, 0)), coefficient=-phi)
wfn = wfn.time_evolve(1.0, op)
if not np.isclose(theta, 0):
op = of.FermionOperator(((2 * i + sigma, 1),
(2 * j + sigma, 0)),
coefficient=-1j * theta) + \
of.FermionOperator(((2 * j + sigma, 1),
(2 * i + sigma, 0)),
coefficient=1j * theta)
wfn = wfn.time_evolve(1.0, op)
# evolve the last diagonal phases
for idx, final_phase in enumerate(diagonal):
if not np.isclose(final_phase, 1.0):
op = of.FermionOperator(
((2 * idx + sigma, 1), (2 * idx + sigma, 0)),
-np.angle(final_phase))
wfn = wfn.time_evolve(1.0, op)
return wfn
def evolve_fqe_charge_charge_sector(wfn: Wavefunction,
vij_mat: np.ndarray,
sector='alpha',
time=1) -> Wavefunction:
r"""Utility for testing evolution of a full 2^{n} wavefunction via
:math:`exp{-i time * \sum_{i,j}v_{i, j}n_{i, alpha}n_{j, beta}}.`
Args:
wfn: fqe_wf with sdim = n
vij_mat: List[(n x n] matrices n is the spatial orbital rank
time: evolution time.
Returns:
New evolved 2^{2 * n} x 1 vector
"""
if sector == 'alpha':
sigma = 0
elif sector == 'beta':
sigma = 1
else:
raise ValueError("Sector must be alpha or beta.")
norbs = vij_mat.shape[0]
for p, q in product(range(norbs), repeat=2):
if np.isclose(vij_mat[p, q], 0):
continue
fop = of.FermionOperator(((2 * p + sigma, 1), (2 * p + sigma, 0),
(2 * q + sigma, 1), (2 * q + sigma, 0)),
coefficient=vij_mat[p, q])
wfn = wfn.time_evolve(time, fop)
return wfn
def test_apply_individual_nbody_error(self):
fop = FermionOperator('1^ 0')
fop += FermionOperator('2^ 0')
fop += FermionOperator('2^ 1')
hamil = sparse_hamiltonian.SparseHamiltonian(fop)
wfn = Wavefunction([[2, 0, 2]], broken=['spin'])
self.assertRaises(ValueError, wfn._apply_individual_nbody, hamil)
self.assertRaises(ValueError, wfn._evolve_individual_nbody, 0.1, hamil)
fop = FermionOperator('1^ 0')
fop += FermionOperator('2^ 0')
hamil = sparse_hamiltonian.SparseHamiltonian(fop)
self.assertRaises(ValueError, wfn._evolve_individual_nbody, 0.1, hamil)
fop = FermionOperator('1^ 0', 1.0)
fop += FermionOperator('0^ 1', 0.9)
hamil = sparse_hamiltonian.SparseHamiltonian(fop)
self.assertRaises(ValueError, wfn._evolve_individual_nbody, 0.1, hamil)
fop = FermionOperator('1^ 0^')
hamil = sparse_hamiltonian.SparseHamiltonian(fop)
self.assertRaises(ValueError, wfn._apply_individual_nbody, hamil)
self.assertRaises(ValueError, wfn._evolve_individual_nbody, 0.1, hamil)
self.assertRaises(TypeError, wfn._evolve_individual_nbody, 0.1, 1)
def test_apply_type_error(self):
data = numpy.zeros((2, 2), dtype=numpy.complex128)
wfn = Wavefunction([[2, 0, 2]], broken=['spin'])
hamil = general_hamiltonian.General((data, ))
hamil._conserve_number = False
self.assertRaises(TypeError, wfn.apply, hamil)
self.assertRaises(TypeError, wfn.time_evolve, 0.1, hamil)
wfn = Wavefunction([[2, 0, 2]], broken=['number'])
hamil = general_hamiltonian.General((data, ))
self.assertRaises(TypeError, wfn.apply, hamil)
self.assertRaises(TypeError, wfn.time_evolve, 0.1, hamil)
wfn = Wavefunction([[2, 0, 2]])
hamil = get_restricted_hamiltonian((data, ))
self.assertRaises(ValueError, wfn.time_evolve, 0.1, hamil, True)
def test_lih_energy(self):
"""Checking total energy with LiH
"""
eref = -8.877719570384043
norb = 6
nalpha = 2
nbeta = 2
nele = nalpha + nbeta
h1e, h2e, lih_ground = build_lih_data.build_lih_data('energy')
elec_hamil = general_hamiltonian.General((h1e, h2e))
wfn = Wavefunction([[nele, nalpha - nbeta, norb]])
wfn.set_wfn(strategy='from_data',
raw_data={(nele, nalpha - nbeta): lih_ground})
ecalc = wfn.expectationValue(elec_hamil)
self.assertAlmostEqual(eref, ecalc, places=8)
def test_apply_spinful_fermionop(self):
"""
Make sure the spin-orbital reordering is working by comparing
apply operation
"""
wfn = Wavefunction([[2, 0, 2]])
wfn.set_wfn(strategy='random')
wfn.normalize()
cirq_wf = to_cirq(wfn).reshape((-1, 1))
op_to_apply = FermionOperator()
test_state = copy.deepcopy(wfn)
test_state.set_wfn('zero')
for p, q, r, s in product(range(2), repeat=4):
op = FermionOperator(
((2 * p, 1), (2 * q + 1, 1), (2 * r + 1, 0), (2 * s, 0)),
coefficient=numpy.random.randn())
op_to_apply += op + hermitian_conjugated(op)
test_state += wfn.apply(op + hermitian_conjugated(op))
opmat = get_sparse_operator(op_to_apply, n_qubits=4).toarray()
new_state_cirq = opmat @ cirq_wf
# this part is because we need to pass a normalized wavefunction
norm_constant = new_state_cirq.conj().T @ new_state_cirq
new_state_cirq /= numpy.sqrt(norm_constant)
new_state_wfn = from_cirq(new_state_cirq.flatten(), thresh=1.0E-12)
new_state_wfn.scale(numpy.sqrt(norm_constant))
self.assertTrue(
numpy.allclose(test_state.get_coeff((2, 0)),
new_state_wfn.get_coeff((2, 0))))
def test_evolve_spinful_fermionop(self):
"""
Make sure the spin-orbital reordering is working by comparing
time evolution
"""
wfn = Wavefunction([[2, 0, 2]])
wfn.set_wfn(strategy='random')
wfn.normalize()
cirq_wf = to_cirq(wfn).reshape((-1, 1))
op_to_apply = FermionOperator()
for p, q, r, s in product(range(2), repeat=4):
op = FermionOperator(
((2 * p, 1), (2 * q + 1, 1), (2 * r + 1, 0), (2 * s, 0)),
coefficient=numpy.random.randn())
op_to_apply += op + hermitian_conjugated(op)
opmat = get_sparse_operator(op_to_apply, n_qubits=4).toarray()
dt = 0.765
new_state_cirq = scipy.linalg.expm(-1j * dt * opmat) @ cirq_wf
new_state_wfn = from_cirq(new_state_cirq.flatten(), thresh=1.0E-12)
test_state = wfn.time_evolve(dt, op_to_apply)
self.assertTrue(
numpy.allclose(test_state.get_coeff((2, 0)),
new_state_wfn.get_coeff((2, 0))))
def test_general_exceptions(self):
"""Test general method exceptions
"""
test1 = Wavefunction(param=[[2, 0, 4]])
test2 = Wavefunction(param=[[4, -4, 8]])
test1.set_wfn(strategy='ones')
test2.set_wfn(strategy='ones')
self.assertRaises(ValueError, test1.ax_plus_y, 1.0, test2)
self.assertRaises(ValueError, test1.__add__, test2)
self.assertRaises(ValueError, test1.__sub__, test2)
self.assertRaises(ValueError, test1.set_wfn, strategy='from_data')
def test_lih_dipole(self):
"""Calculate the LiH dipole
"""
norb = 6
nalpha = 2
nbeta = 2
nele = nalpha + nbeta
au2debye = 2.5417464157449032
dip_ref, dip_mat, lih_ground = build_lih_data.build_lih_data('dipole')
wfn = Wavefunction([[nele, nalpha - nbeta, norb]])
wfn.set_wfn(strategy='from_data',
raw_data={(nele, nalpha - nbeta): lih_ground})
hwfn_x = wfn._apply_array(tuple([dip_mat[0]]), e_0=0. + 0.j)
hwfn_y = wfn._apply_array(tuple([dip_mat[1]]), e_0=0. + 0.j)
hwfn_z = wfn._apply_array(tuple([dip_mat[2]]), e_0=0. + 0.j)
calc_dip = numpy.array([fqe.vdot(wfn, hwfn_x).real, \
fqe.vdot(wfn, hwfn_y).real, \
fqe.vdot(wfn, hwfn_z).real])*au2debye
for card in range(3):
with self.subTest(dip=card):
err = abs(calc_dip[card] - dip_ref[card])
self.assertTrue(err < 1.e-5)
def test_save_read(self):
"""Check that the wavefunction can be properly archived and
retieved
"""
numpy.random.seed(seed=409)
wfn = get_number_conserving_wavefunction(3, 3)
wfn.set_wfn(strategy='random')
wfn.save('test_save_read')
read_wfn = Wavefunction()
read_wfn.read('test_save_read')
for key in read_wfn.sectors():
self.assertTrue(
numpy.allclose(read_wfn._civec[key].coeff,
wfn._civec[key].coeff))
self.assertEqual(read_wfn._symmetry_map, wfn._symmetry_map)
self.assertEqual(read_wfn._conserved, wfn._conserved)
self.assertEqual(read_wfn._conserve_spin, wfn._conserve_spin)
self.assertEqual(read_wfn._conserve_number, wfn._conserve_number)
self.assertEqual(read_wfn._norb, wfn._norb)
os.remove('test_save_read')
wfn = get_spin_conserving_wavefunction(2, 6)
wfn.set_wfn(strategy='random')
wfn.save('test_save_read')
read_wfn = Wavefunction()
read_wfn.read('test_save_read')
for key in read_wfn.sectors():
self.assertTrue(
numpy.allclose(read_wfn._civec[key].coeff,
wfn._civec[key].coeff))
self.assertEqual(read_wfn._symmetry_map, wfn._symmetry_map)
self.assertEqual(read_wfn._conserved, wfn._conserved)
self.assertEqual(read_wfn._conserve_spin, wfn._conserve_spin)
self.assertEqual(read_wfn._conserve_number, wfn._conserve_number)
self.assertEqual(read_wfn._norb, wfn._norb)
os.remove('test_save_read')
def test_apply_number(self):
norb = 4
test = numpy.random.rand(norb, norb)
diag = numpy.random.rand(norb * 2)
diag2 = copy.deepcopy(diag)
e_0 = 0
for i in range(norb):
e_0 += diag[i + norb]
diag2[i + norb] = -diag[i + norb]
hamil = diagonal_hamiltonian.Diagonal(diag2, e_0=e_0)
hamil._conserve_number = False
wfn = Wavefunction([[4, 2, norb]], broken=['number'])
wfn.set_wfn(strategy='from_data', raw_data={(4, 2): test})
out1 = wfn.apply(hamil)
hamil = diagonal_hamiltonian.Diagonal(diag)
wfn = Wavefunction([[4, 2, norb]])
wfn.set_wfn(strategy='from_data', raw_data={(4, 2): test})
out2 = wfn.apply(hamil)
self.assertTrue(
numpy.allclose(out1._civec[(4, 2)].coeff,
out2._civec[(4, 2)].coeff))
def evolve_fqe_diagaonal_coulomb(wfn: Wavefunction, vij_mat: np.ndarray,
time=1) -> Wavefunction:
r"""Utility for testing evolution of a full 2^{n} wavefunction via
:math:`exp{-i time * \sum_{i,j, sigma, tau}v_{i, j}n_{i\sigma}n_{j\tau}}.`
Args:
wfn: 2^{n} x 1 vector.
vij_mat: List[(n//2 x n//2)] matrices
time: evolution time.
Returns:
New evolved 2^{n} x 1 vector
"""
dc_ham = DiagonalCoulomb(vij_mat)
return wfn.time_evolve(time, dc_ham)
def test_lih_ops(self):
"""Check the value of the operators on LiH
"""
norb = 6
nalpha = 2
nbeta = 2
nele = nalpha + nbeta
_, _, lih_ground = build_lih_data.build_lih_data('energy')
wfn = Wavefunction([[nele, nalpha - nbeta, norb]])
wfn.set_wfn(strategy='from_data',
raw_data={(nele, nalpha - nbeta): lih_ground})
operator = S2Operator()
self.assertAlmostEqual(wfn.expectationValue(operator), 0. + 0.j)
operator = SzOperator()
self.assertAlmostEqual(wfn.expectationValue(operator), 0. + 0.j)
operator = TimeReversalOp()
self.assertAlmostEqual(wfn.expectationValue(operator), 1. + 0.j)
operator = NumberOperator()
self.assertAlmostEqual(wfn.expectationValue(operator), 4. + 0.j)
self.assertAlmostEqual(wfn.expectationValue(operator, wfn), 4. + 0.j)
def test_apply_diagonal(self):
wfn = Wavefunction([[2, 0, 2]])
wfn.set_wfn(strategy='random')
data = numpy.random.rand(2)
hamil = diagonal_hamiltonian.Diagonal(data)
out1 = wfn._apply_diagonal(hamil)
fac = 0.5
hamil = diagonal_hamiltonian.Diagonal(data, e_0=fac)
out2 = wfn._apply_diagonal(hamil)
out2.ax_plus_y(-fac, wfn)
self.assertTrue((out1 - out2).norm() < 1.0e-8)
def test_rdm(self):
"""Check that the rdms will properly return the energy
"""
wfn = Wavefunction(param=[[4, 0, 3]])
work, energy = build_wfn.restricted_wfn_energy()
wfn.set_wfn(strategy='from_data', raw_data={(4, 0): work})
rdm1 = wfn.rdm('i^ j')
rdm2 = wfn.rdm('i^ j^ k l')
rdm3 = wfn.rdm('i^ j^ k^ l m n')
rdm4 = wfn.rdm('i^ j^ k^ l^ m n o p')
h1e, h2e, h3e, h4e = build_hamiltonian.build_restricted(3, full=False)
expval = 0. + 0.j
axes = [0, 1]
expval += numpy.tensordot(h1e, rdm1, axes=(axes, axes))
axes = [0, 1, 2, 3]
expval += numpy.tensordot(h2e, rdm2, axes=(axes, axes))
axes = [0, 1, 2, 3, 4, 5]
expval += numpy.tensordot(h3e, rdm3, axes=(axes, axes))
axes = [0, 1, 2, 3, 4, 5, 6, 7]
expval += numpy.tensordot(h4e, rdm4, axes=(axes, axes))
self.assertAlmostEqual(expval, energy)
def test_apply_nbody(self):
wfn = Wavefunction([[2, 0, 2]])
wfn.set_wfn(strategy='random')
fac = 3.14
fop = FermionOperator('1^ 1', fac)
hamil = sparse_hamiltonian.SparseHamiltonian(fop)
out1 = wfn._apply_few_nbody(hamil)
fop = FermionOperator('1 1^', fac)
hamil = sparse_hamiltonian.SparseHamiltonian(fop)
out2 = wfn._apply_few_nbody(hamil)
out2.scale(-1.0)
out2.ax_plus_y(fac, wfn)
self.assertTrue((out1 - out2).norm() < 1.0e-8)
def test_wick(self):
"""Check that wick performs the proper restructuring of the
density matrix given a string of indexes.
"""
norb = 4
nele = 4
s_z = 0
wfn = Wavefunction([[nele, s_z, norb]])
numpy.random.seed(seed=1)
wfn.set_wfn(strategy='random')
wfn.normalize()
rdms = wfn._compute_rdm(4)
out1 = wick.wick('k j^', list(rdms), True)
two = numpy.eye(norb, dtype=out1.dtype) * 2.0
self.assertRaises(ValueError, wick.wick, 'k0 j', list(rdms))
self.assertTrue(numpy.allclose(two - out1.T, rdms[0]))
self.assertRaises(ValueError, wick.wick, 'k^ l i^ j', list(rdms), True)
out2 = wick.wick('k l i^ j^', list(rdms), True)
h_1 = numpy.zeros_like(out1)
for i in range(norb):
h_1[:, :] += out2[:, i, :, i] / (norb * 2 - nele - 1)
self.assertAlmostEqual(numpy.std(out1 + h_1), 0.)
out2a = wick.wick('k l^ i^ j', list(rdms), True)
self.assertAlmostEqual(out2a[2, 3, 0, 1], -rdms[1][0, 3, 2, 1])
out3 = wick.wick('k l m i^ j^ n^', list(rdms), True)
h_2 = numpy.zeros_like(out2)
for i in range(norb):
h_2[:, :, :, :] += out3[:, i, :, :, i, :] / (norb * 2 - nele - 2)
self.assertAlmostEqual(numpy.std(out2 - h_2), 0.)
out4 = wick.wick('k l m x i^ j^ n^ y^', list(rdms), True)
h_3 = numpy.zeros_like(out3)
for i in range(norb):
h_3[:, :, :, :, :, :] += out4[:, i, :, :, :, i, :, :] / (norb * 2 -
nele - 3)
self.assertAlmostEqual(numpy.std(out3 + h_3), 0.)
def evolve_fqe_charge_charge_unrestricted(wfn: Wavefunction,
vij_mat: np.ndarray,
time=1) -> Wavefunction:
r"""Utility for testing evolution of a full 2^{n} wavefunction via
:math:`exp{-i time * \sum_{i,j}v_{i, j}n_{i}n_{j}}.`
Args:
wfn: fqe_wf with sdim = n
vij_mat: List[(n x n] matrices
time: evolution time.
Returns:
New evolved 2^{n} x 1 vector
"""
nso = vij_mat.shape[0]
for p, q in product(range(nso), repeat=2):
if np.isclose(vij_mat[p, q], 0):
continue
fop = of.FermionOperator(((p, 1), (p, 0), (q, 1), (q, 0)),
coefficient=vij_mat[p, q])
wfn = wfn.time_evolve(time, fop)
return wfn
def test_general_functions(self):
"""Test general wavefunction members
"""
test = Wavefunction(param=[[2, 0, 4]])
test.set_wfn(strategy='ones')
self.assertEqual(1. + 0.j, test[(4, 8)])
test[(4, 8)] = 3.14 + 0.00159j
self.assertEqual(3.14 + 0.00159j, test[(4, 8)])
self.assertEqual(3.14 + 0.00159j, test.max_element())
self.assertTrue(test.conserve_spin())
test1 = Wavefunction(param=[[2, 0, 4]])
test2 = Wavefunction(param=[[2, 0, 4]])
test1.set_wfn(strategy='ones')
test2.set_wfn(strategy='ones')
work = test1 + test2
ref = 2.0 * numpy.ones((4, 4), dtype=numpy.complex128)
self.assertTrue(numpy.allclose(ref, work._civec[(2, 0)].coeff))
work = test1 - test2
ref = numpy.zeros((4, 4), dtype=numpy.complex128)
self.assertTrue(numpy.allclose(ref, work._civec[(2, 0)].coeff))
def vbc(self,
initial_wf: Wavefunction,
opt_method: str = 'L-BFGS-B',
opt_options=None,
num_opt_var=None,
v_reconstruct=False,
generator_decomp=None,
generator_rank=None):
"""The variational Brillouin condition method
Solve for the 2-body residual and then variationally determine
the step size. This exact simulation cannot be implemented without
Trotterization. A proxy for the approximate evolution is the update_
rank pameter which limites the rank of the residual.
Args:
initial_wf: initial wavefunction
opt_method: scipy optimizer name
num_opt_var: Number of optimization variables to consider
v_reconstruct: use valdemoro reconstruction of 3-RDM to calculate
the residual
generator_decomp: None, takagi, or svd
generator_rank: number of generator terms to take
"""
if opt_options is None:
opt_options = {}
self.num_opt_var = num_opt_var
nso = 2 * self.sdim
operator_pool: List[Union[ABCHamiltonian, SumOfSquaresOperator]] = []
operator_pool_fqe: List[
Union[ABCHamiltonian, SumOfSquaresOperator]] = []
existing_parameters: List[float] = []
self.energies = []
self.energies = [initial_wf.expectationValue(self.k2_fop)]
self.residuals = []
iteration = 0
while iteration < self.iter_max:
# get current wavefunction
wf = copy.deepcopy(initial_wf)
for op, coeff in zip(operator_pool_fqe, existing_parameters):
if np.isclose(coeff, 0):
continue
if isinstance(op, ABCHamiltonian):
wf = wf.time_evolve(coeff, op)
elif isinstance(op, SumOfSquaresOperator):
for v, cc in zip(op.basis_rotation, op.charge_charge):
wf = evolve_fqe_givens_unrestricted(wf, v.conj().T)
wf = evolve_fqe_charge_charge_unrestricted(
wf, coeff * cc)
wf = evolve_fqe_givens_unrestricted(wf, v)
wf = evolve_fqe_givens_unrestricted(wf,
op.one_body_rotation)
else:
raise ValueError("Can't evolve operator type {}".format(
type(op)))
# calculate rdms for grad
_, tpdm = wf.sector((self.nele, self.sz)).get_openfermion_rdms()
if v_reconstruct:
d3 = 6 * valdemaro_reconstruction_functional(
tpdm / 2, self.nele)
else:
d3 = wf.sector((self.nele, self.sz)).get_three_pdm()
# get ACSE Residual and 2-RDM gradient
acse_residual = two_rdo_commutator_symm(
self.reduced_ham.two_body_tensor, tpdm, d3)
if generator_decomp is None:
fop = get_fermion_op(acse_residual)
elif generator_decomp is 'svd':
new_residual = np.zeros_like(acse_residual)
for p, q, r, s in product(range(nso), repeat=4):
new_residual[p, q, r, s] = (acse_residual[p, q, r, s] -
acse_residual[s, r, q, p]) / 2
fop = self.get_svd_tensor_decomp(new_residual, generator_rank)
elif generator_decomp is 'takagi':
fop = self.get_takagi_tensor_decomp(acse_residual,
generator_rank)
else:
raise ValueError(
"Generator decomp must be None, svd, or takagi")
operator_pool.extend([fop])
fqe_ops: List[Union[ABCHamiltonian, SumOfSquaresOperator]] = []
if isinstance(fop, ABCHamiltonian):
fqe_ops.append(fop)
elif isinstance(fop, SumOfSquaresOperator):
fqe_ops.append(fop)
else:
fqe_ops.append(
build_hamiltonian(1j * fop, self.sdim,
conserve_number=True))
operator_pool_fqe.extend(fqe_ops)
existing_parameters.extend([0])
if self.num_opt_var is not None:
if len(operator_pool_fqe) < self.num_opt_var:
pool_to_op = operator_pool_fqe
params_to_op = existing_parameters
current_wf = copy.deepcopy(initial_wf)
else:
pool_to_op = operator_pool_fqe[-self.num_opt_var:]
params_to_op = existing_parameters[-self.num_opt_var:]
current_wf = copy.deepcopy(initial_wf)
for fqe_op, coeff in zip(
operator_pool_fqe[:-self.num_opt_var],
existing_parameters[:-self.num_opt_var]):
current_wf = current_wf.time_evolve(coeff, fqe_op)
temp_cwf = copy.deepcopy(current_wf)
for fqe_op, coeff in zip(pool_to_op, params_to_op):
if np.isclose(coeff, 0):
continue
temp_cwf = temp_cwf.time_evolve(coeff, fqe_op)
new_parameters, current_e = self.optimize_param(
pool_to_op,
params_to_op,
current_wf,
opt_method,
opt_options=opt_options)
if len(operator_pool_fqe) < self.num_opt_var:
existing_parameters = new_parameters.tolist()
else:
existing_parameters[-self.num_opt_var:] = \
new_parameters.tolist()
else:
new_parameters, current_e = self.optimize_param(
operator_pool_fqe,
existing_parameters,
initial_wf,
opt_method,
opt_options=opt_options)
existing_parameters = new_parameters.tolist()
if self.verbose:
print(iteration, current_e, np.max(np.abs(acse_residual)),
len(existing_parameters))
self.energies.append(current_e)
self.residuals.append(acse_residual)
if np.max(np.abs(acse_residual)) < self.stopping_eps or np.abs(
self.energies[-2] - self.energies[-1]) < self.delta_e_eps:
break
iteration += 1
def test_expectation_value_type_error(self):
wfn = Wavefunction([[4, 0, 4]])
self.assertRaises(TypeError, wfn.expectationValue, 1)
def test_hartree_fock_init(self):
h1e, h2e, _ = build_lih_data('energy')
elec_hamil = get_restricted_hamiltonian((h1e, h2e))
norb = 6
nalpha = 2
nbeta = 2
wfn = Wavefunction([[nalpha + nbeta, nalpha - nbeta, norb]])
wfn.print_wfn()
wfn.set_wfn(strategy='hartree-fock')
wfn.print_wfn()
self.assertEqual(wfn.expectationValue(elec_hamil), -8.857341498221992)
hf_wf = numpy.zeros((int(binom(norb, 2)), int(binom(norb, 2))))
hf_wf[0, 0] = 1.
self.assertTrue(numpy.allclose(wfn.get_coeff((4, 0)), hf_wf))
wfn = Wavefunction([[nalpha + nbeta, nalpha - nbeta, norb],
[nalpha + nbeta, 2, norb]])
self.assertRaises(ValueError, wfn.set_wfn, strategy='hartree-fock')
def adapt_vqe(self,
initial_wf: Wavefunction,
opt_method: str = 'L-BFGS-B',
opt_options=None,
v_reconstruct: bool = True,
num_ops_add: int = 1):
"""
Run ADAPT-VQE using
Args:
initial_wf: Initial wavefunction at the start of the calculation
opt_method: scipy optimizer to use
opt_options: options for scipy optimizer
v_reconstruct: use valdemoro reconstruction
num_ops_add: add this many operators from the pool to the
wavefunction
"""
if opt_options is None:
opt_options = {}
operator_pool = []
operator_pool_fqe: List[ABCHamiltonian] = []
existing_parameters: List[float] = []
self.gradients = []
self.energies = [initial_wf.expectationValue(self.k2_fop)]
iteration = 0
while iteration < self.iter_max:
# get current wavefunction
wf = copy.deepcopy(initial_wf)
for fqe_op, coeff in zip(operator_pool_fqe, existing_parameters):
wf = wf.time_evolve(coeff, fqe_op)
# calculate rdms for grad
_, tpdm = wf.sector((self.nele, self.sz)).get_openfermion_rdms()
if v_reconstruct:
d3 = 6 * valdemaro_reconstruction(tpdm / 2, self.nele)
else:
d3 = wf.sector((self.nele, self.sz)).get_three_pdm()
# get ACSE Residual and 2-RDM gradient
acse_residual = two_rdo_commutator_symm(
self.reduced_ham.two_body_tensor, tpdm, d3)
one_body_residual = one_rdo_commutator_symm(
self.reduced_ham.two_body_tensor, tpdm)
# calculate grad of each operator in the pool
pool_grad = []
for operator in self.operator_pool.op_pool:
grad_val = 0
for op_term, coeff in operator.terms.items():
idx = [xx[0] for xx in op_term]
if len(idx) == 4:
grad_val += acse_residual[tuple(idx)] * coeff
elif len(idx) == 2:
grad_val += one_body_residual[tuple(idx)] * coeff
pool_grad.append(grad_val)
max_grad_terms_idx = \
np.argsort(np.abs(pool_grad))[::-1][:num_ops_add]
pool_terms = [
self.operator_pool.op_pool[i] for i in max_grad_terms_idx
]
operator_pool.extend(pool_terms)
fqe_ops: List[ABCHamiltonian] = []
for f_op in pool_terms:
fqe_ops.append(
build_hamiltonian(1j * f_op,
self.sdim,
conserve_number=True))
operator_pool_fqe.extend(fqe_ops)
existing_parameters.extend([0] * len(fqe_ops))
new_parameters, current_e = self.optimize_param(
operator_pool_fqe,
existing_parameters,
initial_wf,
opt_method,
opt_options=opt_options)
existing_parameters = new_parameters.tolist()
if self.verbose:
print(iteration, current_e, max(np.abs(pool_grad)))
self.energies.append(current_e)
self.gradients.append(pool_grad)
if max(np.abs(pool_grad)) < self.stopping_eps or np.abs(
self.energies[-2] - self.energies[-1]) < self.delta_e_eps:
break
iteration += 1
def get_acse_residual_fqe(fqe_wf: Wavefunction, fqe_ham: RestrictedHamiltonian,
norbs: int) -> np.ndarray:
"""Get the ACSE block by using reduced density operators that are Sz spin
adapted
R^{ij}_{lk} = <psi | [i^ j^ k l, A] | psi>
alpha-alpha, beta-beta, alpha-beta, and beta-alpha blocks
we do not compression over alpha-alpha or beta-beta so these are still
norbs**2 in linear dimension. In other words, we do computation on
elements we know should be zero. This is for simplicity in the code.
Args:
fqe_wf: fqe.Wavefunction object to calculate expectation value with
fqe_ham: fqe.RestrictedHamiltonian operator corresponding to a chemical
Hamiltonian
norbs: Number of orbitals. Number of spatial orbitals
Returns:
Gradient of the i^ j^ k l operator
"""
acse_aa = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex128)
acse_bb = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex128)
acse_ab = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex128)
fqe_appA = fqe_wf.apply(fqe_ham)
for p, q, r, s in product(range(norbs), repeat=4):
# alpha-alpha block real
if p != q and r != s:
rdo = ((2 * p, 1), (2 * q, 1), (2 * r, 0), (2 * s, 0))
rdo = 1j * (of.FermionOperator(rdo) -
of.hermitian_conjugated(of.FermionOperator(rdo)))
val1 = fqe.util.vdot(fqe_appA, fqe_wf.apply(rdo))
val2 = np.conjugate(val1)
acse_aa[p, q, r, s] = (val2 - val1) / 2j
# alpha-alpha block imag
rdo = ((2 * p, 1), (2 * q, 1), (2 * r, 0), (2 * s, 0))
rdo = of.FermionOperator(rdo) + of.hermitian_conjugated(
of.FermionOperator(rdo))
val1 = fqe.util.vdot(fqe_appA, fqe_wf.apply(rdo))
val2 = np.conjugate(val1)
acse_aa[p, q, r, s] += (val2 - val1) / 2
# beta-beta block real
rdo = (
(2 * p + 1, 1),
(2 * q + 1, 1),
(2 * r + 1, 0),
(2 * s + 1, 0),
)
rdo = 1j * (of.FermionOperator(rdo) -
of.hermitian_conjugated(of.FermionOperator(rdo)))
val1 = fqe.util.vdot(fqe_appA, fqe_wf.apply(rdo))
val2 = np.conjugate(val1)
acse_bb[p, q, r, s] += (val2 - val1) / 2j
# beta-beta block imag
rdo = (
(2 * p + 1, 1),
(2 * q + 1, 1),
(2 * r + 1, 0),
(2 * s + 1, 0),
)
rdo = of.FermionOperator(rdo) + of.hermitian_conjugated(
of.FermionOperator(rdo))
val1 = fqe.util.vdot(fqe_appA, fqe_wf.apply(rdo))
val2 = np.conjugate(val1)
acse_bb[p, q, r, s] += (val2 - val1) / 2
# alpha-beta block real
rdo = ((2 * p, 1), (2 * q + 1, 1), (2 * r + 1, 0), (2 * s, 0))
rdo = 1j * (of.FermionOperator(rdo) -
of.hermitian_conjugated(of.FermionOperator(rdo)))
val1 = fqe.util.vdot(fqe_appA, fqe_wf.apply(rdo))
val2 = np.conjugate(val1)
acse_ab[p, q, r, s] += (val2 - val1) / 2j
# alpha-beta block imag
rdo = ((2 * p, 1), (2 * q + 1, 1), (2 * r + 1, 0), (2 * s, 0))
rdo = of.FermionOperator(rdo) + of.hermitian_conjugated(
of.FermionOperator(rdo))
val1 = fqe.util.vdot(fqe_appA, fqe_wf.apply(rdo))
val2 = np.conjugate(val1) # fqe.util.vdot(fqe_wf.apply(rdo), fqe_appA)
acse_ab[p, q, r, s] += (val2 - val1) / 2
# unroll residual blocks into full matrix
acse_residual = np.zeros((2 * norbs, 2 * norbs, 2 * norbs, 2 * norbs),
dtype=np.complex128)
acse_residual[::2, ::2, ::2, ::2] = acse_aa
acse_residual[1::2, 1::2, 1::2, 1::2] = acse_bb
acse_residual[::2, 1::2, 1::2, ::2] = acse_ab
acse_residual[::2, 1::2, ::2, 1::2] = np.einsum("ijkl->ijlk", -acse_ab)
acse_residual[1::2, ::2, ::2, 1::2] = np.einsum("ijkl->jilk", acse_ab)
acse_residual[1::2, ::2,
1::2, ::2] = np.einsum("ijkl->ijlk",
-acse_residual[1::2, ::2, ::2, 1::2])
return acse_residual
def test_set_wfn_random_with_multiple_sectors_is_normalized(self):
wfn = Wavefunction([[2, 0, 4], [2, -2, 4]], broken=None)
wfn.set_wfn(strategy="random")
self.assertAlmostEqual(wfn.norm(), 1.0)
