From 5bef4ce62f586952cfd256aa01d2a4626023be8b Mon Sep 17 00:00:00 2001
From: Hector Brown <hectorjbrown@protonmail.com>
Date: Sun, 8 Feb 2026 15:07:46 +1100
Subject: [PATCH 1/4] feat: add platonic universal dynamic decoupling sequence
 for qudits

---
 qctrlopencontrols/__init__.py                 |   2 +
 .../predefined.py                             | 180 ++++++++++++++++++
 tests/test_predefined_dynamical_decoupling.py | 115 +++++++++++
 3 files changed, 297 insertions(+)

diff --git a/qctrlopencontrols/__init__.py b/qctrlopencontrols/__init__.py
index a796866..bf87611 100644
--- a/qctrlopencontrols/__init__.py
+++ b/qctrlopencontrols/__init__.py
@@ -48,6 +48,7 @@
     new_walsh_sequence,
     new_x_concatenated_sequence,
     new_xy_concatenated_sequence,
+    new_platonic_sequence,
 )
 
 __all__ = [
@@ -76,4 +77,5 @@
     "new_walsh_sequence",
     "new_x_concatenated_sequence",
     "new_xy_concatenated_sequence",
+    "new_platonic_sequence",
 ]
diff --git a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
index 1f77fc1..3e695fc 100644
--- a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
+++ b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
@@ -1228,3 +1228,183 @@ def _concatenation_xy(concatenation_sequence) -> np.ndarray:
     if cumulations[-1] == -2 and cumulations[-2] == -2:
         cumulations = cumulations[0:-2]
     return cumulations
+
+
+def new_platonic_sequence(
+    duration, sequence="Octahedral", pre_post_rotation=False, name=None
+) -> DynamicDecouplingSequence:
+    r"""
+    Creates a platonic sequence.
+
+    Parameters
+    ----------
+    duration : float
+        Total duration of the sequence :math:`\tau` (in seconds).
+    sequence : string, optional.
+        Sequence to follow, one of ``"Dihedral"``, ``"Tetrahedral"``,
+        ``"Octahedral"``, ``"Icosahedral"``. Defaults to ``"Octahedral"``.
+    pre_post_rotation : bool, optional
+        If ``True``, a :math:`X_{\pi/2}` rotation is added at the
+        start and end of the sequence. Defaults to ``False``.
+    name : string, optional
+        Name of the sequence. Defaults to ``None``.
+
+    Returns
+    -------
+    DynamicDecouplingSequence
+        The platonic sequence.
+
+    Notes
+    -----
+    The platonic dynamic decoupling sequences use the symmetry of the point
+    groups associated with certain platonic solids in order to decouple spin-j
+    (:math:`j \le \frac{5}{2}`) systems from higher-order noise. The pulses are
+    equally spaced in time, and their number is set by the specific sequence as
+    illustrated below.
+
+    .. list-table::
+        :widths: 25 25
+        :header-rows: 1
+
+        * - Sequence
+          - Number of pulses
+        * - Dihedral
+          - 8
+        * - Tetrahedral
+          - 24
+        * - Octahedral
+          - 48
+        * - Icosahedral
+          - 120
+
+    For each sequence there are two generators, applied in a specific order so
+    as to traverse every edge of the associated point group which can be found
+    in [#]_ Appendix B. These generators are the rotations listed below,
+
+    .. list-table::
+        :widths: 25 25 25
+        :header-rows: 1
+
+        * - Sequence
+          - Generator :math:`a`
+          - Generator :math:`b`
+        * - Dihedral
+          - :math:`\left(\left(1,0,0\right),\pi\right)`
+          - :math:`\left(\left(0,1,0\right),\pi\right)`
+        * - Tetrahedral
+          - :math:`\left(\left(0,0,1\right),\frac{2\pi}{3}\right)`
+          - :math:`\left(\left(\frac{\sqrt{2}}{3},\sqrt{\frac{2}{3}},\frac{1}{3}\right),\frac{2\pi}{3}\right)`
+        * - Octahedral
+          - :math:`\left(\left(0,0,1\right),\frac{2\pi}{4}\right)`
+          - :math:`\left(\frac{1}{\sqrt{3}}\left(1,1,1\right),\frac{2\pi}{3}\right)`
+        * - Icosahedral
+          - :math:`\left(\frac{\left(0,-1,\phi\right)}{\sqrt{\phi+2}},\frac{2\pi}{5}\right)`
+          - :math:`\left(\frac{\left(1-\phi,0,\phi\right)}{\sqrt{3}},\frac{2\pi}{3}\right)`
+
+    where the rotations are given in axis-angle notation and
+    :math:`\phi=\frac{\sqrt{5}+1}{2}` is the golden ratio.
+
+    References
+    ----------
+    .. [#] `C. Read, E. Serrano-Ensástiga, and J. Martin, Quantum 9, 1661 (2025).
+        <https://doi.org/10.22331/q-2025-03-12-1661>`_
+    """
+    check_arguments(
+        duration > 0, "Sequence duration must be positive.", {"duration": duration}
+    )
+    check_arguments(
+        sequence in ["Dihedral", "Tetrahedral", "Octahedral", "Icosahedral"],
+        'Sequence must be one of "Dihedral", "Tetrahedral", "Octahedral", or "Icosahedral".',
+        {"sequence": sequence},
+    )
+
+    # The sequences outlined in the cited paper, each sequence is constructed
+    # from an Eulerian path on the Cayley graph associated with the relevant
+    # point group. Each sequence is constructed of 2 generating operations, in
+    # the order specified here.
+    # fmt: off
+    eulerian_paths = {
+        "Dihedral": [0, 1, 0, 1, 1, 0, 1, 0],
+        "Tetrahedral": [ 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0],
+        "Octahedral": [ 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1 ],
+        "Icosahedral": [ 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0 ]
+    }
+    # fmt: on
+
+    # The generators assocaited with each point group.
+    phi = (np.sqrt(5) + 1) / 2  # golden ratio
+    generators = {
+        "Dihedral": [
+            {"Rabi": np.pi, "Azimuthal": 0, "Detuning": 0},  # rabi, azimuthal, detuning
+            {"Rabi": np.pi, "Azimuthal": np.pi / 2, "Detuning": 0},
+        ],
+        "Tetrahedral": [
+            {"Rabi": 0, "Azimuthal": 0, "Detuning": 2 * np.pi / 3},
+            {
+                "Rabi": 4 * np.sqrt(2) * np.pi / 9,
+                "Azimuthal": np.pi / 3,
+                "Detuning": 2 * np.pi / 9,
+            },
+        ],
+        "Octahedral": [
+            {"Rabi": 0, "Azimuthal": 0, "Detuning": np.pi / 2},
+            {
+                "Rabi": 2 * np.sqrt(2 / 3) * np.pi / 3,
+                "Azimuthal": np.pi / 4,
+                "Detuning": 2 * np.pi / 3 / np.sqrt(3),
+            },
+        ],
+        "Icosahedral": [
+            {
+                "Rabi": 2 * np.pi / 5 / np.sqrt(phi + 2),
+                "Azimuthal": 3 * np.pi / 2,
+                "Detuning": 2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            },
+            {
+                "Rabi": 2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+                "Azimuthal": np.pi,
+                "Detuning": 2 * np.pi * phi / 3 / np.sqrt(3),
+            },
+        ],
+    }
+
+    # Re-use the CPMG offset function to obtain equally spaced pulses along a certain duration.
+    offsets = _carr_purcell_meiboom_gill_offsets(
+        duration, len(eulerian_paths[sequence])
+    )
+    rabi_rotations = np.array(
+        [generators[sequence][idx]["Rabi"] for idx in eulerian_paths[sequence]]
+    )
+    azimuthal_angles = np.array(
+        [generators[sequence][idx]["Azimuthal"] for idx in eulerian_paths[sequence]]
+    )
+    detuning_rotations = np.array(
+        [generators[sequence][idx]["Detuning"] for idx in eulerian_paths[sequence]]
+    )
+
+    if pre_post_rotation:
+        # Use a pi/2 followed by a -pi/2 X rotation as all the sequences
+        # correspond with an effective identity gate.
+        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.insert(
+            azimuthal_angles,
+            [0, azimuthal_angles.shape[0]],
+            [0, np.pi],
+        )
+        detuning_rotations = np.insert(
+            detuning_rotations,
+            [0, detuning_rotations.shape[0]],
+            [0, 0],
+        )
+
+    return DynamicDecouplingSequence(
+        duration=duration,
+        offsets=offsets,
+        rabi_rotations=rabi_rotations,
+        azimuthal_angles=azimuthal_angles,
+        detuning_rotations=detuning_rotations,
+        name=name,
+    )
diff --git a/tests/test_predefined_dynamical_decoupling.py b/tests/test_predefined_dynamical_decoupling.py
index daf3a90..109646c 100644
--- a/tests/test_predefined_dynamical_decoupling.py
+++ b/tests/test_predefined_dynamical_decoupling.py
@@ -29,6 +29,7 @@
     new_walsh_sequence,
     new_x_concatenated_sequence,
     new_xy_concatenated_sequence,
+    new_platonic_sequence,
 )
 from qctrlopencontrols.constants import (
     SIGMA_X,
@@ -843,3 +844,117 @@ def test_if_xy_concatenated_sequence_is_identity():
     )
 
     assert _pulses_produce_identity(xy_concat_sequence)
+
+
+def test_platonic_sequence():
+    """
+    Tests the platonic sequence.
+    """
+
+    duration = 10.0
+
+    for order in ["Dihedral", "Tetrahedral", "Octahedral", "Icosahedral"]:
+        sequence = new_platonic_sequence(duration=duration, sequence=order)
+
+        count = {
+            "Dihedral": 8,
+            "Tetrahedral": 24,
+            "Octahedral": 48,
+            "Icosahedral": 120,
+        }[order]
+        _spacing = duration / count
+
+        _offsets = np.array([(_spacing * 0.5 + i * _spacing) for i in range(count)])
+        # fmt: off
+        eulerian_paths = {
+            "Dihedral": [0, 1, 0, 1, 1, 0, 1, 0],
+            "Tetrahedral": [ 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0],
+            "Octahedral": [ 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1 ],
+            "Icosahedral": [ 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0 ]
+        }
+        # fmt: on
+        phi = (np.sqrt(5) + 1) / 2  # golden ratio
+
+        _rabi_rotations = {
+            "Dihedral": np.ones(_offsets.shape) * np.pi,
+            "Tetrahedral": np.array(eulerian_paths["Tetrahedral"])
+            * 4
+            * np.sqrt(2)
+            * np.pi
+            / 9,
+            "Octahedral": np.array(eulerian_paths["Octahedral"])
+            * 2
+            * np.sqrt(2 / 3)
+            * np.pi
+            / 3,
+            "Icosahedral": -(np.array(eulerian_paths["Icosahedral"]) - 1)
+            * 2
+            * np.pi
+            / 5
+            / np.sqrt(phi + 2)
+            + np.array(eulerian_paths["Icosahedral"])
+            * 2
+            * np.pi
+            * (phi - 1)
+            / 3
+            / np.sqrt(3),
+        }[order]
+
+        _azimuthal_angles = {
+            "Dihedral": np.array(eulerian_paths["Dihedral"]) * np.pi / 2,
+            "Tetrahedral": np.array(eulerian_paths["Tetrahedral"]) * np.pi / 3,
+            "Octahedral": np.array(eulerian_paths["Octahedral"]) * np.pi / 4,
+            "Icosahedral": -(np.array(eulerian_paths["Icosahedral"]) - 1)
+            * 3
+            * np.pi
+            / 2
+            + np.array(eulerian_paths["Icosahedral"]) * np.pi,
+        }[order]
+
+        _detuning_rotations = {
+            "Dihedral": np.zeros(_offsets.shape),
+            "Tetrahedral": -(np.array(eulerian_paths["Tetrahedral"]) - 1)
+            * 2
+            * np.pi
+            / 3
+            + np.array(eulerian_paths["Tetrahedral"]) * 2 * np.pi / 9,
+            "Octahedral": -(np.array(eulerian_paths["Octahedral"]) - 1) * np.pi / 2
+            + np.array(eulerian_paths["Octahedral"]) * 2 * np.pi / 3 / np.sqrt(3),
+            "Icosahedral": -(np.array(eulerian_paths["Icosahedral"]) - 1)
+            * 2
+            * np.pi
+            * phi
+            / 5
+            / np.sqrt(phi + 2)
+            + np.array(eulerian_paths["Icosahedral"])
+            * 2
+            * np.pi
+            * phi
+            / 3
+            / np.sqrt(3),
+        }[order]
+
+        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_platonic_sequence(
+            duration=duration, sequence=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.insert(
+            _azimuthal_angles, [0, _azimuthal_angles.shape[0]], [0, np.pi]
+        )
+        _detuning_rotations = np.insert(
+            _detuning_rotations, [0, _detuning_rotations.shape[0]], [0, 0]
+        )
+
+        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)

From 7569ca30880405ac930dc0b678cc45502980d931 Mon Sep 17 00:00:00 2001
From: Q-CTRL Robot <61040384+qctrlrobot@users.noreply.github.com>
Date: Wed, 4 Feb 2026 12:44:42 +1100
Subject: [PATCH 2/4] chore: Update licensing comments (#333)

---
 docs/conf.py                                                    | 2 +-
 qctrlopencontrols/__init__.py                                   | 2 +-
 qctrlopencontrols/constants.py                                  | 2 +-
 qctrlopencontrols/driven_controls/__init__.py                   | 2 +-
 qctrlopencontrols/driven_controls/driven_control.py             | 2 +-
 qctrlopencontrols/driven_controls/predefined.py                 | 2 +-
 qctrlopencontrols/dynamic_decoupling_sequences/__init__.py      | 2 +-
 .../dynamic_decoupling_sequences/dynamic_decoupling_sequence.py | 2 +-
 qctrlopencontrols/dynamic_decoupling_sequences/predefined.py    | 2 +-
 qctrlopencontrols/exceptions.py                                 | 2 +-
 qctrlopencontrols/utils.py                                      | 2 +-
 tests/__init__.py                                               | 2 +-
 tests/test_driven_controls.py                                   | 2 +-
 tests/test_dynamical_decoupling.py                              | 2 +-
 tests/test_predefined_driven_controls.py                        | 2 +-
 tests/test_predefined_dynamical_decoupling.py                   | 2 +-
 16 files changed, 16 insertions(+), 16 deletions(-)

diff --git a/docs/conf.py b/docs/conf.py
index c08c8c4..86b2dc2 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/__init__.py b/qctrlopencontrols/__init__.py
index bf87611..aff8490 100644
--- a/qctrlopencontrols/__init__.py
+++ b/qctrlopencontrols/__init__.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/constants.py b/qctrlopencontrols/constants.py
index d16167f..b667dac 100644
--- a/qctrlopencontrols/constants.py
+++ b/qctrlopencontrols/constants.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/driven_controls/__init__.py b/qctrlopencontrols/driven_controls/__init__.py
index 7acd2fc..46c05a7 100644
--- a/qctrlopencontrols/driven_controls/__init__.py
+++ b/qctrlopencontrols/driven_controls/__init__.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/driven_controls/driven_control.py b/qctrlopencontrols/driven_controls/driven_control.py
index 68cc59e..3a65e18 100644
--- a/qctrlopencontrols/driven_controls/driven_control.py
+++ b/qctrlopencontrols/driven_controls/driven_control.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/driven_controls/predefined.py b/qctrlopencontrols/driven_controls/predefined.py
index 524142f..dabf5e5 100644
--- a/qctrlopencontrols/driven_controls/predefined.py
+++ b/qctrlopencontrols/driven_controls/predefined.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/dynamic_decoupling_sequences/__init__.py b/qctrlopencontrols/dynamic_decoupling_sequences/__init__.py
index 7acd2fc..46c05a7 100644
--- a/qctrlopencontrols/dynamic_decoupling_sequences/__init__.py
+++ b/qctrlopencontrols/dynamic_decoupling_sequences/__init__.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/dynamic_decoupling_sequences/dynamic_decoupling_sequence.py b/qctrlopencontrols/dynamic_decoupling_sequences/dynamic_decoupling_sequence.py
index 57a5ce0..e546d1d 100644
--- a/qctrlopencontrols/dynamic_decoupling_sequences/dynamic_decoupling_sequence.py
+++ b/qctrlopencontrols/dynamic_decoupling_sequences/dynamic_decoupling_sequence.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
index 3e695fc..20d8ce8 100644
--- a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
+++ b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/exceptions.py b/qctrlopencontrols/exceptions.py
index e503f78..a17bb90 100644
--- a/qctrlopencontrols/exceptions.py
+++ b/qctrlopencontrols/exceptions.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/qctrlopencontrols/utils.py b/qctrlopencontrols/utils.py
index ea6aa31..4e1777d 100644
--- a/qctrlopencontrols/utils.py
+++ b/qctrlopencontrols/utils.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/tests/__init__.py b/tests/__init__.py
index a41e90d..e2b52da 100644
--- a/tests/__init__.py
+++ b/tests/__init__.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/tests/test_driven_controls.py b/tests/test_driven_controls.py
index 4034e31..0de90ff 100644
--- a/tests/test_driven_controls.py
+++ b/tests/test_driven_controls.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/tests/test_dynamical_decoupling.py b/tests/test_dynamical_decoupling.py
index 18d6a39..669527f 100644
--- a/tests/test_dynamical_decoupling.py
+++ b/tests/test_dynamical_decoupling.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/tests/test_predefined_driven_controls.py b/tests/test_predefined_driven_controls.py
index 901b8bd..13a6247 100644
--- a/tests/test_predefined_driven_controls.py
+++ b/tests/test_predefined_driven_controls.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
diff --git a/tests/test_predefined_dynamical_decoupling.py b/tests/test_predefined_dynamical_decoupling.py
index 109646c..4e9ddbf 100644
--- a/tests/test_predefined_dynamical_decoupling.py
+++ b/tests/test_predefined_dynamical_decoupling.py
@@ -1,4 +1,4 @@
-# Copyright 2025 Q-CTRL
+# Copyright 2026 Q-CTRL
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.

From a165dc8f0be5f15e832b9d9dee3003802245d058 Mon Sep 17 00:00:00 2001
From: Hector Brown <hectorjbrown@protonmail.com>
Date: Wed, 1 Apr 2026 16:46:09 +1100
Subject: [PATCH 3/4] split platonic test by sequence order and hardcode arrays

---
 tests/test_predefined_dynamical_decoupling.py | 1092 +++++++++++++++--
 1 file changed, 987 insertions(+), 105 deletions(-)

diff --git a/tests/test_predefined_dynamical_decoupling.py b/tests/test_predefined_dynamical_decoupling.py
index 4e9ddbf..33df83a 100644
--- a/tests/test_predefined_dynamical_decoupling.py
+++ b/tests/test_predefined_dynamical_decoupling.py
@@ -846,115 +846,997 @@ def test_if_xy_concatenated_sequence_is_identity():
     assert _pulses_produce_identity(xy_concat_sequence)
 
 
-def test_platonic_sequence():
+def test_dihedral_platonic_sequence():
     """
-    Tests the platonic sequence.
+    Tests the Dihedral order of the platonic sequence.
     """
+    duration = 10.0
+    sequence = new_platonic_sequence(duration=duration, sequence="Dihedral")
+    count = 8
+
+    _spacing = duration / count
+
+    _offsets = np.array(
+        [
+            _spacing * 0.5,
+            _spacing * 0.5 + _spacing,
+            _spacing * 0.5 + 2 * _spacing,
+            _spacing * 0.5 + 3 * _spacing,
+            _spacing * 0.5 + 4 * _spacing,
+            _spacing * 0.5 + 5 * _spacing,
+            _spacing * 0.5 + 6 * _spacing,
+            _spacing * 0.5 + 7 * _spacing,
+        ]
+    )
+
+    _rabi_rotations = np.ones(_offsets.shape) * np.pi
+
+    _azimuthal_angles = np.array(
+        [0, np.pi / 2, 0, np.pi / 2, np.pi / 2, 0, np.pi / 2, 0]
+    )
+
+    _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_platonic_sequence(
+        duration=duration, sequence="Dihedral", 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.insert(
+        _azimuthal_angles, [0, _azimuthal_angles.shape[0]], [0, np.pi]
+    )
+    _detuning_rotations = np.insert(
+        _detuning_rotations, [0, _detuning_rotations.shape[0]], [0, 0]
+    )
+
+    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_tetrahedral_platonic_sequence():
+    """
+    Tests the Tetrahedral order of the platonic sequence.
+    """
     duration = 10.0
+    sequence = new_platonic_sequence(duration=duration, sequence="Tetrahedral")
 
-    for order in ["Dihedral", "Tetrahedral", "Octahedral", "Icosahedral"]:
-        sequence = new_platonic_sequence(duration=duration, sequence=order)
-
-        count = {
-            "Dihedral": 8,
-            "Tetrahedral": 24,
-            "Octahedral": 48,
-            "Icosahedral": 120,
-        }[order]
-        _spacing = duration / count
-
-        _offsets = np.array([(_spacing * 0.5 + i * _spacing) for i in range(count)])
-        # fmt: off
-        eulerian_paths = {
-            "Dihedral": [0, 1, 0, 1, 1, 0, 1, 0],
-            "Tetrahedral": [ 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0],
-            "Octahedral": [ 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1 ],
-            "Icosahedral": [ 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0 ]
-        }
-        # fmt: on
-        phi = (np.sqrt(5) + 1) / 2  # golden ratio
-
-        _rabi_rotations = {
-            "Dihedral": np.ones(_offsets.shape) * np.pi,
-            "Tetrahedral": np.array(eulerian_paths["Tetrahedral"])
-            * 4
-            * np.sqrt(2)
-            * np.pi
-            / 9,
-            "Octahedral": np.array(eulerian_paths["Octahedral"])
-            * 2
-            * np.sqrt(2 / 3)
-            * np.pi
-            / 3,
-            "Icosahedral": -(np.array(eulerian_paths["Icosahedral"]) - 1)
-            * 2
-            * np.pi
-            / 5
-            / np.sqrt(phi + 2)
-            + np.array(eulerian_paths["Icosahedral"])
-            * 2
-            * np.pi
-            * (phi - 1)
-            / 3
-            / np.sqrt(3),
-        }[order]
-
-        _azimuthal_angles = {
-            "Dihedral": np.array(eulerian_paths["Dihedral"]) * np.pi / 2,
-            "Tetrahedral": np.array(eulerian_paths["Tetrahedral"]) * np.pi / 3,
-            "Octahedral": np.array(eulerian_paths["Octahedral"]) * np.pi / 4,
-            "Icosahedral": -(np.array(eulerian_paths["Icosahedral"]) - 1)
-            * 3
-            * np.pi
-            / 2
-            + np.array(eulerian_paths["Icosahedral"]) * np.pi,
-        }[order]
-
-        _detuning_rotations = {
-            "Dihedral": np.zeros(_offsets.shape),
-            "Tetrahedral": -(np.array(eulerian_paths["Tetrahedral"]) - 1)
-            * 2
-            * np.pi
-            / 3
-            + np.array(eulerian_paths["Tetrahedral"]) * 2 * np.pi / 9,
-            "Octahedral": -(np.array(eulerian_paths["Octahedral"]) - 1) * np.pi / 2
-            + np.array(eulerian_paths["Octahedral"]) * 2 * np.pi / 3 / np.sqrt(3),
-            "Icosahedral": -(np.array(eulerian_paths["Icosahedral"]) - 1)
-            * 2
-            * np.pi
-            * phi
-            / 5
-            / np.sqrt(phi + 2)
-            + np.array(eulerian_paths["Icosahedral"])
-            * 2
-            * np.pi
-            * phi
-            / 3
-            / np.sqrt(3),
-        }[order]
-
-        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_platonic_sequence(
-            duration=duration, sequence=order, pre_post_rotation=True
-        )
+    count = 24
+    _spacing = duration / count
 
-        _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.insert(
-            _azimuthal_angles, [0, _azimuthal_angles.shape[0]], [0, np.pi]
-        )
-        _detuning_rotations = np.insert(
-            _detuning_rotations, [0, _detuning_rotations.shape[0]], [0, 0]
-        )
+    _offsets = np.array(
+        [
+            _spacing * 0.5,
+            _spacing * 0.5 + _spacing,
+            _spacing * 0.5 + 2 * _spacing,
+            _spacing * 0.5 + 3 * _spacing,
+            _spacing * 0.5 + 4 * _spacing,
+            _spacing * 0.5 + 5 * _spacing,
+            _spacing * 0.5 + 6 * _spacing,
+            _spacing * 0.5 + 7 * _spacing,
+            _spacing * 0.5 + 8 * _spacing,
+            _spacing * 0.5 + 9 * _spacing,
+            _spacing * 0.5 + 10 * _spacing,
+            _spacing * 0.5 + 11 * _spacing,
+            _spacing * 0.5 + 12 * _spacing,
+            _spacing * 0.5 + 13 * _spacing,
+            _spacing * 0.5 + 14 * _spacing,
+            _spacing * 0.5 + 15 * _spacing,
+            _spacing * 0.5 + 16 * _spacing,
+            _spacing * 0.5 + 17 * _spacing,
+            _spacing * 0.5 + 18 * _spacing,
+            _spacing * 0.5 + 19 * _spacing,
+            _spacing * 0.5 + 20 * _spacing,
+            _spacing * 0.5 + 21 * _spacing,
+            _spacing * 0.5 + 22 * _spacing,
+            _spacing * 0.5 + 23 * _spacing,
+        ]
+    )
 
-        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)
+    _rabi_rotations = np.array(
+        [
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            4 * np.sqrt(2) * np.pi / 9,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            4 * np.sqrt(2) * np.pi / 9,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            4 * np.sqrt(2) * np.pi / 9,
+            4 * np.sqrt(2) * np.pi / 9,
+            0,
+            0,
+        ]
+    )
+
+    _azimuthal_angles = np.array(
+        [
+            0,
+            np.pi / 3,
+            0,
+            0,
+            np.pi / 3,
+            0,
+            np.pi / 3,
+            np.pi / 3,
+            np.pi / 3,
+            0,
+            0,
+            np.pi / 3,
+            0,
+            np.pi / 3,
+            np.pi / 3,
+            np.pi / 3,
+            0,
+            0,
+            np.pi / 3,
+            0,
+            np.pi / 3,
+            np.pi / 3,
+            0,
+            0,
+        ]
+    )
+
+    _detuning_rotations = np.array(
+        [
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 9,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 9,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 9,
+            2 * np.pi / 9,
+            2 * np.pi / 3,
+            2 * np.pi / 3,
+        ]
+    )
+
+    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_platonic_sequence(
+        duration=duration, sequence="Tetrahedral", 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.insert(
+        _azimuthal_angles, [0, _azimuthal_angles.shape[0]], [0, np.pi]
+    )
+    _detuning_rotations = np.insert(
+        _detuning_rotations, [0, _detuning_rotations.shape[0]], [0, 0]
+    )
+
+    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_octahedral_platonic_sequence():
+    """
+    Tests the Octahedral order of the platonic sequence.
+    """
+    duration = 10.0
+    sequence = new_platonic_sequence(duration=duration, sequence="Octahedral")
+
+    count = 48
+    _spacing = duration / count
+
+    _offsets = np.array(
+        [
+            _spacing * 0.5,
+            _spacing * 0.5 + _spacing,
+            _spacing * 0.5 + 2 * _spacing,
+            _spacing * 0.5 + 3 * _spacing,
+            _spacing * 0.5 + 4 * _spacing,
+            _spacing * 0.5 + 5 * _spacing,
+            _spacing * 0.5 + 6 * _spacing,
+            _spacing * 0.5 + 7 * _spacing,
+            _spacing * 0.5 + 8 * _spacing,
+            _spacing * 0.5 + 9 * _spacing,
+            _spacing * 0.5 + 10 * _spacing,
+            _spacing * 0.5 + 11 * _spacing,
+            _spacing * 0.5 + 12 * _spacing,
+            _spacing * 0.5 + 13 * _spacing,
+            _spacing * 0.5 + 14 * _spacing,
+            _spacing * 0.5 + 15 * _spacing,
+            _spacing * 0.5 + 16 * _spacing,
+            _spacing * 0.5 + 17 * _spacing,
+            _spacing * 0.5 + 18 * _spacing,
+            _spacing * 0.5 + 19 * _spacing,
+            _spacing * 0.5 + 20 * _spacing,
+            _spacing * 0.5 + 21 * _spacing,
+            _spacing * 0.5 + 22 * _spacing,
+            _spacing * 0.5 + 23 * _spacing,
+            _spacing * 0.5 + 24 * _spacing,
+            _spacing * 0.5 + 25 * _spacing,
+            _spacing * 0.5 + 26 * _spacing,
+            _spacing * 0.5 + 27 * _spacing,
+            _spacing * 0.5 + 28 * _spacing,
+            _spacing * 0.5 + 29 * _spacing,
+            _spacing * 0.5 + 30 * _spacing,
+            _spacing * 0.5 + 31 * _spacing,
+            _spacing * 0.5 + 32 * _spacing,
+            _spacing * 0.5 + 33 * _spacing,
+            _spacing * 0.5 + 34 * _spacing,
+            _spacing * 0.5 + 35 * _spacing,
+            _spacing * 0.5 + 36 * _spacing,
+            _spacing * 0.5 + 37 * _spacing,
+            _spacing * 0.5 + 38 * _spacing,
+            _spacing * 0.5 + 39 * _spacing,
+            _spacing * 0.5 + 40 * _spacing,
+            _spacing * 0.5 + 41 * _spacing,
+            _spacing * 0.5 + 42 * _spacing,
+            _spacing * 0.5 + 43 * _spacing,
+            _spacing * 0.5 + 44 * _spacing,
+            _spacing * 0.5 + 45 * _spacing,
+            _spacing * 0.5 + 46 * _spacing,
+            _spacing * 0.5 + 47 * _spacing,
+        ]
+    )
+
+    _rabi_rotations = np.array(
+        [
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            0,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            0,
+            0,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            0,
+            0,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            0,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+            2 * np.sqrt(2 / 3) * np.pi / 3,
+        ]
+    )
+
+    _azimuthal_angles = np.array(
+        [
+            0,
+            np.pi / 4,
+            0,
+            0,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+            np.pi / 4,
+            0,
+            np.pi / 4,
+            0,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+            np.pi / 4,
+            0,
+            0,
+            np.pi / 4,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+            0,
+            0,
+            0,
+            0,
+            np.pi / 4,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+            np.pi / 4,
+            0,
+            np.pi / 4,
+            0,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+            0,
+            0,
+            0,
+            0,
+            np.pi / 4,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+            np.pi / 4,
+            0,
+            np.pi / 4,
+            np.pi / 4,
+        ]
+    )
+
+    _detuning_rotations = np.array(
+        [
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            np.pi / 2,
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            np.pi / 2,
+            np.pi / 2,
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            np.pi / 2,
+            np.pi / 2,
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+            np.pi / 2,
+            2 * np.pi / 3 / np.sqrt(3),
+            2 * np.pi / 3 / np.sqrt(3),
+        ]
+    )
+
+    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_platonic_sequence(
+        duration=duration, sequence="Octahedral", 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.insert(
+        _azimuthal_angles, [0, _azimuthal_angles.shape[0]], [0, np.pi]
+    )
+    _detuning_rotations = np.insert(
+        _detuning_rotations, [0, _detuning_rotations.shape[0]], [0, 0]
+    )
+
+    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_icosahedral_platonic_sequence():
+    """
+    Tests the Icosahedral order of the platonic sequence.
+    """
+    duration = 10.0
+
+    sequence = new_platonic_sequence(duration=duration, sequence="Icosahedral")
+
+    count = 120
+    _spacing = duration / count
+
+    _offsets = np.array(
+        [
+            _spacing * 0.5,
+            _spacing * 0.5 + _spacing,
+            _spacing * 0.5 + 2 * _spacing,
+            _spacing * 0.5 + 3 * _spacing,
+            _spacing * 0.5 + 4 * _spacing,
+            _spacing * 0.5 + 5 * _spacing,
+            _spacing * 0.5 + 6 * _spacing,
+            _spacing * 0.5 + 7 * _spacing,
+            _spacing * 0.5 + 8 * _spacing,
+            _spacing * 0.5 + 9 * _spacing,
+            _spacing * 0.5 + 10 * _spacing,
+            _spacing * 0.5 + 11 * _spacing,
+            _spacing * 0.5 + 12 * _spacing,
+            _spacing * 0.5 + 13 * _spacing,
+            _spacing * 0.5 + 14 * _spacing,
+            _spacing * 0.5 + 15 * _spacing,
+            _spacing * 0.5 + 16 * _spacing,
+            _spacing * 0.5 + 17 * _spacing,
+            _spacing * 0.5 + 18 * _spacing,
+            _spacing * 0.5 + 19 * _spacing,
+            _spacing * 0.5 + 20 * _spacing,
+            _spacing * 0.5 + 21 * _spacing,
+            _spacing * 0.5 + 22 * _spacing,
+            _spacing * 0.5 + 23 * _spacing,
+            _spacing * 0.5 + 24 * _spacing,
+            _spacing * 0.5 + 25 * _spacing,
+            _spacing * 0.5 + 26 * _spacing,
+            _spacing * 0.5 + 27 * _spacing,
+            _spacing * 0.5 + 28 * _spacing,
+            _spacing * 0.5 + 29 * _spacing,
+            _spacing * 0.5 + 30 * _spacing,
+            _spacing * 0.5 + 31 * _spacing,
+            _spacing * 0.5 + 32 * _spacing,
+            _spacing * 0.5 + 33 * _spacing,
+            _spacing * 0.5 + 34 * _spacing,
+            _spacing * 0.5 + 35 * _spacing,
+            _spacing * 0.5 + 36 * _spacing,
+            _spacing * 0.5 + 37 * _spacing,
+            _spacing * 0.5 + 38 * _spacing,
+            _spacing * 0.5 + 39 * _spacing,
+            _spacing * 0.5 + 40 * _spacing,
+            _spacing * 0.5 + 41 * _spacing,
+            _spacing * 0.5 + 42 * _spacing,
+            _spacing * 0.5 + 43 * _spacing,
+            _spacing * 0.5 + 44 * _spacing,
+            _spacing * 0.5 + 45 * _spacing,
+            _spacing * 0.5 + 46 * _spacing,
+            _spacing * 0.5 + 47 * _spacing,
+            _spacing * 0.5 + 48 * _spacing,
+            _spacing * 0.5 + 49 * _spacing,
+            _spacing * 0.5 + 50 * _spacing,
+            _spacing * 0.5 + 51 * _spacing,
+            _spacing * 0.5 + 52 * _spacing,
+            _spacing * 0.5 + 53 * _spacing,
+            _spacing * 0.5 + 54 * _spacing,
+            _spacing * 0.5 + 55 * _spacing,
+            _spacing * 0.5 + 56 * _spacing,
+            _spacing * 0.5 + 57 * _spacing,
+            _spacing * 0.5 + 58 * _spacing,
+            _spacing * 0.5 + 59 * _spacing,
+            _spacing * 0.5 + 60 * _spacing,
+            _spacing * 0.5 + 61 * _spacing,
+            _spacing * 0.5 + 62 * _spacing,
+            _spacing * 0.5 + 63 * _spacing,
+            _spacing * 0.5 + 64 * _spacing,
+            _spacing * 0.5 + 65 * _spacing,
+            _spacing * 0.5 + 66 * _spacing,
+            _spacing * 0.5 + 67 * _spacing,
+            _spacing * 0.5 + 68 * _spacing,
+            _spacing * 0.5 + 69 * _spacing,
+            _spacing * 0.5 + 70 * _spacing,
+            _spacing * 0.5 + 71 * _spacing,
+            _spacing * 0.5 + 72 * _spacing,
+            _spacing * 0.5 + 73 * _spacing,
+            _spacing * 0.5 + 74 * _spacing,
+            _spacing * 0.5 + 75 * _spacing,
+            _spacing * 0.5 + 76 * _spacing,
+            _spacing * 0.5 + 77 * _spacing,
+            _spacing * 0.5 + 78 * _spacing,
+            _spacing * 0.5 + 79 * _spacing,
+            _spacing * 0.5 + 80 * _spacing,
+            _spacing * 0.5 + 81 * _spacing,
+            _spacing * 0.5 + 82 * _spacing,
+            _spacing * 0.5 + 83 * _spacing,
+            _spacing * 0.5 + 84 * _spacing,
+            _spacing * 0.5 + 85 * _spacing,
+            _spacing * 0.5 + 86 * _spacing,
+            _spacing * 0.5 + 87 * _spacing,
+            _spacing * 0.5 + 88 * _spacing,
+            _spacing * 0.5 + 89 * _spacing,
+            _spacing * 0.5 + 90 * _spacing,
+            _spacing * 0.5 + 91 * _spacing,
+            _spacing * 0.5 + 92 * _spacing,
+            _spacing * 0.5 + 93 * _spacing,
+            _spacing * 0.5 + 94 * _spacing,
+            _spacing * 0.5 + 95 * _spacing,
+            _spacing * 0.5 + 96 * _spacing,
+            _spacing * 0.5 + 97 * _spacing,
+            _spacing * 0.5 + 98 * _spacing,
+            _spacing * 0.5 + 99 * _spacing,
+            _spacing * 0.5 + 100 * _spacing,
+            _spacing * 0.5 + 101 * _spacing,
+            _spacing * 0.5 + 102 * _spacing,
+            _spacing * 0.5 + 103 * _spacing,
+            _spacing * 0.5 + 104 * _spacing,
+            _spacing * 0.5 + 105 * _spacing,
+            _spacing * 0.5 + 106 * _spacing,
+            _spacing * 0.5 + 107 * _spacing,
+            _spacing * 0.5 + 108 * _spacing,
+            _spacing * 0.5 + 109 * _spacing,
+            _spacing * 0.5 + 110 * _spacing,
+            _spacing * 0.5 + 111 * _spacing,
+            _spacing * 0.5 + 112 * _spacing,
+            _spacing * 0.5 + 113 * _spacing,
+            _spacing * 0.5 + 114 * _spacing,
+            _spacing * 0.5 + 115 * _spacing,
+            _spacing * 0.5 + 116 * _spacing,
+            _spacing * 0.5 + 117 * _spacing,
+            _spacing * 0.5 + 118 * _spacing,
+            _spacing * 0.5 + 119 * _spacing,
+        ]
+    )
+
+    phi = (np.sqrt(5) + 1) / 2  # golden ratio
+
+    _rabi_rotations = np.array(
+        [
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+            2 * np.pi / 5 / np.sqrt(phi + 2),
+        ]
+    )
+
+    _azimuthal_angles = np.array(
+        [
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            np.pi,
+            np.pi,
+            3 * np.pi / 2,
+            np.pi,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+            3 * np.pi / 2,
+        ]
+    )
+
+    _detuning_rotations = np.array(
+        [
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 3 / np.sqrt(3),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+            2 * np.pi * phi / 5 / np.sqrt(phi + 2),
+        ]
+    )
+
+    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_platonic_sequence(
+        duration=duration, sequence="Icosahedral", 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.insert(
+        _azimuthal_angles, [0, _azimuthal_angles.shape[0]], [0, np.pi]
+    )
+    _detuning_rotations = np.insert(
+        _detuning_rotations, [0, _detuning_rotations.shape[0]], [0, 0]
+    )
+
+    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)

From 0effe70d081b8b765faedc9fe7ef8e4cae633434 Mon Sep 17 00:00:00 2001
From: Hector Brown <hectorjbrown@protonmail.com>
Date: Wed, 1 Apr 2026 16:46:39 +1100
Subject: [PATCH 4/4] change platonic udd sequence generator to if-else chain +
 use numpy to generate

---
 .../predefined.py                             | 107 ++++++++----------
 1 file changed, 46 insertions(+), 61 deletions(-)

diff --git a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
index 20d8ce8..f8005b4 100644
--- a/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
+++ b/qctrlopencontrols/dynamic_decoupling_sequences/predefined.py
@@ -1318,69 +1318,54 @@ def new_platonic_sequence(
         {"sequence": sequence},
     )
 
-    # The sequences outlined in the cited paper, each sequence is constructed
-    # from an Eulerian path on the Cayley graph associated with the relevant
-    # point group. Each sequence is constructed of 2 generating operations, in
-    # the order specified here.
-    # fmt: off
-    eulerian_paths = {
-        "Dihedral": [0, 1, 0, 1, 1, 0, 1, 0],
-        "Tetrahedral": [ 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0],
-        "Octahedral": [ 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1 ],
-        "Icosahedral": [ 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0 ]
-    }
-    # fmt: on
-
-    # The generators assocaited with each point group.
-    phi = (np.sqrt(5) + 1) / 2  # golden ratio
-    generators = {
-        "Dihedral": [
-            {"Rabi": np.pi, "Azimuthal": 0, "Detuning": 0},  # rabi, azimuthal, detuning
-            {"Rabi": np.pi, "Azimuthal": np.pi / 2, "Detuning": 0},
-        ],
-        "Tetrahedral": [
-            {"Rabi": 0, "Azimuthal": 0, "Detuning": 2 * np.pi / 3},
-            {
-                "Rabi": 4 * np.sqrt(2) * np.pi / 9,
-                "Azimuthal": np.pi / 3,
-                "Detuning": 2 * np.pi / 9,
-            },
-        ],
-        "Octahedral": [
-            {"Rabi": 0, "Azimuthal": 0, "Detuning": np.pi / 2},
-            {
-                "Rabi": 2 * np.sqrt(2 / 3) * np.pi / 3,
-                "Azimuthal": np.pi / 4,
-                "Detuning": 2 * np.pi / 3 / np.sqrt(3),
-            },
-        ],
-        "Icosahedral": [
-            {
-                "Rabi": 2 * np.pi / 5 / np.sqrt(phi + 2),
-                "Azimuthal": 3 * np.pi / 2,
-                "Detuning": 2 * np.pi * phi / 5 / np.sqrt(phi + 2),
-            },
-            {
-                "Rabi": 2 * np.pi * (phi - 1) / 3 / np.sqrt(3),
-                "Azimuthal": np.pi,
-                "Detuning": 2 * np.pi * phi / 3 / np.sqrt(3),
-            },
-        ],
-    }
+    rabi_rotations, azimuthal_angles, detuning_rotations = None, None, None
+
+    if sequence == "Dihedral":
+        eulerian_path = np.array([0, 1, 0, 1, 1, 0, 1, 0])
+
+        rabi_rotations = np.ones(eulerian_path.shape[0]) * np.pi
+        azimuthal_angles = eulerian_path * np.pi / 2
+        detuning_rotations = np.zeros(eulerian_path.shape[0])
+    elif sequence == "Tetrahedral":
+        eulerian_path = np.array(
+            [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]
+        )
+
+        rabi_rotations = eulerian_path * 4 * np.sqrt(2) * np.pi / 9
+        azimuthal_angles = eulerian_path * np.pi / 3
+        detuning_rotations = (
+            1 ^ eulerian_path
+        ) * 2 * np.pi / 3 + eulerian_path * 2 * np.pi / 9
+    elif sequence == "Octahedral":
+        # fmt:off
+        eulerian_path = np.array(
+            [ 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1 ]
+        )
+        # fmt:on
+
+        rabi_rotations = eulerian_path * 2 * np.sqrt(2 / 3) * np.pi / 3
+        azimuthal_angles = eulerian_path * np.pi / 4
+        detuning_rotations = (
+            1 ^ eulerian_path
+        ) * np.pi / 2 + eulerian_path * 2 * np.pi / 3 / np.sqrt(3)
+    else:
+        # fmt:off
+        eulerian_path = np.array(
+            [ 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0 ]
+        )
+        # fmt:on
+
+        phi = (np.sqrt(5) + 1) / 2  # golden ratio
+        rabi_rotations = (1 ^ eulerian_path) * 2 * np.pi / 5 / np.sqrt(
+            phi + 2
+        ) + eulerian_path * 2 * np.pi * (phi - 1) / 3 / np.sqrt(3)
+        azimuthal_angles = (1 ^ eulerian_path) * 3 * np.pi / 2 + eulerian_path * np.pi
+        detuning_rotations = (1 ^ eulerian_path) * 2 * np.pi * phi / 5 / np.sqrt(
+            phi + 2
+        ) + eulerian_path * 2 * np.pi * phi / 3 / np.sqrt(3)
 
     # Re-use the CPMG offset function to obtain equally spaced pulses along a certain duration.
-    offsets = _carr_purcell_meiboom_gill_offsets(
-        duration, len(eulerian_paths[sequence])
-    )
-    rabi_rotations = np.array(
-        [generators[sequence][idx]["Rabi"] for idx in eulerian_paths[sequence]]
-    )
-    azimuthal_angles = np.array(
-        [generators[sequence][idx]["Azimuthal"] for idx in eulerian_paths[sequence]]
-    )
-    detuning_rotations = np.array(
-        [generators[sequence][idx]["Detuning"] for idx in eulerian_paths[sequence]]
-    )
+    offsets = _carr_purcell_meiboom_gill_offsets(duration, rabi_rotations.shape[0])
 
     if pre_post_rotation:
         # Use a pi/2 followed by a -pi/2 X rotation as all the sequences