# 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
try:
import matplotlib
from matplotlib import pyplot as plt
from matplotlib import animation
from mpl_toolkits.mplot3d import Axes3D
from qiskit.visualization.bloch import Bloch
from qiskit.visualization.exceptions import VisualizationError
HAS_MATPLOTLIB = True
except ImportError:
HAS_MATPLOTLIB = False
try:
from IPython.display import HTML
HAS_IPYTHON = True
except ImportError:
HAS_IPYTHON = False
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.)
x = x * sin(theta/2.)
y = y * sin(theta/2.)
z = z * sin(theta/2.)
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("Input vector has invalid length {0}".format(len(b)))
return self._multiply_with_vector(b)
else:
raise Exception("Multiplication with unknown type {0}".format(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 "(({0}; {1}, {2}, {3}))".format(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)
[docs]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 computiational
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:
ImportError: Must have Matplotlib (and/or IPython) installed.
VisualizationError: Given gate(s) are not supported.
"""
jupyter = False
if ('ipykernel' in sys.modules) and ('spyder' not in sys.modules):
jupyter = True
if not HAS_MATPLOTLIB:
raise ImportError("Must have Matplotlib installed.")
if not HAS_IPYTHON and jupyter is True:
raise ImportError("Must have IPython installed.")
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
gates = dict()
gates['x'] = ('x', _Quaternion.from_axisangle(np.pi / frames_per_gate, [1, 0, 0]), '#1abc9c')
gates['y'] = ('y', _Quaternion.from_axisangle(np.pi / frames_per_gate, [0, 1, 0]), '#2ecc71')
gates['z'] = ('z', _Quaternion.from_axisangle(np.pi / frames_per_gate, [0, 0, 1]), '#3498db')
gates['s'] = ('s', _Quaternion.from_axisangle(np.pi / 2 / frames_per_gate,
[0, 0, 1]), '#9b59b6')
gates['sdg'] = ('sdg', _Quaternion.from_axisangle(-np.pi / 2 / frames_per_gate, [0, 0, 1]),
'#8e44ad')
gates['h'] = ('h', _Quaternion.from_axisangle(np.pi / frames_per_gate, _normalize([1, 0, 1])),
'#34495e')
gates['t'] = ('t', _Quaternion.from_axisangle(np.pi / 4 / frames_per_gate, [0, 0, 1]),
'#e74c3c')
gates['tdg'] = ('tdg', _Quaternion.from_axisangle(-np.pi / 4 / frames_per_gate, [0, 0, 1]),
'#c0392b')
implemented_gates = ['h', 'x', 'y', 'z', 'rx', 'ry', 'rz', 's', 'sdg', 't', 'tdg', 'u1']
simple_gates = ['h', 'x', 'y', 'z', 's', 'sdg', 't', 'tdg']
list_of_circuit_gates = []
for gate in circuit._data:
if gate[0].name not in implemented_gates:
raise VisualizationError("Gate {0} is not supported".format(gate[0].name))
if gate[0].name in simple_gates:
list_of_circuit_gates.append(gates[gate[0].name])
else:
theta = gate[0].params[0]
rad = np.deg2rad(theta)
if gate[0].name == 'rx':
quaternion = _Quaternion.from_axisangle(rad / frames_per_gate, [1, 0, 0])
list_of_circuit_gates.append(('rx:'+str(theta), quaternion, '#16a085'))
elif gate[0].name == 'ry':
quaternion = _Quaternion.from_axisangle(rad / frames_per_gate, [0, 1, 0])
list_of_circuit_gates.append(('ry:'+str(theta), quaternion, '#27ae60'))
elif gate[0].name == 'rz':
quaternion = _Quaternion.from_axisangle(rad / frames_per_gate, [0, 0, 1])
list_of_circuit_gates.append(('rz:'+str(theta), quaternion, '#2980b9'))
elif gate[0].name == 'u1':
quaternion = _Quaternion.from_axisangle(rad / frames_per_gate, [0, 0, 1])
list_of_circuit_gates.append(('u1:'+str(theta), quaternion, '#f1c40f'))
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))
_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 = [1.4, -0.45, 1.7]
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():
sphere.vector_color = ['r']
return _ax
ani = animation.FuncAnimation(fig,
animate,
range(frames_per_gate * len(list_of_circuit_gates)+1),
init_func=init,
blit=False,
repeat=False,
interval=time_between_frames)
if saveas:
ani.save(saveas, fps=30)
if jupyter:
# This is necessary to overcome matplotlib memory limit
matplotlib.rcParams['animation.embed_limit'] = 50
return HTML(ani.to_jshtml())
plt.show()
plt.close(fig)
return None