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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2018.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","","\"\"\"","Visualization function for animation of state transitions by applying gates to single qubit.","\"\"\"","import sys","from math import sin, cos, acos, sqrt","import numpy as np","","from qiskit.exceptions import MissingOptionalLibraryError","","","def _normalize(v, tolerance=0.00001):"," \"\"\"Makes sure magnitude of the vector is 1 with given tolerance\"\"\"",""," mag2 = sum(n * n for n in v)"," if abs(mag2 - 1.0) > tolerance:"," mag = sqrt(mag2)"," v = tuple(n / mag for n in v)"," return np.array(v)","","","class _Quaternion:"," \"\"\"For calculating vectors on unit sphere\"\"\"",""," def __init__(self):"," self._val = None",""," @staticmethod"," def from_axisangle(theta, v):"," \"\"\"Create quaternion from axis\"\"\""," v = _normalize(v)",""," new_quaternion = _Quaternion()"," new_quaternion._axisangle_to_q(theta, v)"," return new_quaternion",""," @staticmethod"," def from_value(value):"," \"\"\"Create quaternion from vector\"\"\""," new_quaternion = _Quaternion()"," new_quaternion._val = value"," return new_quaternion",""," def _axisangle_to_q(self, theta, v):"," \"\"\"Convert axis and angle to quaternion\"\"\""," x = v[0]"," y = v[1]"," z = v[2]",""," w = cos(theta / 2.0)"," x = x * sin(theta / 2.0)"," y = y * sin(theta / 2.0)"," z = z * sin(theta / 2.0)",""," self._val = np.array([w, x, y, z])",""," def __mul__(self, b):"," \"\"\"Multiplication of quaternion with quaternion or vector\"\"\"",""," if isinstance(b, _Quaternion):"," return self._multiply_with_quaternion(b)"," elif isinstance(b, (list, tuple, np.ndarray)):"," if len(b) != 3:"," raise Exception(f\"Input vector has invalid length {len(b)}\")"," return self._multiply_with_vector(b)"," else:"," raise Exception(f\"Multiplication with unknown type {type(b)}\")",""," def _multiply_with_quaternion(self, q_2):"," \"\"\"Multiplication of quaternion with quaternion\"\"\""," w_1, x_1, y_1, z_1 = self._val"," w_2, x_2, y_2, z_2 = q_2._val"," w = w_1 * w_2 - x_1 * x_2 - y_1 * y_2 - z_1 * z_2"," x = w_1 * x_2 + x_1 * w_2 + y_1 * z_2 - z_1 * y_2"," y = w_1 * y_2 + y_1 * w_2 + z_1 * x_2 - x_1 * z_2"," z = w_1 * z_2 + z_1 * w_2 + x_1 * y_2 - y_1 * x_2",""," result = _Quaternion.from_value(np.array((w, x, y, z)))"," return result",""," def _multiply_with_vector(self, v):"," \"\"\"Multiplication of quaternion with vector\"\"\""," q_2 = _Quaternion.from_value(np.append((0.0), v))"," return (self * q_2 * self.get_conjugate())._val[1:]",""," def get_conjugate(self):"," \"\"\"Conjugation of quaternion\"\"\""," w, x, y, z = self._val"," result = _Quaternion.from_value(np.array((w, -x, -y, -z)))"," return result",""," def __repr__(self):"," theta, v = self.get_axisangle()"," return f\"(({theta}; {v[0]}, {v[1]}, {v[2]}))\"",""," def get_axisangle(self):"," \"\"\"Returns angle and vector of quaternion\"\"\""," w, v = self._val[0], self._val[1:]"," theta = acos(w) * 2.0",""," return theta, _normalize(v)",""," def tolist(self):"," \"\"\"Converts quaternion to a list\"\"\""," return self._val.tolist()",""," def vector_norm(self):"," \"\"\"Calculates norm of quaternion\"\"\""," _, v = self.get_axisangle()"," return np.linalg.norm(v)","","","def visualize_transition(circuit, trace=False, saveas=None, fpg=100, spg=2):"," \"\"\""," Creates animation showing transitions between states of a single"," qubit by applying quantum gates.",""," Args:"," circuit (QuantumCircuit): Qiskit single-qubit QuantumCircuit. Gates supported are"," h,x, y, z, rx, ry, rz, s, sdg, t, tdg and u1."," trace (bool): Controls whether to display tracing vectors - history of 10 past vectors"," at each step of the animation."," saveas (str): User can choose to save the animation as a video to their filesystem."," This argument is a string of path with filename and extension (e.g. \"movie.mp4\" to"," save the video in current working directory)."," fpg (int): Frames per gate. Finer control over animation smoothness and computational"," needs to render the animation. Works well for tkinter GUI as it is, for jupyter GUI"," it might be preferable to choose fpg between 5-30."," spg (int): Seconds per gate. How many seconds should animation of individual gate"," transitions take.",""," Returns:"," IPython.core.display.HTML:"," If arg jupyter is set to True. Otherwise opens tkinter GUI and returns"," after the GUI is closed.",""," Raises:"," MissingOptionalLibraryError: Must have Matplotlib (and/or IPython) installed."," VisualizationError: Given gate(s) are not supported.",""," \"\"\""," try:"," from IPython.display import HTML",""," has_ipython = True"," except ImportError:"," has_ipython = False",""," try:"," import matplotlib"," from matplotlib import pyplot as plt"," from matplotlib import animation"," from mpl_toolkits.mplot3d import Axes3D"," from .bloch import Bloch"," from .exceptions import VisualizationError",""," has_matplotlib = True"," except ImportError:"," has_matplotlib = False",""," jupyter = False"," if (\"ipykernel\" in sys.modules) and (\"spyder\" not in sys.modules):"," jupyter = True",""," if not has_matplotlib:"," raise MissingOptionalLibraryError("," libname=\"Matplotlib\","," name=\"visualize_transition\","," pip_install=\"pip install matplotlib\","," )"," if not has_ipython and jupyter is True:"," raise MissingOptionalLibraryError("," libname=\"IPython\","," name=\"visualize_transition\","," pip_install=\"pip install ipython\","," )"," if len(circuit.qubits) != 1:"," raise VisualizationError(\"Only one qubit circuits are supported\")",""," frames_per_gate = fpg"," time_between_frames = (spg * 1000) / fpg",""," # quaternions of gates which don't take parameters"," simple_gates = {}"," simple_gates[\"x\"] = ("," \"x\","," _Quaternion.from_axisangle(np.pi / frames_per_gate, [1, 0, 0]),"," \"#1abc9c\","," )"," simple_gates[\"y\"] = ("," \"y\","," _Quaternion.from_axisangle(np.pi / frames_per_gate, [0, 1, 0]),"," \"#2ecc71\","," )"," simple_gates[\"z\"] = ("," \"z\","," _Quaternion.from_axisangle(np.pi / frames_per_gate, [0, 0, 1]),"," \"#3498db\","," )"," simple_gates[\"s\"] = ("," \"s\","," _Quaternion.from_axisangle(np.pi / 2 / frames_per_gate, [0, 0, 1]),"," \"#9b59b6\","," )"," simple_gates[\"sdg\"] = ("," \"sdg\","," _Quaternion.from_axisangle(-np.pi / 2 / frames_per_gate, [0, 0, 1]),"," \"#8e44ad\","," )"," simple_gates[\"h\"] = ("," \"h\","," _Quaternion.from_axisangle(np.pi / frames_per_gate, _normalize([1, 0, 1])),"," \"#34495e\","," )"," simple_gates[\"t\"] = ("," \"t\","," _Quaternion.from_axisangle(np.pi / 4 / frames_per_gate, [0, 0, 1]),"," \"#e74c3c\","," )"," simple_gates[\"tdg\"] = ("," \"tdg\","," _Quaternion.from_axisangle(-np.pi / 4 / frames_per_gate, [0, 0, 1]),"," \"#c0392b\","," )",""," list_of_circuit_gates = []",""," for gate, _, _ in circuit._data:"," if gate.name == \"barrier\":"," continue"," if gate.name in simple_gates:"," list_of_circuit_gates.append(simple_gates[gate.name])"," elif gate.name == \"rx\":"," theta = gate.params[0]"," quaternion = _Quaternion.from_axisangle(theta / frames_per_gate, [1, 0, 0])"," list_of_circuit_gates.append((f\"{gate.name}: {theta:.2f}\", quaternion, \"#16a085\"))"," elif gate.name == \"ry\":"," theta = gate.params[0]"," quaternion = _Quaternion.from_axisangle(theta / frames_per_gate, [0, 1, 0])"," list_of_circuit_gates.append((f\"{gate.name}: {theta:.2f}\", quaternion, \"#27ae60\"))"," elif gate.name == \"rz\":"," theta = gate.params[0]"," quaternion = _Quaternion.from_axisangle(theta / frames_per_gate, [0, 0, 1])"," list_of_circuit_gates.append((f\"{gate.name}: {theta:.2f}\", quaternion, \"#2980b9\"))"," elif gate.name == \"u1\":"," theta = gate.params[0]"," quaternion = _Quaternion.from_axisangle(theta / frames_per_gate, [0, 0, 1])"," list_of_circuit_gates.append((f\"{gate.name}: {theta:.2f}\", quaternion, \"#f1c40f\"))"," else:"," raise VisualizationError(f\"Gate {gate.name} is not supported\")",""," if len(list_of_circuit_gates) == 0:"," raise VisualizationError(\"Nothing to visualize.\")",""," starting_pos = _normalize(np.array([0, 0, 1]))",""," fig = plt.figure(figsize=(5, 5))"," if tuple(int(x) for x in matplotlib.__version__.split(\".\")) >= (3, 4, 0):"," _ax = Axes3D(fig, auto_add_to_figure=False)"," fig.add_axes(_ax)"," else:"," _ax = Axes3D(fig)",""," _ax.set_xlim(-10, 10)"," _ax.set_ylim(-10, 10)"," sphere = Bloch(axes=_ax)",""," class Namespace:"," \"\"\"Helper class serving as scope container\"\"\"",""," def __init__(self):"," self.new_vec = []"," self.last_gate = -2"," self.colors = []"," self.pnts = []",""," namespace = Namespace()"," namespace.new_vec = starting_pos",""," def animate(i):"," sphere.clear()",""," # starting gate count from -1 which is the initial vector"," gate_counter = (i - 1) // frames_per_gate"," if gate_counter != namespace.last_gate:"," namespace.pnts.append([[], [], []])"," namespace.colors.append(list_of_circuit_gates[gate_counter][2])",""," # starts with default vector [0,0,1]"," if i == 0:"," sphere.add_vectors(namespace.new_vec)"," namespace.pnts[0][0].append(namespace.new_vec[0])"," namespace.pnts[0][1].append(namespace.new_vec[1])"," namespace.pnts[0][2].append(namespace.new_vec[2])"," namespace.colors[0] = \"r\""," sphere.make_sphere()"," return _ax",""," namespace.new_vec = list_of_circuit_gates[gate_counter][1] * namespace.new_vec",""," namespace.pnts[gate_counter + 1][0].append(namespace.new_vec[0])"," namespace.pnts[gate_counter + 1][1].append(namespace.new_vec[1])"," namespace.pnts[gate_counter + 1][2].append(namespace.new_vec[2])",""," sphere.add_vectors(namespace.new_vec)"," if trace:"," # sphere.add_vectors(namespace.points)"," for point_set in namespace.pnts:"," sphere.add_points([point_set[0], point_set[1], point_set[2]])",""," sphere.vector_color = [list_of_circuit_gates[gate_counter][2]]"," sphere.point_color = namespace.colors"," sphere.point_marker = \"o\"",""," annotation_text = list_of_circuit_gates[gate_counter][0]"," annotationvector = [1.40, -0.45, 1.65]"," sphere.add_annotation("," annotationvector,"," annotation_text,"," color=list_of_circuit_gates[gate_counter][2],"," fontsize=30,"," horizontalalignment=\"left\","," )",""," sphere.make_sphere()",""," namespace.last_gate = gate_counter"," return _ax",""," def init():"," 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