-
Notifications
You must be signed in to change notification settings - Fork 0
/
bloch_sphere.py
417 lines (341 loc) · 17.2 KB
/
bloch_sphere.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
from __future__ import division, print_function
# https://www.glowscript.org/docs/VPythonDocs/index.html
import cmath
from visual import *
from numpy import matrix
import wx
from qc_gate import QuantumGates
DEBUG = False
DEBUGU = True
class Qubit:
"""
In this class we apply the Quantum Gate Transformation Matrix
to a qubit.
"""
def __init__(self, radius):
self.r = radius # radius
# row-1, col-1 element is theta, row-1, col-2 element is phi
self.polarCord = matrix([0.0, 0.0]) # polar co-ordinate of qubit
# row-1, col-1 element is probability |0> state, row-1, col-2 element is the probability of state |1>
self.qubit = matrix([1 + 0j, 0 + 0j]).T # Qubit Amplitudes 2*1 matrix
def setVector(self, theta, phi):
"""
Sets a qubit to a position
:param theta: is angle from positive z-axis where 0<= theta <= 180
:param phi: is angle from positive x-axis where 0<= phi <= 360
"""
# self.polarCord[0, 0] = theta # set (0,0) element of the matrix to theta
# self.polarCord[0, 1] = phi
self.polarCord = matrix([theta, phi])
# Calculate Cartesian coordinates from theta and phi
# will use this co-ordinates to draw the world in 3D sphere.
x = ((math.cos(phi) * math.sin(theta)))
y = ((math.sin(phi) * math.sin(theta)))
z = ((math.cos(theta)))
# Put world-frame cartesian coordinates back onto bloch sphere frame
position = vector(x, y, z)
vpy_point.pos = qubitFrame.world_to_frame(position * self.r)
def setAmplitudes(self, alpha, beta):
"""
set a superposition sate of global aubit
:param alpha: is probability of state |0>
:param beta: is probability of state |1>
"""
self.qubit[0] = alpha
self.qubit[1] = beta
def applyTransformation(self, U):
"""
apply transformation to the qubit
:param U: is the unitary matrix to apply linear transformation to qubit
"""
self.qubit = U * self.qubit
def updatePosition(self):
"""
Updates the all positions (arrow & rings) based upon point position
"""
pointer.axis = vpy_point.pos
# Find the point position in world frame
xPos = qubitFrame.frame_to_world(vpy_point.pos).x
yPos = qubitFrame.frame_to_world(vpy_point.pos).y
zPos = qubitFrame.frame_to_world(vpy_point.pos).z
# Move and scale rings accordingly
xRing.pos.x = xPos
yRing.pos.y = yPos
zRing.pos.z = zPos
try:
xRing.radius = math.sqrt(self.r ** 2 - xPos ** 2)
yRing.radius = math.sqrt(self.r ** 2 - yPos ** 2)
zRing.radius = math.sqrt(self.r ** 2 - zPos ** 2)
except:
a = 1
# Find polar angles, Get Amplitudes, and update labels
# theta = math.atan2(xPos, zPos)
theta = math.atan2(math.sqrt(xPos ** 2 + yPos ** 2), zPos) # bug fix by @author Hasan Masum
# phi = ((2 * pi) - math.atan2(yPos, xPos)) % (2 * pi) # clockwise positive
phi = (math.atan2(yPos, xPos)) % (2 * pi) # anti clockwise positive
self.setDataLabels(self.qubit[0], self.qubit[1], theta, phi)
# setVector(theta,phi)
def setDataLabels(self, alpha, beta, theta, phi):
"""
update the labels
:param alpha: probability of state |0>
:param beta: probability of state |1>
:param theta: angle with positive z-axis
:param phi: angle with positive x-axis
"""
a = str(round(alpha.real, 3)) + '+' + str(round(alpha.imag, 3)) + 'i'
b = str(round(beta.real, 3)) + '+' + str(round(beta.imag, 3)) + 'i'
c = str(round((alpha.real ** 2), 3)) + '+' + str(round((alpha.imag ** 2), 3)) + 'i'
d = str(round((beta.real ** 2), 3)) + '+' + str(round((beta.imag ** 2), 3)) + 'i'
label = ('Alpha: (' + a + ') \nBeta: (' + b + ')')
dataText1.SetLabel(label)
label = ('Alpha^2: (' + c + ') \nBeta^2: (' + d + ')')
dataText1a.SetLabel(label)
a = str(round(theta.real, 3))
b = str(round(phi.real, 3))
c = str(round(theta.real / pi, 3))
d = str(round(phi.real / pi, 3))
e = str(round(math.degrees(theta.real), 0))
f = str(round(math.degrees(phi.real), 0) % 360)
label = ('Theta: ' + a + '\nTheta/Pi: ' + c + '\nTheta(Deg): ' + e)
dataText2.SetLabel(label)
label = ('Phi: ' + b + '\nPhi/Pi: ' + d + '\nPhi(Deg): ' + f)
dataText2a.SetLabel(label)
class BlochSphereVisualizer:
TAG = "BlochSphereVisualizer->"
def __init__(self, qubit, qubitFrame):
print ("init BlochSphereVisualizer")
self.qubit = qubit
self.qubitFrame = qubitFrame
def setVector(self, theta, phi):
"""
Sets a qubit to a position
:param theta: is angle from positive z-axis where 0<= theta <= 180
:param phi: is angle from positive x-axis where 0<= phi <= 360
"""
# self.polarCord[0, 0] = theta # set (0,0) element of the matrix to theta
# self.polarCord[0, 1] = phi
self.qubit.polarCord = matrix([theta, phi])
# Calculate Cartesian coordinates from theta and phi
# will use this co-ordinates to draw the world in 3D sphere.
x = ((math.cos(phi) * math.sin(theta)))
y = ((math.sin(phi) * math.sin(theta)))
z = ((math.cos(theta)))
# Put world-frame cartesian coordinates back onto bloch sphere frame
position = vector(x, y, z)
vpy_point.pos = qubitFrame.world_to_frame(position * self.qubit.r)
def animateQubit(self, axis, angle):
print (BlochSphereVisualizer.TAG, "animateQubit()")
fps = 128
for i in range(0, fps):
rate(fps) # number of frames or loop iteration per second
# https://www.glowscript.org/docs/VPythonDocs/rotation.html
self.qubitFrame.rotate(axis=axis, angle= angle / fps) # for anti-clockwise rotation w.r.t z-axis
self.qubit.updatePosition()
# apply gates with animation ===================================================
def setHadamard(self, evt):
print(BlochSphereVisualizer.TAG,'Hadamard')
self.qubit.applyTransformation(QuantumGates.H)
self.animateQubit(axis=(1 / math.sqrt(2), 0, 1 / math.sqrt(2)), angle=pi)
def setPauliX(self, evt):
print('Pauli X')
self.qubit.applyTransformation(QuantumGates.X)
# pi radian rotation w.r.t x-axis
self.animateQubit(axis=(1, 0, 0), angle=pi )
def setPauliY(self, evt):
print('Pauli Y')
self.qubit.applyTransformation(QuantumGates.Y)
# pi radian rotation w.r.t y-axis
self.animateQubit(axis=(0, 1, 0), angle=(pi) )
def setPauliZ(self, evt):
print('Pauli Z')
self.qubit.applyTransformation(QuantumGates.Z)
# pi radian rotation w.r.t y-axis
self.animateQubit(axis=(0, 0, 1), angle=(pi) )
def setPhase(self, evt):
print('Phase')
self.qubit.applyTransformation(QuantumGates.S)
# pi/2 radian clockwise rotation w.r.t z-axis
# self.animateQubit(axis=(0, 0, 1), angle= -1 *(pi / 2) )
# pi/2 radian anti-clockwise rotation w.r.t z-axis
self.animateQubit(axis=(0, 0, 1), angle=(pi / 2) )
def setPI8(self, evt):
print('PI 8')
self.qubit.applyTransformation(QuantumGates.T)
# pi/4 radian clockwise rotation w.r.t z-axis
# self.animateQubit(axis=(0, 0, 1), angle= -1 *(pi / 4) )
# pi/4 radian anti-clockwise rotation w.r.t z-axis
self.animateQubit(axis=(0, 0, 1), angle=(pi / 4) )
def setsNot(self, evt):
print('sqrt Not')
self.qubit.applyTransformation(QuantumGates.sN)
for i in range(0, 128):
rate(128)
self.qubitFrame.rotate(axis=(0, 1, 0), angle=1 * (pi / 4) / 128)
self.qubit.updatePosition()
# set positions without any animation ==========================================
def setTheta(self, evt):
thetaValue = thetaSlider.GetValue()
thetaSliderLab.SetLabel('Theta (Deg): ' + str(thetaValue))
self.setVector(math.radians(thetaValue), self.polarCord[0, 1])
self.qubit.setAmplitudes(0, 0)
self.qubit.updatePosition()
def setPhi(self, evt):
phiValue = phiSlider.GetValue()
phiSliderLab.SetLabel('Phi (Deg): ' + str(phiValue))
self.setVector(self.polarCord[0, 0], math.radians(phiValue))
self.qubit.setAmplitudes(0, 0)
self.qubit.updatePosition()
def setqZero(self, evt):
self.setVector(0, 0.0)
self.qubit.setAmplitudes(1, 0)
self.qubit.applyTransformation(QuantumGates.I)
self.qubit.updatePosition()
def setqOne(self, evt):
self.setVector(pi, 0)
self.qubit.setAmplitudes(0, 1)
self.qubit.applyTransformation(QuantumGates.I)
self.qubit.updatePosition()
def setqPos(self, evt):
self.setqZero(wx.EVT_SHOW)
self.setHadamard(wx.EVT_SHOW)
def setqNeg(self, evt):
self.setqOne(wx.EVT_SHOW)
self.setHadamard(wx.EVT_SHOW)
# The window=======================================================================================
wWidth = 310
wHeight = 725
M = 720
L = 10
d = 20
r = 100
Top = 40
TopB = 15
# w = window(width=wWidth, height=wHeight,menus=True, title='Bloch Sphere')
# display(window=w, x=d, y=d, width=L-2*d, height=L-2*d, forward=(1,-1,0))
# display(x=1024, y=0, width=M, height=M, forward=(-1,-.5,-.5))
w = window(width=wWidth, height=wHeight, menus=True, title='Bloch Sphere')
# disp = display(window=w,width=2*d, height=2*d, forward=(1,-1,0))
disp = display(window=w, x=d, y=d, width=M, height=M, forward=(-1, -.5, -.5))
disp2 = display(x=300, y=0, width=M, height=M, forward=(-1, -.5, -.5))
# The Qubit frame after creating windows
sceneFrame = frame()
qubitFrame = frame(frame=sceneFrame)
# create a bloch sphere
qubit = Qubit(r)
bsVisualizer = BlochSphereVisualizer(qubit
=qubit,qubitFrame=qubitFrame)
color_temp = vector(1, 1, 1)
local_light(pos=(r * 2, r * 2, 0), color=color_temp)
local_light(pos=(r * -2, r * 2, 0), color=color_temp)
local_light(pos=(r * 2, r * -2, 0), color=color_temp)
local_light(pos=(r * -2, r * -2, 0), color=color_temp)
# Buttons, Text, Window Setup
bSize = 50
p = w.panel
title = wx.StaticText(p, pos=(L * 2, 0), size=(300, 25), label='Qubit Bloch Sphere', style=wx.ALIGN_CENTRE)
title.SetFont(wx.Font(14, wx.MODERN, wx.NORMAL, wx.BOLD))
about1 = wx.StaticText(p, pos=(L, wHeight - 150), size=(400, 25), label='Created By: Tyler Dwyer', style=wx.ALIGN_LEFT)
about1.SetFont(wx.Font(8, wx.MODERN, wx.NORMAL, wx.NORMAL))
about2 = wx.StaticText(p, pos=(L, wHeight - 130), size=(400, 25), label='Email: tdwyer@sfu.ca', style=wx.ALIGN_LEFT)
about2.SetFont(wx.Font(8, wx.MODERN, wx.NORMAL, wx.NORMAL))
about3 = wx.StaticText(p, pos=(L, wHeight - 110), size=(400, 25), label='Web: www.sfu.ca\~tdwyer', style=wx.ALIGN_LEFT)
about3.SetFont(wx.Font(8, wx.MODERN, wx.NORMAL, wx.NORMAL))
about3 = wx.StaticText(p, pos=(wWidth / 2 - 110, wHeight - 90), size=(400, 25), label='Simon Fraser University',
style=wx.ALIGN_LEFT)
about3.SetFont(wx.Font(8, wx.MODERN, wx.NORMAL, wx.NORMAL))
# Row Zero/One
wx.StaticText(p, pos=(L + 0 * bSize, 0 * bSize + Top), label='Base States:', style=wx.ALIGN_LEFT)
qZero = wx.Button(p, label='|0>', pos=(L + 0 * bSize, 1 * bSize + TopB), size=(bSize, bSize))
qOne = wx.Button(p, label='|1>', pos=(L + 1 * bSize, 1 * bSize + TopB), size=(bSize, bSize))
wx.StaticText(p, pos=(L + 3 * bSize, 0 * bSize + Top), label='Superposition:', style=wx.ALIGN_LEFT)
qPos = wx.Button(p, label='|+>', pos=(L + 3 * bSize, 1 * bSize + TopB), size=(bSize, bSize))
qNeg = wx.Button(p, label='|->', pos=(L + 4 * bSize, 1 * bSize + TopB), size=(bSize, bSize))
# Row Two/Three
wx.StaticText(p, pos=(L + 0 * bSize, 2 * bSize + Top), label='Hadamard', style=wx.ALIGN_LEFT)
hadamard = wx.Button(p, label='H', pos=(L + 0 * bSize, 3 * bSize + TopB), size=(bSize, bSize))
wx.StaticText(p, pos=(L + 2 * bSize, 2 * bSize + Top), label='Pauli', style=wx.ALIGN_LEFT)
pauliX = wx.Button(p, label='X', pos=(L + 2 * bSize, 3 * bSize + TopB), size=(bSize, bSize))
pauliY = wx.Button(p, label='Y', pos=(L + 3 * bSize, 3 * bSize + TopB), size=(bSize, bSize))
pauliZ = wx.Button(p, label='Z', pos=(L + 4 * bSize, 3 * bSize + TopB), size=(bSize, bSize))
# Row Four/Five
wx.StaticText(p, pos=(L + 0 * bSize, 4 * bSize + Top), label='Phase', style=wx.ALIGN_LEFT)
phase = wx.Button(p, label='S', pos=(L + 0 * bSize, 5 * bSize + TopB), size=(bSize, bSize))
wx.StaticText(p, pos=(L + 2 * bSize, 4 * bSize + Top), label='Pi/8', style=wx.ALIGN_LEFT)
pi8 = wx.Button(p, label='T', pos=(L + 2 * bSize, 5 * bSize + TopB), size=(bSize, bSize))
wx.StaticText(p, pos=(L + 4 * bSize, 4 * bSize + Top), label='Sqrt(Not)', style=wx.ALIGN_LEFT)
sNot = wx.Button(p, label='sN', pos=(L + 4 * bSize, 5 * bSize + TopB), size=(bSize, bSize))
# Row Six/Seven
thetaSliderLab = wx.StaticText(p, pos=(L + 0 * bSize, 6 * bSize + Top), label='Theta (Deg):', style=wx.ALIGN_LEFT)
thetaSlider = wx.Slider(p, pos=(L + 0 * bSize, 7 * bSize + TopB), size=(5 * bSize, 20), minValue=0, maxValue=179)
thetaSlider.Bind(wx.EVT_SCROLL, bsVisualizer.setTheta)
phiSliderLab = wx.StaticText(p, pos=(L + 0 * bSize, 7 * bSize + Top), label='Phi (Deg):', style=wx.ALIGN_LEFT)
phiSlider = wx.Slider(p, pos=(L + 0 * bSize, 8 * bSize + TopB), size=(5 * bSize, 20), minValue=0, maxValue=359)
phiSlider.Bind(wx.EVT_SCROLL, bsVisualizer.setPhi)
# Row Eight/Nine
dataText1 = wx.StaticText(p, pos=(L, 8 * bSize + Top), label='Loading ...', style=wx.ALIGN_LEFT)
dataText2 = wx.StaticText(p, pos=(L, 9 * bSize + Top), label='Loading ...', style=wx.ALIGN_LEFT)
dataText1a = wx.StaticText(p, pos=(L + 2.75 * bSize, 8 * bSize + Top), label='Loading ...', style=wx.ALIGN_LEFT)
dataText2a = wx.StaticText(p, pos=(L + 2.75 * bSize, 9 * bSize + Top), label='Loading ...', style=wx.ALIGN_LEFT)
# Button Bindings
hadamard.Bind(wx.EVT_BUTTON, bsVisualizer.setHadamard) # bind with setHadamard() function
pauliX.Bind(wx.EVT_BUTTON, bsVisualizer.setPauliX)
pauliY.Bind(wx.EVT_BUTTON, bsVisualizer.setPauliY)
pauliZ.Bind(wx.EVT_BUTTON, bsVisualizer.setPauliZ)
phase.Bind(wx.EVT_BUTTON, bsVisualizer.setPhase)
pi8.Bind(wx.EVT_BUTTON, bsVisualizer.setPI8)
sNot.Bind(wx.EVT_BUTTON, bsVisualizer.setsNot)
qZero.Bind(wx.EVT_BUTTON, bsVisualizer.setqZero)
qOne.Bind(wx.EVT_BUTTON, bsVisualizer.setqOne)
qPos.Bind(wx.EVT_BUTTON, bsVisualizer.setqPos)
qNeg.Bind(wx.EVT_BUTTON, bsVisualizer.setqNeg)
# floor = box(pos=(0, -r, 0), length=r * 2, height=r / 1000, width=r * 2, color=color.cyan)
# ball = sphere(frame=qubitFrame, pos=(0, 0, 0), radius=r, material=materials.earth, opacity=.5)
ball = sphere(frame=qubitFrame, pos=(0, 0, 0), radius=r, opacity=.3)
pointer = arrow(frame=qubitFrame, pos=(0, 0, 0), axis=(0, 0, r), shaftwidth=r / 25, color=color.red)
# red point on top of arrow which is in sphere surface
vpy_point = sphere(frame=qubitFrame, pos=(0, 0, r), radius=r / 25, color=color.red)
# ring perpendicular to x-axis
xRing = ring(frame=sceneFrame, pos=(1, 0, 0), axis=(1, 0, 0), radius=r, thickness=r / 100, color=color.green)
# ring perpendicular to y-axis
yRing = ring(frame=sceneFrame, pos=(0, 1, 0), axis=(0, 1, 0), radius=r, thickness=r / 100, color=color.blue)
# ring perpendicular to y-axis
zRing = ring(frame=sceneFrame, pos=(0, 0, 1), axis=(0, 0, 1), radius=r, thickness=r / 100, color=color.yellow)
rodx = cylinder(frame=sceneFrame, pos=((r * 2.5) / -2, 0, 0), axis=(r * 2.5, 0, 0), radius=r / 100, color=color.green)
rody = cylinder(frame=sceneFrame, pos=(0, (r * 2.5) / -2, 0), axis=(0, r * 2.5, 0), radius=r / 100, color=color.blue)
rodz = cylinder(frame=sceneFrame, pos=(0, 0, (r * 2.5) / -2), axis=(0, 0, r * 2.5), radius=r / 100, color=color.yellow)
# Labels
zero = text(frame=sceneFrame, text='|0>', pos=(0, 0, r * 1.5), height=r * .25, align='center', depth=r * -0.03,
color=color.green, axis=(0, 0, 1))
one = text(frame=sceneFrame, text='|1>', pos=(0, 0, r * -1.5), height=r * .25, align='center', depth=r * -0.03,
color=color.green, axis=(0, 0, 1))
xtext = text(frame=sceneFrame, text='x', pos=(r * .5, 0, 0), height=r * .15, align='center', depth=r * -0.02,
color=color.green, axis=(0, 0, 1))
ytext = text(frame=sceneFrame, text='y', pos=(0, r * .5, 0), height=r * .15, align='center', depth=r * -0.02,
color=color.blue, axis=(0, 0, 1))
ztext = text(frame=sceneFrame, text='z', pos=(0, 0, r * .5), height=r * .15, align='center', depth=r * -0.02,
color=color.yellow, axis=(0, 0, 1))
# Setting up qubit
bsVisualizer.setVector(0, 0.0)
# Initial scene/camera rotations
sceneFrame.rotate(axis=(1, 0, 0), angle=-1 * pi / 2)
zero.rotate(axis=(1, 0, 0), angle=-1 * pi / 2)
one.rotate(axis=(1, 0, 0), angle=-1 * pi / 2)
ball.rotate(axis=(1, 0, 0), angle=1 * pi / 2)
ball.rotate(axis=(0, 0, 1), angle=2 * pi / 2)
ztext.rotate(axis=(1, 0, 0), angle=1 * pi / 2)
ytext.rotate(axis=(1, 0, 0), angle=1 * pi / 2)
xtext.rotate(axis=(1, 0, 0), angle=1 * pi / 2)
bsVisualizer.setqZero(wx.EVT_SHOW)
# setPauliX(wx.EVT_SHOW)
# setHadamard(wx.EVT_SHOW)
# setPauliY(wx.EVT_SHOW)
# setPauliY(wx.EVT_SHOW)
# setPauliZ(wx.EVT_SHOW)
# setPauliZ(wx.EVT_SHOW)
# setHadamard(wx.EVT_SHOW)
# Main running loop
while 1:
rate(128)
# Keep things updated
# updatePosition()