def test_2mode_ffft_correct_frequencies(self):
n_qubits = 2
frequencies_seen = numpy.zeros(n_qubits)
for qubit in range(n_qubits):
engine = MainEngine()
register = engine.allocate_qureg(n_qubits)
X | register[qubit]
ffft(engine, register, n_qubits)
engine.flush()
wavefunction = ordered_wavefunction(engine)
nonzero_wavefunction_elmts = []
for el in wavefunction:
if abs(el) > 10 ** -5:
nonzero_wavefunction_elmts.append(el)
All(Measure) | register
phase_factor = (nonzero_wavefunction_elmts[1] /
nonzero_wavefunction_elmts[0])
offset = numpy.angle(nonzero_wavefunction_elmts[0])
self.assertAlmostEqual(offset, 0.0)
for i in range(1, len(nonzero_wavefunction_elmts)):
self.assertAlmostEqual(phase_factor,
(nonzero_wavefunction_elmts[i] /
nonzero_wavefunction_elmts[i - 1]))
frequencies_seen[qubit] = numpy.angle(phase_factor)
frequencies_seen = numpy.sort(frequencies_seen)
expected = numpy.sort(2 * numpy.pi * numpy.arange(n_qubits) / n_qubits)
self.assertTrue(numpy.allclose(frequencies_seen, expected))
def test_8mode_ffft_with_external_swaps_on_single_logical_state(self):
n_qubits = 8
grid = Grid(dimensions=1, length=n_qubits, scale=1.0)
eng = MainEngine()
register = eng.allocate_qureg(n_qubits)
state_index = 157
prepare_logical_state(register, state_index)
ffft(eng, register, n_qubits)
Ph(3 * numpy.pi / 4) | register[0]
eng.flush()
wvfn = ordered_wavefunction(eng)
fermion_operator = prepare_integer_fermion_operator(state_index)
# Swap 01234567 to 45670123 for fourier_transform. Additionally,
# the FFFT's ordering is 04261537, so swap 04261537 to 01234567,
# and then 01234567 to 45670123.
swap_mode_list = ([1, 3, 5, 2, 4, 1, 3, 5] +
[3, 2, 4, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 2, 4, 3])
for mode in swap_mode_list:
fermion_operator = normal_ordered(fermion_operator)
fermion_operator = swap_adjacent_fermionic_modes(
fermion_operator, mode)
ffft_result = fourier_transform(fermion_operator,
grid, spinless=True)
ffft_result = normal_ordered(ffft_result)
# After the FFFT, swap 45670123 -> 01234567.
swap_mode_list = [3, 2, 4, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 2, 4, 3]
for mode in swap_mode_list:
ffft_result = swap_adjacent_fermionic_modes(ffft_result, mode)
converted_wvfn = numpy.zeros(2 ** n_qubits, dtype=complex)
for term in ffft_result.terms:
index = sum(2 ** site[0] for site in term)
converted_wvfn[index] = ffft_result.terms[term]
All(Measure) | register
self.assertTrue(numpy.allclose(wvfn, converted_wvfn))
def test_ffft_2modes_properly_applied(self):
eng_ft_0 = MainEngine()
reg_ft_0 = eng_ft_0.allocate_qureg(2)
eng_ffft_recursive = MainEngine()
reg_ffft_recursive = eng_ffft_recursive.allocate_qureg(2)
ffft(eng_ffft_recursive, reg_ffft_recursive, 2)
fourier_transform_0(reg_ft_0, 0, 1)
eng_ffft_recursive.flush()
eng_ft_0.flush()
All(Measure) | reg_ffft_recursive
All(Measure) | reg_ft_0
self.assertTrue(numpy.allclose(
ordered_wavefunction(eng_ffft_recursive),
ordered_wavefunction(eng_ft_0)))
def test_4mode_ffft_with_external_swaps_all_logical_states(self):
n_qubits = 4
grid = Grid(dimensions=1, length=n_qubits, scale=1.0)
for i in range(2**n_qubits):
eng = MainEngine()
register = eng.allocate_qureg(n_qubits)
prepare_logical_state(register, i)
ffft(eng, register, n_qubits)
Ph(3 * numpy.pi / 4) | register[0]
eng.flush()
wvfn = ordered_wavefunction(eng)
fermion_operator = prepare_integer_fermion_operator(i)
# Reorder the modes for correct input to the FFFT.
# Swap 0123 to 2301 for fourier_transform. Additionally, the
# FFFT's ordering is 0213, so connect 0213 -> 0123 -> 2301.
swap_mode_list = [1] + [1, 0, 2, 1]
for mode in swap_mode_list:
fermion_operator = normal_ordered(fermion_operator)
fermion_operator = swap_adjacent_fermionic_modes(
fermion_operator, mode)
ffft_result = fourier_transform(fermion_operator,
grid,
spinless=True)
ffft_result = normal_ordered(ffft_result)
swap_mode_list = [1, 0, 2, 1] # After FFFT, swap 2301 -> 0123
for mode in swap_mode_list:
ffft_result = swap_adjacent_fermionic_modes(ffft_result, mode)
converted_wvfn = numpy.zeros(2**n_qubits, dtype=complex)
for term in ffft_result.terms:
index = sum(2**site[0] for site in term)
converted_wvfn[index] = ffft_result.terms[term]
All(Measure) | register
self.assertTrue(numpy.allclose(wvfn, converted_wvfn))
def test_8mode_ffft_with_external_swaps_equal_expectation_values(self):
n_qubits = 8
grid = Grid(dimensions=1, length=n_qubits, scale=1.0)
dual_basis = jellium_model(grid, spinless=True, plane_wave=False)
ffft_result = normal_ordered(dual_basis)
# Swap 01234567 to 45670123 for fourier_transform. Additionally,
# the FFFT's ordering is 04261537, so swap 04261537 to 01234567,
# and then 01234567 to 45670123.
swap_mode_list = ([1, 3, 5, 2, 4, 1, 3, 5] +
[3, 2, 4, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 2, 4, 3])
for mode in swap_mode_list:
ffft_result = swap_adjacent_fermionic_modes(ffft_result, mode)
ffft_result = normal_ordered(ffft_result)
ffft_result = fourier_transform(ffft_result,
grid, spinless=True)
ffft_result = normal_ordered(ffft_result)
# After the FFFT, swap 45670123 -> 01234567.
swap_mode_list = [3, 2, 4, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 2, 4, 3]
for mode in swap_mode_list:
ffft_result = swap_adjacent_fermionic_modes(ffft_result, mode)
ffft_result = normal_ordered(ffft_result)
jw_dual_basis = jordan_wigner(dual_basis)
jw_plane_wave = jordan_wigner(ffft_result)
# Do plane wave and dual basis calculations simultaneously.
pw_engine = MainEngine()
pw_wavefunction = pw_engine.allocate_qureg(n_qubits)
db_engine = MainEngine()
db_wavefunction = db_engine.allocate_qureg(n_qubits)
pw_engine.flush()
db_engine.flush()
# Choose random state.
state = numpy.zeros(2 ** n_qubits, dtype=complex)
for i in range(len(state)):
state[i] = (random.random() *
numpy.exp(1j * 2 * numpy.pi * random.random()))
state /= numpy.linalg.norm(state)
# Put randomly chosen state in the registers.
pw_engine.backend.set_wavefunction(state, pw_wavefunction)
db_engine.backend.set_wavefunction(state, db_wavefunction)
prepare_logical_state(pw_wavefunction, i)
prepare_logical_state(db_wavefunction, i)
All(H) | [pw_wavefunction[1], pw_wavefunction[3]]
All(H) | [db_wavefunction[1], db_wavefunction[3]]
ffft(db_engine, db_wavefunction, n_qubits)
Ph(3 * numpy.pi / 4) | db_wavefunction[0]
# Flush the engine and compute expectation values and eigenvalues.
pw_engine.flush()
db_engine.flush()
plane_wave_expectation_value = (
pw_engine.backend.get_expectation_value(
jw_dual_basis, pw_wavefunction))
dual_basis_expectation_value = (
db_engine.backend.get_expectation_value(
jw_plane_wave, db_wavefunction))
All(Measure) | pw_wavefunction
All(Measure) | db_wavefunction
self.assertAlmostEqual(plane_wave_expectation_value,
dual_basis_expectation_value)
def test_ffft_1mode_error(self):
eng = MainEngine()
reg = eng.allocate_qureg(1)
with self.assertRaises(ValueError):
ffft(eng, reg, 1)
