def test_if_quadratic_sequence_with_even_inner_pulses_is_identity():
"""
Tests if the product of the pulses in a quadratic sequence with pre/post
pi/2-pulses is an identity, when the total number of inner pulses is even.
"""
inner_even_quadratic_sequence = new_quadratic_sequence(
duration=10.0,
inner_offset_count=8,
outer_offset_count=7,
pre_post_rotation=True,
)
# n_outer + n_inner*(n_outer+1) pi-pulses + 2 pi/2-pulses
# total number here is even
assert len(inner_even_quadratic_sequence.offsets) == 7 + 8 * (7 + 1) + 2
assert _pulses_produce_identity(inner_even_quadratic_sequence)
def test_quadratic_sequence():
"""
Tests the quadratic sequence.
"""
duration = 10.0
inner_offset_count = 4
outer_offset_count = 4
sequence = new_quadratic_sequence(
duration=duration,
inner_offset_count=inner_offset_count,
outer_offset_count=outer_offset_count,
)
_offsets = np.zeros((outer_offset_count + 1, inner_offset_count + 1))
constant = 0.5 / (outer_offset_count + 1)
_delta_positions = [
duration * (np.sin(np.pi * (k + 1) * constant))**2
for k in range(outer_offset_count)
]
_outer_offsets = np.array(_delta_positions)
_offsets[0:outer_offset_count, -1] = _outer_offsets
_outer_offsets = np.insert(
_outer_offsets,
[0, _outer_offsets.shape[0]],
[0, duration],
)
_inner_durations = _outer_offsets[1:] - _outer_offsets[0:-1]
constant = 0.5 / (inner_offset_count + 1)
_delta_positions = [(np.sin(np.pi * (k + 1) * constant))**2
for k in range(inner_offset_count)]
_delta_positions = np.array(_delta_positions)
for inner_sequence_idx in range(_inner_durations.shape[0]):
_inner_deltas = _inner_durations[inner_sequence_idx] * _delta_positions
_inner_deltas = _outer_offsets[inner_sequence_idx] + _inner_deltas
_offsets[inner_sequence_idx, 0:inner_offset_count] = _inner_deltas
_rabi_rotations = np.zeros(_offsets.shape)
_detuning_rotations = np.zeros(_offsets.shape)
_rabi_rotations[0:outer_offset_count, -1] = np.pi
_detuning_rotations[0:(outer_offset_count + 1),
0:inner_offset_count] = np.pi
_offsets = np.reshape(_offsets, (-1, ))
_rabi_rotations = np.reshape(_rabi_rotations, (-1, ))
_detuning_rotations = np.reshape(_detuning_rotations, (-1, ))
_offsets = _offsets[0:-1]
_rabi_rotations = _rabi_rotations[0:-1]
_detuning_rotations = _detuning_rotations[0:-1]
_azimuthal_angles = np.zeros(_offsets.shape)
assert np.allclose(_offsets, sequence.offsets)
assert np.allclose(_rabi_rotations, sequence.rabi_rotations)
assert np.allclose(_azimuthal_angles, sequence.azimuthal_angles)
assert np.allclose(_detuning_rotations, sequence.detuning_rotations)
sequence = new_quadratic_sequence(
duration=duration,
inner_offset_count=inner_offset_count,
outer_offset_count=outer_offset_count,
pre_post_rotation=True,
)
_offsets = np.insert(_offsets, [0, _offsets.shape[0]], [0, duration])
_rabi_rotations = np.insert(_rabi_rotations, [0, _rabi_rotations.shape[0]],
[np.pi / 2, np.pi / 2])
_detuning_rotations = np.insert(_detuning_rotations,
[0, _detuning_rotations.shape[0]], [0, 0])
_azimuthal_angles = np.zeros(_offsets.shape)
_azimuthal_angles[-1] = np.pi
assert np.allclose(_offsets, sequence.offsets)
assert np.allclose(_rabi_rotations, sequence.rabi_rotations)
assert np.allclose(_azimuthal_angles, sequence.azimuthal_angles)
assert np.allclose(_detuning_rotations, sequence.detuning_rotations)