Merge pull request #94 from qctrl/dd

Fix pre-post rotations

Author: tachikoma-li

qctrlopencontrols/dynamic_decoupling_sequences/predefined.py

@@ -39,17 +39,12 @@
 def _add_pre_post_rotations(
     duration, offsets, rabi_rotations, azimuthal_angles, detuning_rotations
 ):
-    """Adds a pre-post pi.2 rotation at the
-    start and end of the sequence.
+    """Adds a pre and post X rotation at the start and end of the sequence.
 
-    The parameters of the pi/2-pulses are chosen in order to cancel out the
-    product of the pulses in the DSS, so that its total effect in the
-    absence of noise is an identity.
-
-    For a DSS that already produces an identity, this function adds X pi/2-pulses
-    in opposite directions, so that they cancel out. If the DDS produces an X
-    gate, the X pi/2-pulses will be in the same direction. If the DDS produces
-    a Y (Z) gate, the pi/2-pulses are around the Y (Z) axis.
+    Note that with these two pre and post X rotations, the net effect of the DDS does not
+    necessarily have to be an identity, but it will always be either an identity or Z pi rotation.
+    For example, given a CPMG sequence of odd number Y pi rotations in the middle with the pre
+    (pi/2) and post(-pi/2) X rotations, the net effect will be a Z gate.
 
     This function assumes that the sequences only have X, Y, and Z pi-pulses.
     An exception is thrown if that is not the case.
@@ -118,6 +113,12 @@ def _add_pre_post_rotations(
             },
         )
 
+    # parameters for pre-post pulses
+    rabi_value = np.pi / 2
+    detuning_value = 0
+    initial_azimuthal = 0  # for pre-pulse
+    final_azimuthal = 0  # for post-pulse
+
     # The sequence will preserve the state |0> is it has an even number
     # of X and Y pi-pulses
     preserves_10 = (x_pi_pulses + y_pi_pulses) % 2 == 0
@@ -126,40 +127,12 @@ def _add_pre_post_rotations(
     # of Y and Z pi-pulses
     preserves_11 = (y_pi_pulses + z_pi_pulses) % 2 == 0
 
-    # When states |0> and |0>+|1> are preserved, the sequence already produces
-    # an identity, so that we want the the pi/2-pulses to cancel each other out
-    if preserves_10 and preserves_11:
-        rabi_value = np.pi / 2
-        initial_azimuthal = 0
+    # the direction of the post rotation depends on the property of DDS.
+    # if the net effect of the sequences is an identity gate or Y rotation, the post rotation
+    # is chosen to be -pi/2 X pulse, otherwise use pi/2 X pulse, to ensure the net effect is an
+    # identity or Z rotation.
+    if (preserves_10 and preserves_11) or (not preserves_10 and not preserves_11):
         final_azimuthal = np.pi
-        detuning_value = 0
-
-    # When only state |0>+|1> is not preserved, the sequence results in a Z rotation.
-    # In this case, we want both pi/2-pulses to be in the Z direction,
-    # so that the remaining rotation is cancelled out
-    if preserves_10 and not preserves_11:
-        rabi_value = 0
-        initial_azimuthal = 0
-        final_azimuthal = 0
-        detuning_value = np.pi / 2
-
-    # When only state |0> is not preserved, the sequence results in an X rotation.
-    # In this case, we want both pi/2-pulses to be in the X direction,
-    # so that the remaining rotation is cancelled out
-    if not preserves_10 and preserves_11:
-        rabi_value = np.pi / 2
-        initial_azimuthal = 0
-        final_azimuthal = 0
-        detuning_value = 0
-
-    # When neither state is preserved, the sequence results in a Y rotation.
-    # In this case, we want both pi/2-pulses to be in the Y direction,
-    # so that the remaining rotation is cancelled out
-    if not preserves_10 and not preserves_11:
-        rabi_value = np.pi / 2
-        initial_azimuthal = np.pi / 2
-        final_azimuthal = np.pi / 2
-        detuning_value = 0
 
     offsets = np.insert(offsets, [0, offsets.shape[0]], [0, duration],)
     rabi_rotations = np.insert(

tests/test_predefined_dynamical_decoupling.py

@@ -36,6 +36,10 @@
 )
 from qctrlopencontrols.exceptions import ArgumentsValueError
 
+SIGMA_X = np.array([[0.0, 1.0], [1.0, 0.0]])
+SIGMA_Y = np.array([[0.0, -1.0j], [1.0j, 0.0]])
+SIGMA_Z = np.array([[1.0, 0.0], [0.0, -1.0]])
+
 
 def test_ramsey():
 
@@ -672,16 +676,13 @@ def test_attribute_values():
 
 def _pulses_produce_identity(sequence):
     """
-    Tests if the pulses of a DDS sequence produce an identity in absence of noise.
+    Tests if the pulses of a DDS sequence produce an identity or Z rotation in absence of noise.
     We check this by creating the unitary of each pulse and then multiplying them
     by each other to check the complete evolution.
     """
-    sigma_x = np.array([[0.0, 1.0], [1.0, 0.0]])
-    sigma_y = np.array([[0.0, -1.0j], [1.0j, 0.0]])
-    sigma_z = np.array([[1.0, 0.0], [0.0, -1.0]])
 
     # The unitary evolution due to an instantaneous pulse can be written as
-    # U = cos(|n|) I -i sin(|n|) *(n_x sigma_x + n_y sigma_y + n_z sigma_z)/|n|
+    # U = cos(|n|) I -i sin(|n|) *(n_x SIGMA_x + n_y SIGMA_y + n_z SIGMA_z)/|n|
     # where n is a vector with components
     # n_x = rabi * cos(azimuthal)/2
     # n_y = rabi * sin(azimuthal)/2
@@ -697,9 +698,9 @@ def _pulses_produce_identity(sequence):
         mod_n = np.sqrt(n_x ** 2 + n_y ** 2 + n_z ** 2)
         unitary = (
             np.cos(mod_n) * np.identity(2)
-            - 1.0j * (np.sin(mod_n) * n_x / mod_n) * sigma_x
-            - 1.0j * (np.sin(mod_n) * n_y / mod_n) * sigma_y
-            - 1.0j * (np.sin(mod_n) * n_z / mod_n) * sigma_z
+            - 1.0j * (np.sin(mod_n) * n_x / mod_n) * SIGMA_X
+            - 1.0j * (np.sin(mod_n) * n_y / mod_n) * SIGMA_Y
+            - 1.0j * (np.sin(mod_n) * n_z / mod_n) * SIGMA_Z
         )
         matrix_product = np.matmul(unitary, matrix_product)
 
@@ -708,7 +709,9 @@ def _pulses_produce_identity(sequence):
 
     expected_matrix_product = np.identity(2)
 
-    return np.allclose(matrix_product, expected_matrix_product)
+    return np.allclose(matrix_product, expected_matrix_product) or np.allclose(
+        SIGMA_Z.dot(matrix_product), expected_matrix_product
+    )
 
 
 def test_if_ramsey_sequence_is_identity():
@@ -762,7 +765,7 @@ def test_if_carr_purcell_sequence_with_even_pulses_is_identity():
 def test_if_cpmg_sequence_with_odd_pulses_is_identity():
     """
     Tests if the product of the pulses in a CPMG sequence with pre/post
-    pi/2-pulses is an identity, when the number of pulses is odd.
+    pi/2-pulses and an extra Z rotation is an identity, when the number of pulses is odd.
     """
     odd_cpmg_sequence = new_predefined_dds(
         scheme=CARR_PURCELL_MEIBOOM_GILL,
@@ -792,7 +795,7 @@ def test_if_cpmg_sequence_with_even_pulses_is_identity():
 def test_if_uhrig_sequence_with_odd_pulses_is_identity():
     """
     Tests if the product of the pulses in an Uhrig sequence with pre/post
-    pi/2-pulses is an identity, when the number of pulses is odd.
+    pi/2-pulses and an extra Z rotation is an identity, when the number of pulses is odd.
     """
     odd_uhrig_sequence = new_predefined_dds(
         scheme=UHRIG_SINGLE_AXIS,
@@ -924,7 +927,8 @@ def test_if_quadratic_sequence_with_even_pulses_is_identity():
 def test_if_quadratic_sequence_with_odd_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 odd.
+    pi/2-pulses and an extra rotation is an identity, when the total number
+    of inner pulses is odd.
     """
     inner_odd_quadratic_sequence = new_predefined_dds(
         scheme=QUADRATIC,