def test_walsh_sequence():
"""
Tests the Walsh sequence.
"""
duration = 10.0
paley_order = 20
sequence = new_walsh_sequence(duration=duration, paley_order=paley_order)
hamming_weight = 5
samples = 2**hamming_weight
relative_offset = np.arange(1.0 / (2 * samples), 1.0, 1.0 / samples)
binary_string = np.binary_repr(paley_order)
binary_order = [int(binary_string[i]) for i in range(hamming_weight)]
walsh_array = np.ones([samples])
for i in range(hamming_weight):
walsh_array *= (np.sign(
np.sin(2**(i + 1) * np.pi *
relative_offset))**binary_order[hamming_weight - 1 - i])
walsh_relative_offsets = []
for i in range(samples - 1):
if walsh_array[i] != walsh_array[i + 1]:
walsh_relative_offsets.append((i + 1) * (1.0 / samples))
walsh_relative_offsets = np.array(walsh_relative_offsets, dtype=np.float)
_offsets = duration * walsh_relative_offsets
_offsets = np.array(_offsets)
_rabi_rotations = np.pi * np.ones(_offsets.shape)
_azimuthal_angles = np.zeros(_offsets.shape)
_detuning_rotations = 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_walsh_sequence(
duration=duration,
paley_order=paley_order,
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])
_azimuthal_angles = np.zeros(_offsets.shape)
_azimuthal_angles[-1] = np.pi
_detuning_rotations = 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)
def test_if_walsh_sequence_with_even_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 number of pulses is even.
"""
even_walsh_sequence = new_walsh_sequence(duration=10.0,
paley_order=6,
pre_post_rotation=True)
# A Walsh sequence with paley_order 6 has 4 pi-pulses + 2 pi/2-pulses,
# see https://arxiv.org/pdf/1109.6002.pdf
assert len(even_walsh_sequence.offsets) == 4 + 2
assert _pulses_produce_identity(even_walsh_sequence)
def test_if_walsh_sequence_with_odd_pulses_is_identity():
"""
Tests if the product of the pulses in a Walsh sequence with pre/post
pi/2-pulses is an identity, when the number of pulses is odd.
"""
odd_walsh_sequence = new_walsh_sequence(duration=10.0,
paley_order=7,
pre_post_rotation=True)
# A Walsh sequence with paley_order 7 has 5 pi-pulses + 2 pi/2-pulses,
# see https://arxiv.org/pdf/1109.6002.pdf
assert len(odd_walsh_sequence.offsets) == 5 + 2
assert _pulses_produce_identity(odd_walsh_sequence)