def __init__(self,
l=10,
grid_length=10,
num_grid_points=201,
alpha=1.0,
a=0.25,
Omega=0.25,
omega=2,
epsilon0=1,
nparticles=2,
potential=None,
antisymmetrize=False):
self.potential = ODQD.HOPotential(Omega)
self.system = ODQD(l,
grid_length,
num_grid_points,
a,
alpha,
potential=self.potential)
self.nparticles = nparticles
self.Omega = Omega
self.omega = omega
self.epsilon0 = epsilon0
def __init__(self,
l=10,
grid_length=10,
num_grid_points=201,
alpha=1.0,
a=0.25,
Omega=0.25,
omega=2,
epsilon0=1,
nparticles=2,
antisymmetrize=True):
self.potential = ODQD.HOPotential(Omega)
odho = ODQD(l,
grid_length,
num_grid_points,
a,
alpha,
potential=self.potential)
self.system = GeneralOrbitalSystem(n=nparticles,
basis_set=odho,
anti_symmetrize=antisymmetrize)
self.nparticles = nparticles
self.Omega = Omega
self.omega = omega
self.epsilon0 = epsilon0
def get_oddw_smooth():
n = 2
l = 20
grid_length = 5
num_grid_points = 1001
a = 5
oddw_smooth = ODQD(n, l, grid_length, num_grid_points)
oddw_smooth.setup_system(potential=DWPotentialSmooth(a=a))
return oddw_smooth
def get_odho():
n = 2
l = 20
grid_length = 5
num_grid_points = 1001
omega = 1
odho = ODQD(n, l, grid_length, num_grid_points)
odho.setup_system(potential=HOPotential(omega))
return odho
def get_oddw():
n = 2
l = 20
grid_length = 6
num_grid_points = 1001
omega = 1
length_of_dw = 5
oddw = ODQD(n, l, grid_length, num_grid_points)
oddw.setup_system(potential=DWPotential(omega, length_of_dw))
return oddw
def get_odho_ao():
n = 2
l = 20
grid_length = 5
num_grid_points = 1001
omega = 1
odho = ODQD(n, l, grid_length, num_grid_points)
odho.setup_system(
potential=HOPotential(omega), add_spin=False, anti_symmetrize=False
)
return odho
def test_open_odqd():
n = 5
n_a = 3
n_b = n - n_a
l = 20
odho_res = ODQD(n, l, 11, 201, n_a=n_a)
odho_res.setup_system(add_spin=False, anti_symmetrize=False)
odho = ODQD(n, l, 11, 201, n_a=n_a)
odho.setup_system()
np.testing.assert_allclose(
odho_res.spf[:n_a],
odho.spf[odho.o_a],
)
np.testing.assert_allclose(
odho_res.spf[:n - n_a],
odho.spf[odho.o_b],
)
np.testing.assert_allclose(odho_res.h[:n_a, :n_a], odho.h[odho.o_a,
odho.o_a])
np.testing.assert_allclose(odho_res.h[:n - n_a, :n - n_a],
odho.h[odho.o_b, odho.o_b])
np.testing.assert_allclose(np.zeros((n_a, n_b)), odho.h[odho.o_a,
odho.o_b])
np.testing.assert_allclose(np.zeros((n_b, n_a)), odho.h[odho.o_b,
odho.o_a])
def get_qdot_matrix(n, l, omega, grid_length=5, n_grid=1001):
odho = ODQD(n, l, grid_length, n_grid)
odho.setup_system(potential=HOPotential(omega), add_spin=True)
one_body = odho.h
one_body[np.absolute(one_body) < 1e-8] = 0
two_body = odho.u
two_body[np.absolute(two_body) < 1e-8] = 0
# Coupled Cluster
Eref = odho.compute_reference_energy()
ccsd = CCSD(odho, verbose=False)
ccsd.compute_ground_state()
Ecc = ccsd.compute_energy()
return one_body, two_body, [Eref, Ecc]
def get_odho():
n = 2
l = 10
grid_length = 5
num_grid_points = 1001
omega = 1
odho = GeneralOrbitalSystem(
n,
ODQD(
l, grid_length, num_grid_points, potential=ODQD.HOPotential(omega)
),
)
return odho
def get_odgauss():
n = 2
l = 20
grid_length = 20
num_grid_points = 1001
weight = 1
center = 0
deviation = 2.5
odgauss = ODQD(n, l, grid_length, num_grid_points)
odgauss.setup_system(
potential=GaussianPotential(weight, center, deviation, np=np)
)
return odgauss
def get_oddw_smooth():
n = 2
l = 10
grid_length = 5
num_grid_points = 1001
a = 5
oddw_smooth = GeneralOrbitalSystem(
n,
ODQD(
l,
grid_length,
num_grid_points,
potential=ODQD.DWPotentialSmooth(a=a),
),
)
return oddw_smooth
def test_spin_squared():
n = 2
l = 2
dim = 2
spas = SpatialOrbitalSystem(n, RandomBasisSet(l, dim))
spas = SpatialOrbitalSystem(
n, ODQD(l, 8, 1001, potential=ODQD.HOPotential(1)))
gos = spas.construct_general_orbital_system(a=[1, 0], b=[0, 1])
overlap = spas.s
overlap_sq = np.einsum("pr, qs -> pqrs", overlap, overlap)
a = gos._basis_set.a
b = gos._basis_set.b
aa = np.kron(a, a)
ab = np.kron(a, b)
ba = np.kron(b, a)
bb = np.kron(b, b)
triplets = [aa, 1 / np.sqrt(2) * (ab + ba), bb]
singlet = [1 / np.sqrt(2) * (ab - ba)]
# S^2 with alpha = [1, 0]^T and beta = [0, 1]^T
S_sq_spin = np.zeros((4, 4))
S_sq_spin[0, 0] = 2
S_sq_spin[3, 3] = 2
S_sq_spin[1, 1] = 1
S_sq_spin[2, 2] = 1
S_sq_spin[1, 2] = 1
S_sq_spin[2, 1] = 1
S_sq_spin = S_sq_spin.reshape(2, 2, 2, 2)
for trip in triplets:
# Check that the eigenvalue of all triplet states is 2
np.testing.assert_allclose(trip.T @ S_sq_spin.reshape(4, 4) @ trip, 2)
# Check that the eigenvalue of the singlet state is 0
np.testing.assert_allclose(
singlet[0].T @ S_sq_spin.reshape(4, 4) @ singlet[0], 0)
def get_oddw():
n = 2
l = 10
grid_length = 6
num_grid_points = 1001
omega = 1
length_of_dw = 5
oddw = GeneralOrbitalSystem(
n,
ODQD(
l,
grid_length,
num_grid_points,
potential=ODQD.DWPotential(omega, length_of_dw),
),
)
return oddw
def test_copy():
odho = GeneralOrbitalSystem(2, ODQD(12, 11, 201))
odho_2 = odho.copy_system()
assert id(odho) != id(odho_2)
assert id(odho.h) != id(odho_2.h)
np.testing.assert_allclose(odho.h, odho_2.h)
odho.h[0, 0] = 10
assert not np.equal(odho.h, odho_2.h).all()
def get_odgauss():
n = 2
l = 10
grid_length = 20
num_grid_points = 1001
weight = 1
center = 0
deviation = 2.5
odgauss = GeneralOrbitalSystem(
n,
ODQD(
l,
grid_length,
num_grid_points,
potential=ODQD.GaussianPotential(weight, center, deviation, np=np),
),
)
return odgauss
def test_copy():
odho = ODQD(2, 12, 11, 201)
odho.setup_system()
odho_2 = odho.copy_system()
assert id(odho) != id(odho_2)
assert id(odho.h) != id(odho_2.h)
np.testing.assert_allclose(odho.h, odho_2.h)
odho.h[0, 0] = 10
assert not np.equal(odho.h, odho_2.h).all()
from quantum_circuit import QuantumCircuit, SecondQuantizedHamiltonian
from quantum_systems import ODQD
from quantum_systems.quantum_dots.one_dim.one_dim_potentials import HOPotential
from coupled_cluster import CCSD
l = 4
n = 2
# Generate system
omega = 1
grid_length = 5
num_grid_points = 1001
odho = ODQD(n, l, grid_length, num_grid_points)
odho.setup_system(potential=HOPotential(omega), add_spin=True)
one_body = odho.h
one_body[np.absolute(one_body) < 1e-8] = 0
two_body = odho.u
two_body[np.absolute(two_body) < 1e-8] = 0
# Coupled Cluster
print('Reference energy:', odho.compute_reference_energy())
ccsd = CCSD(odho, verbose=False)
ccsd.compute_ground_state()
print('ECCSD =', ccsd.compute_energy())
# Prepare circuit list
H2 = SecondQuantizedHamiltonian(n, l)
def save_data(system, system_name):
np.save(f"{system_name}_dipole_moment", system.dipole_moment)
np.save(f"{system_name}_h", system.h)
np.save(f"{system_name}_u", system.u)
np.save(f"{system_name}_spf", system.spf)
n = 2
l = 20
grid_length = 5
num_grid_points = 1001
omega = 1
odho = ODQD(n, l, grid_length, num_grid_points)
odho.setup_system(potential=ODQD.HOPotential(omega))
save_data(odho, "odho")
length_of_dw = 5
oddw = ODQD(n, l, 6, num_grid_points)
oddw.setup_system(potential=ODQD.DWPotential(omega, length_of_dw))
save_data(oddw, "oddw")
weight = 1
center = 0
deviation = 2.5
odgauss = ODQD(n, l, 20, num_grid_points)
odgauss.setup_system(
system.spf[2 * i].real**2 + system.eigen_energies[i],
label=fr"$\psi_{i}(x)$",
)
plt.plot(system.grid, system.potential(system.grid), label=r"$v(x)$")
plt.legend(loc="best")
plt.show()
n = 2
l = 20
grid_length = 100
num_grid_points = 2001
omega = 1
odho = ODQD(n, l, grid_length, num_grid_points)
odho.setup_system(potential=ODQD.HOPotential(omega))
plot_one_body_system(odho)
length_of_dw = 5
dw = ODQD(n, l, 6, num_grid_points)
dw.setup_system(potential=ODQD.DWPotential(omega, length_of_dw))
plot_one_body_system(dw)
weight = 1
center = 0
deviation = 2.5
gauss = ODQD(n, l, 20, num_grid_points)
gauss.setup_system(
def test_restricted_odho():
n = 4
l = 20
odho_res = ODQD(n, l, 11, 201)
odho_res.setup_system(add_spin=False, anti_symmetrize=False)
odho = ODQD(n, l, 11, 201)
odho.setup_system()
assert odho.h.shape == tuple(2 * s for s in odho_res.h.shape)
assert odho.u.shape == tuple(2 * s for s in odho_res.u.shape)
np.testing.assert_allclose(
odho.spf[odho.o_a],
odho.spf[odho.o_b],
)
np.testing.assert_allclose(
odho.spf[odho.v_a],
odho.spf[odho.v_b],
)
np.testing.assert_allclose(odho.h[odho.o_a, odho.o_a], odho.h[odho.o_b,
odho.o_b])
np.testing.assert_allclose(odho.h[odho.v_a, odho.v_a], odho.h[odho.v_b,
odho.v_b])
np.testing.assert_allclose(np.zeros((n // 2, n // 2)), odho.h[odho.o_b,
odho.o_a])
np.testing.assert_allclose(np.zeros((n // 2, n // 2)), odho.h[odho.o_a,
odho.o_b])
np.testing.assert_allclose(
odho.u[odho.o_a, odho.o_a, odho.o_a, odho.o_a],
odho.u[odho.o_b, odho.o_b, odho.o_b, odho.o_b],
)
np.testing.assert_allclose(
odho.u[odho.v_a, odho.v_a, odho.v_a, odho.v_a],
odho.u[odho.v_b, odho.v_b, odho.v_b, odho.v_b],
)
o_res = slice(0, odho_res.n // 2)
v_res = slice(odho_res.n // 2, odho_res.l // 2)
np.testing.assert_allclose(
odho_res.spf[o_res],
odho.spf[odho.o_a],
)
np.testing.assert_allclose(
odho_res.spf[v_res],
odho.spf[odho.v_a],
)
np.testing.assert_allclose(odho_res.h[o_res, o_res], odho.h[odho.o_a,
odho.o_a])
np.testing.assert_allclose(odho_res.h[o_res, o_res], odho.h[odho.o_b,
odho.o_b])
np.testing.assert_allclose(odho_res.h[v_res, v_res], odho.h[odho.v_a,
odho.v_a])
np.testing.assert_allclose(odho_res.h[v_res, v_res], odho.h[odho.v_b,
odho.v_b])
import numpy as np
import matplotlib.pyplot as plt
from quantum_systems import ODQD
n = 2
l = 10
odqd = ODQD(n, l, 4, 201)
odqd.setup_system(potential=ODQD.DWPotentialSmooth(a=4.5))
plt.plot(odqd.grid, odqd.potential(odqd.grid))
for i in range(l // 2):
plt.plot(odqd.grid, odqd.eigen_energies[i] + np.abs(odqd.spf[i * 2])**2)
plt.show()