def test_init_exceptions(self):
M = 5
st = np.array([], dtype=float)
hs = HilbertSpace([make_space_fermion(i) for i in range(M)])
# Multiple fermions
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(M, M + 1)):
NFermionSectorViewR(st, hs, M + 1)
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(M, M + 1)):
NFermionSectorViewC(st, hs, M + 1)
# Fermions and bosons
hs.add(make_space_boson(2, 5))
hs.add(make_space_boson(3, 6))
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(M, M + 1)):
NFermionSectorViewR(st, hs, M + 1)
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(M, M + 1)):
NFermionSectorViewC(st, hs, M + 1)
# Purely bosonic Hilbert space
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
NFermionSectorViewR(st, hs_b, 1)
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
NFermionSectorViewC(st, hs_b, 1)
def setUpClass(cls):
# Fermionic elementary spaces
cls.fermion_es = [
make_space_fermion("dn", 0),
make_space_fermion("up", 0)
]
# Bosonic elementary spaces (4 bits)
cls.boson_es = [
make_space_boson(4, "x", 0),
make_space_boson(4, "y", 0)
]
# Spin-1/2 algebra elementary spaces
cls.spin_es = [
make_space_spin(0.5, "i", 0),
make_space_spin(0.5, "j", 0)
]
# Spin-1 algebra elementary spaces
cls.spin1_es = [
make_space_spin(1.0, "i", 0),
make_space_spin(1.0, "j", 0)
]
# Spin-3/2 algebra elementary spaces
cls.spin32_es = [
make_space_spin(3 / 2, "i", 0),
make_space_spin(3 / 2, "j", 0)
]
def test_n_fermion_sector_size(self):
hs = HilbertSpace()
# Empty Hilbert space
self.assertEqual(n_fermion_sector_size(hs, 0), 0)
self.assertEqual(n_fermion_sector_size(hs, 1), 0)
# Purely fermionic Hilbert spaces
hs.add(make_space_fermion(0))
self.assertEqual(n_fermion_sector_size(hs, 0), 1)
self.assertEqual(n_fermion_sector_size(hs, 1), 1)
hs.add(make_space_fermion(1))
self.assertEqual(n_fermion_sector_size(hs, 0), 1)
self.assertEqual(n_fermion_sector_size(hs, 1), 2)
self.assertEqual(n_fermion_sector_size(hs, 2), 1)
hs.add(make_space_fermion(2))
self.assertEqual(n_fermion_sector_size(hs, 0), 1)
self.assertEqual(n_fermion_sector_size(hs, 1), 3)
self.assertEqual(n_fermion_sector_size(hs, 2), 3)
self.assertEqual(n_fermion_sector_size(hs, 3), 1)
# Fermions and bosons
hs.add(make_space_boson(4, 3))
self.assertEqual(n_fermion_sector_size(hs, 0), 16)
self.assertEqual(n_fermion_sector_size(hs, 1), 48)
self.assertEqual(n_fermion_sector_size(hs, 2), 48)
self.assertEqual(n_fermion_sector_size(hs, 3), 16)
# Purely bosonic Hilbert space
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
self.assertEqual(n_fermion_sector_size(hs_b, 0), 32)
self.assertEqual(n_fermion_sector_size(hs_b, 1), 0)
def test_n_fermion_sector_basis_states(self):
M = 8
st = np.array([], dtype=float)
hs = HilbertSpace()
self.assertEqual(n_fermion_sector_basis_states(hs, 0), [])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_sector_basis_states(hs, 1)
def build_basis_states_ref(hs, N):
view = NFermionSectorViewR(st, hs, N)
basis_states = [-1] * n_fermion_sector_size(hs, N)
for index in range(hs.dim):
if popcount(index, M) == N:
basis_states[view.map_index(index)] = index
return basis_states
# Purely fermionic Hilbert spaces
for i in range(M):
hs.add(make_space_fermion(i))
for N in range(M + 1):
ref = build_basis_states_ref(hs, N)
self.assertEqual(n_fermion_sector_basis_states(hs, N), ref)
# Fermions and bosons
hs.add(make_space_boson(2, M))
hs.add(make_space_boson(2, M + 1))
for N in range(M + 1):
ref = build_basis_states_ref(hs, N)
self.assertEqual(n_fermion_sector_basis_states(hs, N), ref)
# Purely bosonic Hilbert space
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_sector_basis_states(hs_b, 1)
ref = list(range(n_fermion_sector_size(hs_b, 0)))
self.assertEqual(n_fermion_sector_basis_states(hs_b, 0), ref)
def test_map_index(self):
M = 8
st = np.array([], dtype=float)
hs = HilbertSpace()
def check_map_index(view, m, n):
mapped_indices = []
for index in range(hs.dim):
if popcount(index, m) == n:
mapped_indices.append(view.map_index(index))
mapped_indices.sort()
mapped_indices_ref = list(range(n_fermion_sector_size(hs, n)))
self.assertEqual(mapped_indices, mapped_indices_ref)
# Purely fermionic Hilbert spaces
for i in range(M):
hs.add(make_space_fermion(i))
for N in range(M + 1):
check_map_index(NFermionSectorViewR(st, hs, N), M, N)
check_map_index(NFermionSectorViewC(st, hs, N), M, N)
# Fermions and bosons
hs.add(make_space_boson(2, M))
hs.add(make_space_boson(2, M + 1))
for N in range(M + 1):
check_map_index(NFermionSectorViewR(st, hs, N), M, N)
check_map_index(NFermionSectorViewC(st, hs, N), M, N)
# Purely bosonic Hilbert space
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
ref_indices = list(range(hs_b.dim))
view = NFermionSectorViewR(st, hs_b, 0)
indices = [view.map_index(index) for index in range(hs_b.dim)]
self.assertEqual(indices, ref_indices)
view = NFermionSectorViewC(st, hs_b, 0)
indices = [view.map_index(index) for index in range(hs_b.dim)]
self.assertEqual(indices, ref_indices)
def setUpClass(cls):
# Fermionic elementary spaces
cls.es_f_dn = make_space_fermion("dn", 0)
cls.es_f_up = make_space_fermion("up", 0)
cls.fermion_es = [cls.es_f_dn, cls.es_f_up]
# Bosonic elementary spaces (4 bits)
cls.es_b_x = make_space_boson(4, "x", 0)
cls.es_b_y = make_space_boson(4, "y", 0)
cls.boson_es = [cls.es_b_x, cls.es_b_y]
# Spin-1/2 elementary spaces
cls.es_s_i = make_space_spin(0.5, "i", 0)
cls.es_s_j = make_space_spin(0.5, "j", 0)
cls.spin_es = [cls.es_s_i, cls.es_s_j]
# Spin-1 elementary spaces
cls.es_s1_i = make_space_spin(1.0, "i", 0)
cls.es_s1_j = make_space_spin(1.0, "j", 0)
cls.spin1_es = [cls.es_s1_i, cls.es_s1_j]
# Spin-3/2 elementary spaces
cls.es_s32_i = make_space_spin(3 / 2, "i", 0)
cls.es_s32_j = make_space_spin(3 / 2, "j", 0)
cls.spin32_es = [cls.es_s32_i, cls.es_s32_j]
def test_loperator(self):
M = 5
hs = HilbertSpace([make_space_boson(2, 0)])
for i in range(M):
hs.add(make_space_fermion(i))
H = (n(0) + n(1) + n(2) + n(3) + n(4)) * (a_dag(0) + a(0))
for src_type, dst_type, lop_type in [(float, float, LOperatorR),
(float, complex, LOperatorR),
(complex, complex, LOperatorR),
(float, complex, LOperatorC),
(complex, complex, LOperatorC)]:
src_view_type = NFermionSectorViewR if (src_type == float) \
else NFermionSectorViewC
dst_view_type = NFermionSectorViewR if (dst_type == float) \
else NFermionSectorViewC
Hop = lop_type(H if lop_type == LOperatorR else make_complex(H),
hs)
for N in range(M + 1):
src = np.zeros(n_fermion_sector_size(hs, N), dtype=src_type)
view_src = src_view_type(src, hs, N)
dst = np.zeros(n_fermion_sector_size(hs, N), dtype=dst_type)
view_dst = dst_view_type(dst, hs, N)
# 1 boson, fermions in the first N modes
index_in_f = sum(2**i for i in range(N))
src[view_src.map_index(index_in_f + (2**M))] = 1
Hop(view_src, view_dst)
ref = np.zeros(n_fermion_sector_size(hs, N), dtype=dst_type)
# 0 bosons
ref[view_dst.map_index(index_in_f)] = N
# 2 bosons
ref[view_dst.map_index(index_in_f + (2 ** (M + 1)))] = \
N * np.sqrt(2)
assert_allclose(dst, ref)
def test_n_fermion_multisector_size(self):
hs = HilbertSpace()
#
# Empty Hilbert space
#
self.assertEqual(n_fermion_multisector_size(hs, []), 0)
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(1)):
n_fermion_multisector_size(hs, [self.sda(1)])
#
# Empty sectors
#
self.assertEqual(n_fermion_multisector_size(hs, [self.sde(0)]), 0)
self.assertEqual(n_fermion_multisector_size(hs, [self.sde(1)]), 0)
self.assertEqual(
n_fermion_multisector_size(hs,
[self.sde(0), self.sde(0)]), 0)
self.assertEqual(
n_fermion_multisector_size(hs,
[self.sde(1), self.sde(1)]), 0)
#
# Purely fermionic Hilbert spaces
#
for i in range(self.M_total):
hs.add(make_space_fermion(i))
# Empty sectors
self.assertEqual(n_fermion_multisector_size(hs, [self.sde(0)]), 2048)
self.assertEqual(n_fermion_multisector_size(hs, [self.sde(1)]), 0)
self.assertEqual(
n_fermion_multisector_size(hs,
[self.sde(0), self.sde(0)]), 2048)
self.assertEqual(
n_fermion_multisector_size(hs,
[self.sde(1), self.sde(1)]), 0)
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
n_fermion_multisector_size(hs, [self.sda(2), ([(6, )], 1)])
self.assertEqual(n_fermion_multisector_size(hs, []), 2048)
# One sector
for N in range(self.Na_max + 1):
self.assertEqual(n_fermion_multisector_size(hs, [self.sda(N)]),
self.ab_size_ref[N] * 128)
for N in range(self.N5_max + 1):
self.assertEqual(n_fermion_multisector_size(hs, [self.sd5(N)]),
1024)
for N in range(self.Nb_max + 1):
self.assertEqual(n_fermion_multisector_size(hs, [self.sdb(N)]),
self.ab_size_ref[N] * 128)
# Two sectors
for N1, N2 in product(range(self.Na_max + 1), range(self.Nb_max + 1)):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sda(N1), self.sdb(N2)]),
self.ab_size_ref[N1] * self.ab_size_ref[N2] * 8)
# Three sectors
for N1, N2, N3 in product(range(self.Na_max + 1),
range(self.N5_max + 1),
range(self.Nb_max + 1)):
self.assertEqual(
n_fermion_multisector_size(
hs,
[self.sda(N1), self.sd5(N2),
self.sdb(N3)]),
self.ab_size_ref[N1] * self.ab_size_ref[N3] * 4)
# Mixture with the empty sector
for N in range(self.Na_max + 1):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sda(N), self.sde(0)]), self.ab_size_ref[N] * 128)
for N in range(self.N5_max + 1):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sd5(N), self.sde(0)]), 1024)
for N in range(self.Nb_max + 1):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sdb(N), self.sde(0)]), self.ab_size_ref[N] * 128)
#
# Fermions and bosons
#
hs.add(make_space_boson(2, 0))
self.assertEqual(n_fermion_multisector_size(hs, []), 8192)
# One sector
for N in range(self.Na_max + 1):
self.assertEqual(n_fermion_multisector_size(hs, [self.sda(N)]),
self.ab_size_ref[N] * 512)
for N in range(self.N5_max + 1):
self.assertEqual(n_fermion_multisector_size(hs, [self.sd5(N)]),
4096)
for N in range(self.Nb_max + 1):
self.assertEqual(n_fermion_multisector_size(hs, [self.sdb(N)]),
self.ab_size_ref[N] * 512)
# Two sectors
for N1, N2 in product(range(self.Na_max + 1), range(self.Nb_max + 1)):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sda(N1), self.sdb(N2)]),
self.ab_size_ref[N1] * self.ab_size_ref[N2] * 32)
# Three sectors
for N1, N2, N3 in product(range(self.Na_max + 1),
range(self.N5_max + 1),
range(self.Nb_max + 1)):
self.assertEqual(
n_fermion_multisector_size(
hs,
[self.sda(N1), self.sd5(N2),
self.sdb(N3)]),
self.ab_size_ref[N1] * self.ab_size_ref[N3] * 16)
# Mixture with the empty sector
for N in range(self.Na_max + 1):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sda(N), self.sde(0)]), self.ab_size_ref[N] * 512)
for N in range(self.N5_max + 1):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sd5(N), self.sde(0)]), 4096)
for N in range(self.Nb_max + 1):
self.assertEqual(
n_fermion_multisector_size(
hs, [self.sdb(N), self.sde(0)]), self.ab_size_ref[N] * 512)
#
# Purely bosonic Hilbert space
#
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
self.assertEqual(n_fermion_multisector_size(hs_b, []), 32)
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(1)):
n_fermion_multisector_size(hs_b, [self.sda(1)])
def test_loperator(self):
hs = HilbertSpace([make_space_boson(2, 0)])
for i in range(self.M_total):
hs.add(make_space_fermion(i))
sector_a_modes = [1, 2, 6, 7]
sector_b_modes = [3, 4, 8, 9]
Ha = (n(1) + n(2) + n(6) + n(7)) * (a_dag(0) + a(0))
Hb = (n(3) + n(4) + n(8) + n(9)) * (a_dag(0) + a(0))
for src_type, dst_type, lop_type in [(float, float, LOperatorR),
(float, complex, LOperatorR),
(complex, complex, LOperatorR),
(float, complex, LOperatorC),
(complex, complex, LOperatorC)]:
src_view_type = NFermionMultiSectorViewR if (src_type == float) \
else NFermionMultiSectorViewC
dst_view_type = NFermionMultiSectorViewR if (dst_type == float) \
else NFermionMultiSectorViewC
lop_is_real = lop_type == LOperatorR
Hopa = lop_type(Ha if lop_is_real else make_complex(Ha), hs)
Hopb = lop_type(Hb if lop_is_real else make_complex(Hb), hs)
for N1, N2 in product(range(self.Na_max + 1),
range(self.Nb_max + 1)):
sectors = [self.sda(N1), self.sdb(N2)]
src = np.zeros(n_fermion_multisector_size(hs, sectors),
dtype=src_type)
view_src = src_view_type(src, hs, sectors)
dst = np.zeros(n_fermion_multisector_size(hs, sectors),
dtype=dst_type)
view_dst = dst_view_type(dst, hs, sectors)
# Input:
# First N1 modes of sector A are occupied
# First N2 modes of sector B are occupied
# 1 boson
index_in_f = sum(2**sector_a_modes[n1] for n1 in range(N1))
index_in_f += sum(2**sector_b_modes[n2] for n2 in range(N2))
src[view_src.map_index(index_in_f + (2**self.M_total))] = 1
Hopa(view_src, view_dst)
ref = np.zeros(n_fermion_multisector_size(hs, sectors),
dtype=dst_type)
# 0 bosons
ref[view_dst.map_index(index_in_f)] = N1
# 2 bosons
ref[view_dst.map_index(index_in_f + (2 ** (self.M_total + 1)))]\
= N1 * np.sqrt(2)
assert_allclose(dst, ref)
Hopb(view_src, view_dst)
ref = np.zeros(n_fermion_multisector_size(hs, sectors),
dtype=dst_type)
# 0 bosons
ref[view_dst.map_index(index_in_f)] = N2
# 2 bosons
ref[view_dst.map_index(index_in_f + (2 ** (self.M_total + 1)))]\
= N2 * np.sqrt(2)
assert_allclose(dst, ref)
def test_n_fermion_sector_basis_states(self):
st = np.array([], dtype=float)
# Build a reference list of basis states for
# n_fermion_multisector_basis_states() by repeatedly calling map_index()
def build_basis_states_ref(hs, sectors, selector):
view = NFermionMultiSectorViewR(st, hs, sectors)
basis_states = [-1] * n_fermion_multisector_size(hs, sectors)
for index in range(hs.dim):
if selector(index):
basis_states[view.map_index(index)] = index
return basis_states
hs = HilbertSpace()
#
# Empty Hilbert space
#
self.assertEqual(n_fermion_multisector_basis_states(hs, []), [])
self.assertEqual(n_fermion_multisector_basis_states(hs, [self.sde(0)]),
[])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(hs, [self.sde(1)])
self.assertEqual(
n_fermion_multisector_basis_states(
hs, [self.sde(0), self.sde(0)]), [])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(hs, [self.sde(0), self.sde(1)])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(hs, [self.sde(1), self.sde(0)])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(hs, [self.sde(1), self.sde(1)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(0)):
n_fermion_multisector_basis_states(hs, [self.sd0(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(0)):
n_fermion_multisector_basis_states(hs, [self.sd0(1)])
#
# Purely fermionic Hilbert spaces
#
for i in range(self.M_total):
hs.add(make_space_fermion(i))
for N in range(self.N5_max + 1):
sectors = [self.sd5(N)]
ref = build_basis_states_ref(hs, sectors,
self.sd5_index_selector(N))
self.assertEqual(n_fermion_multisector_basis_states(hs, sectors),
ref)
for N1, N2 in product(range(self.Na_max + 1), range(self.Nb_max + 1)):
sectors = [self.sda(N1), self.sdb(N2)]
ref = build_basis_states_ref(hs, sectors,
self.sdab_index_selector(N1, N2))
self.assertEqual(n_fermion_multisector_basis_states(hs, sectors),
ref)
for N1, N2, N3 in product(range(self.Na_max + 1),
range(self.N5_max + 1),
range(self.Nb_max + 1)):
sectors = [self.sda(N1), self.sd5(N2), self.sdb(N3)]
ref = build_basis_states_ref(hs, sectors,
self.sda5b_index_selector(N1, N2, N3))
self.assertEqual(n_fermion_multisector_basis_states(hs, sectors),
ref)
#
# Fermions and bosons
#
hs.add(make_space_boson(2, self.M_total))
hs.add(make_space_boson(2, self.M_total + 1))
for N in range(self.N5_max + 1):
sectors = [self.sd5(N)]
ref = build_basis_states_ref(hs, sectors,
self.sd5_index_selector(N))
self.assertEqual(n_fermion_multisector_basis_states(hs, sectors),
ref)
for N1, N2 in product(range(self.Na_max + 1), range(self.Nb_max + 1)):
sectors = [self.sda(N1), self.sdb(N2)]
ref = build_basis_states_ref(hs, sectors,
self.sdab_index_selector(N1, N2))
self.assertEqual(n_fermion_multisector_basis_states(hs, sectors),
ref)
for N1, N2, N3 in product(range(self.Na_max + 1),
range(self.N5_max + 1),
range(self.Nb_max + 1)):
sectors = [self.sda(N1), self.sd5(N2), self.sdb(N3)]
ref = build_basis_states_ref(hs, sectors,
self.sda5b_index_selector(N1, N2, N3))
self.assertEqual(n_fermion_multisector_basis_states(hs, sectors),
ref)
#
# Purely bosonic Hilbert space
#
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
ref = list(range(n_fermion_multisector_size(hs_b, [])))
self.assertEqual(n_fermion_multisector_basis_states(hs_b, []), ref)
self.assertEqual(
n_fermion_multisector_basis_states(hs_b, [self.sde(0)]), ref)
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(hs_b, [self.sde(1)])
self.assertEqual(
n_fermion_multisector_basis_states(
hs_b, [self.sde(0), self.sde(0)]), ref)
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(
hs_b, [self.sde(0), self.sde(1)])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(
hs_b, [self.sde(1), self.sde(0)])
with self.assertRaisesRegex(RuntimeError, self.wrong_n_error_msg(0,
1)):
n_fermion_multisector_basis_states(
hs_b, [self.sde(1), self.sde(1)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(0)):
n_fermion_multisector_basis_states(hs_b, [self.sd0(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(0)):
n_fermion_multisector_basis_states(hs_b, [self.sd0(1)])
def test_map_index(self):
st = np.array([], dtype=float)
# Check that values returned by map_index() form a continuous
# sequence [0; expected_multisector_size)
def check_map_index(view, hs, selector, expected_multisector_size):
mapped_indices = []
for index in range(hs.dim):
if selector(index):
mapped_indices.append(view.map_index(index))
mapped_indices.sort()
mapped_indices_ref = list(range(expected_multisector_size))
self.assertEqual(mapped_indices, mapped_indices_ref)
#
# Purely fermionic Hilbert spaces
#
hs = HilbertSpace([make_space_fermion(i) for i in range(self.M_total)])
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
for N in range(self.N5_max + 1):
check_map_index(ViewType(st, hs, [self.sd5(N)]), hs,
self.sd5_index_selector(N),
2**(self.M_total - 1))
for N1, N2 in product(range(self.Na_max + 1),
range(self.Nb_max + 1)):
check_map_index(
ViewType(st, hs, [self.sda(N1), self.sdb(N2)]), hs,
self.sdab_index_selector(N1, N2),
comb(4, N1) * comb(4, N2) * (2**(self.M_total - 8)))
for N1, N2, N3 in product(range(self.Na_max + 1),
range(self.N5_max + 1),
range(self.Nb_max + 1)):
check_map_index(
ViewType(st, hs,
[self.sda(N1),
self.sd5(N2),
self.sdb(N3)]), hs,
self.sda5b_index_selector(N1, N2, N3),
comb(4, N1) * comb(4, N3) * (2**(self.M_total - 9)))
#
# Fermions and bosons
#
hs.add(make_space_boson(2, self.M_total))
hs.add(make_space_boson(2, self.M_total + 1))
M = self.M_total + 4
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
for N in range(self.N5_max + 1):
check_map_index(ViewType(st, hs, [self.sd5(N)]), hs,
self.sd5_index_selector(N), 2**(M - 1))
for N1, N2 in product(range(self.Na_max + 1),
range(self.Nb_max + 1)):
check_map_index(ViewType(
st, hs, [self.sda(N1), self.sdb(N2)]), hs,
self.sdab_index_selector(N1, N2),
comb(4, N1) * comb(4, N2) * (2**(M - 8)))
for N1, N2, N3 in product(range(self.Na_max + 1),
range(self.N5_max + 1),
range(self.Nb_max + 1)):
check_map_index(
ViewType(st, hs,
[self.sda(N1),
self.sd5(N2),
self.sdb(N3)]), hs,
self.sda5b_index_selector(N1, N2, N3),
comb(4, N1) * comb(4, N3) * (2**(M - 9)))
#
# Purely bosonic Hilbert space
#
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
view = ViewType(st, hs_b, [self.sde(0)])
for index in range(hs_b.dim):
self.assertEqual(view.map_index(index), index)
def test_init_exceptions(self):
st = np.array([], dtype=float)
hs = HilbertSpace()
#
# Empty Hilbert space
#
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(1)):
ViewType(st, hs, [self.sda(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(1)):
ViewType(st, hs, [self.sda(1)])
#
# One fermion
#
hs.add(make_space_fermion(0))
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(1, 2)):
ViewType(st, hs, [self.sd0(2)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(1)):
ViewType(st, hs, [self.sda(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(1)):
ViewType(st, hs, [self.sda(1)])
#
# Multiple fermions
#
for i in range(1, self.M_total):
hs.add(make_space_fermion(i))
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
for N in range(self.Na_max):
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sda(N), self.sda(N)])
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sde(0), self.sda(N), self.sda(N)])
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sda(N), self.sde(0), self.sda(N)])
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sda(N), self.sda(N), self.sde(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(1, 2)):
ViewType(st, hs, [self.sd0(2)])
#
# Fermions and bosons
#
hs.add(make_space_boson(1, 5))
hs.add(make_space_boson(2, 6))
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
for N in range(self.Na_max):
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sda(N), self.sda(N)])
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sde(0), self.sda(N), self.sda(N)])
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sda(N), self.sde(0), self.sda(N)])
with self.assertRaisesRegex(RuntimeError,
"^Some of the sectors overlap$"):
ViewType(st, hs, [self.sda(N), self.sda(N), self.sde(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_n_error_msg(1, 2)):
ViewType(st, hs, [self.sd0(2)])
#
# Purely bosonic Hilbert space
#
hs_b = HilbertSpace([make_space_boson(2, 0), make_space_boson(3, 1)])
for ViewType in (NFermionMultiSectorViewR, NFermionMultiSectorViewC):
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(0)):
ViewType(st, hs_b, [self.sd0(0)])
with self.assertRaisesRegex(RuntimeError,
self.wrong_indices_error_msg(0)):
ViewType(st, hs_b, [self.sd0(1)])
# Qubit-oscillator coupling constants as a 2x1 array.
g = np.array([[0.5], [0.6]])
# Create the Tavis-Cummings Hamiltonian.
H = jaynes_cummings(eps, omega, g)
# Construct state space of our problem as a direct product of two
# two-dimensional Hilbert spaces (qubits) and one truncated bosonic Hilbert
# space.
# make_space_boson(4) returns the truncated bosonic space with allowed
# occupation numbers N = 0, 1, ..., (2^4-1).
hs = HilbertSpace([
make_space_spin(1 / 2, 0), # Qubit 1: spin-1/2, index 0
make_space_spin(1 / 2, 1), # Qubit 2: spin-1/2, index 1
make_space_boson(4, 0) # Oscillator, index 0
])
# Construct a linear operator corresponding to 'H' and acting in the Hilbert
# space 'hs'.
H_op = LOperatorR(H, hs)
#
# Prepare a matrix representation of 'H_op'
#
# Method I (manual).
H_mat1 = np.zeros((hs.dim, hs.dim))
for i in range(hs.dim):
# A column vector psi = {0, 0, ..., 1, ..., 0}
psi = np.zeros(hs.dim)