This repository was archived by the owner on Oct 7, 2019. It is now read-only.
-
Notifications
You must be signed in to change notification settings - Fork 20
/
Copy pathgates.py
301 lines (222 loc) · 7.95 KB
/
gates.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
r"""
Standard gate set, as detailed in Quil whitepaper (arXiV:1608:03355v2)
Currently includes:
I - identity :math:`\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}`
X - Pauli-X :math:`\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}`
Y - Pauli-Y :math:`\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}`
Z - Pauli-Z :math:`\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}`
H - Hadamard
:math:`\frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}`
S - PHASE(pi/2)
:math:`\begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}`
T - PHASE(pi/4)
:math:`\begin{pmatrix} 1 & 0 \\ 0 & e^{i \pi / 4} \end{pmatrix}`
PHASE(:math:`\phi`) - PHASE
:math:`\begin{pmatrix} 1 & 0 \\ 0 & e^{i \phi} \end{pmatrix}`
RX(:math:`\phi`) - RX
:math:`\begin{pmatrix} \cos(\phi / 2) & -i \sin(\phi/2) \\
-i \sin(\phi/2) & \cos(\phi/2) \end{pmatrix}`
RY(:math:`\phi`) - RY
:math:`\begin{pmatrix} \cos(\phi / 2) & -\sin(\phi / 2) \\
\sin(\phi/2) & \cos(\phi/2) \end{pmatrix}`
RZ(:math:`\phi`) - RZ
:math:`\begin{pmatrix} \cos(\phi/2) - i \sin(\phi/2) & 0 \\
0 & \cos(\phi/2) + i \sin(\phi/2) \end{pmatrix}`
CZ - controlled-Z
:math:`P_0 \otimes I + P_1 \otimes Z = \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\
0&0&1&0 \\ 0&0&0&-1 \end{pmatrix}`
CNOT - controlled-X / controlled-NOT
:math:`P_0 \otimes I + P_1 \otimes X = \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\
0&0&0&1 \\ 0&0&1&0 \end{pmatrix}`
CCNOT - double-controlled-X
:math:`P_0 \otimes P_0 \otimes I + P_0 \otimes P_1 \otimes I + P_1 \otimes P_0 \otimes I
+ P_1 \otimes P_1 \otimes X`
CPHASE00(:math:`\phi`) - controlled-phase-on-|00>
:math:`\text{diag}(e^{i \phi}, 1, 1, 1,)`
CPHASE01(:math:`\phi`) - controlled-phase-on-|01>
:math:`\text{diag}(1, e^{i \phi}, 1, 1,)`
CPHASE10(:math:`\phi`) - controlled-phase-on-|10>
:math:`\text{diag}(1, 1, e^{i \phi}, 1)`
CPHASE(:math:`\phi`) - controlled-phase-on-|11>
:math:`\text{diag}(1, 1, 1, e^{i \phi})`
SWAP - swap
:math:`\begin{pmatrix} 1&0&0&0 \\ 0&0&1&0 \\ 0&1&0&0 \\ 0&0&0&1 \end{pmatrix}`
CSWAP - controlled-swap
:math:`P_0 \otimes I_2 + P_1 \otimes \text{SWAP}`
ISWAP - i-phase-swap
:math:`\begin{pmatrix} 1&0&0&0 \\ 0&0&i&0 \\ 0&i&0&0 \\ 0&0&0&1 \end{pmatrix}`
PSWAP(:math:`\phi`) - phi-phase-swap
:math:`\begin{pmatrix} 1&0&0&0 \\ 0&0&e^{i\phi}&0 \\ 0&e^{i\phi}&0&0 \\ 0&0&0&1 \end{pmatrix}`
Specialized gates / internal utility gates:
BARENCO(:math:`\alpha, \phi, \theta`) - Barenco gate
:math:`\begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&e^{i\phi} \cos\theta & -i e^{i(\alpha-\phi)}
\sin\theta \\ 0&0&-i e^{i(\alpha+\phi)} \sin\theta & e^{i\alpha} \cos\theta \end{pmatrix}`
P0 - project-onto-zero
:math:`\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}`
P1 - project-onto-one
:math:`\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}`
"""
import numpy as np
import cmath
I = np.array([[1.0, 0.0], [0.0, 1.0]])
X = np.array([[0.0, 1.0], [1.0, 0.0]])
Y = np.array([[0.0, 0.0 - 1.0j], [0.0 + 1.0j, 0.0]])
Z = np.array([[1.0, 0.0], [0.0, -1.0]])
H = (1.0 / np.sqrt(2.0)) * np.array([[1.0, 1.0], [1.0, -1.0]])
S = np.array([[1.0, 0.0], [0.0, 1.0j]])
T = np.array([[1.0, 0.0], [0.0, cmath.exp(1.0j * np.pi / 4.0)]])
def PHASE(phi):
return np.array([[1.0, 0.0], [0.0, np.exp(1j * phi)]])
def RX(phi):
return np.array([[np.cos(phi / 2.0), -1j * np.sin(phi / 2.0)],
[-1j * np.sin(phi / 2.0), np.cos(phi / 2.0)]])
def RY(phi):
return np.array([[np.cos(phi / 2.0), -np.sin(phi / 2.0)],
[np.sin(phi / 2.0), np.cos(phi / 2.0)]])
def RZ(phi):
return np.array([[np.cos(phi / 2.0) - 1j * np.sin(phi / 2.0), 0],
[0, np.cos(phi / 2.0) + 1j * np.sin(phi / 2.0)]])
CZ = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, -1]])
CNOT = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 1],
[0, 0, 1, 0]])
CCNOT = np.array([[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 1, 0]])
def CPHASE00(phi):
return np.diag([np.exp(1j * phi), 1.0, 1.0, 1.0])
def CPHASE01(phi):
return np.diag([1.0, np.exp(1j * phi), 1.0, 1.0])
def CPHASE10(phi):
return np.diag([1.0, 1.0, np.exp(1j * phi), 1.0])
def CPHASE(phi):
return np.diag([1.0, 1.0, 1.0, np.exp(1j * phi)])
SWAP = np.array([[1, 0, 0, 0],
[0, 0, 1, 0],
[0, 1, 0, 0],
[0, 0, 0, 1]])
CSWAP = np.array([[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1]])
ISWAP = np.array([[1, 0, 0, 0],
[0, 0, 1j, 0],
[0, 1j, 0, 0],
[0, 0, 0, 1]])
def PSWAP(phi):
return np.array([[1, 0, 0, 0],
[0, 0, np.exp(1j * phi), 0],
[0, np.exp(1j * phi), 0, 0],
[0, 0, 0, 1]])
# Utility gates for internal QVM use
P0 = np.array([[1, 0], [0, 0]])
P1 = np.array([[0, 0], [0, 1]])
utility_gates = {'P0': P0, 'P1': P1}
# Specialized useful gates; not officially in standard gate set
def BARENCO(alpha, phi, theta):
lower_unitary = np.array([
[np.exp(1j * phi) * np.cos(theta), -1j * np.exp(1j * (alpha - phi)) * np.sin(theta)],
[-1j * np.exp(1j * (alpha + phi)) * np.sin(theta), np.exp(1j * alpha) * np.cos(theta)]])
return np.kron(P0, np.eye(2)) + np.kron(P1, lower_unitary)
"""
Dictionary of gates for use in referenceqvm.
"""
gate_matrix = {
'I': I,
'X': X,
'Y': Y,
'Z': Z,
'H': H,
'S': S,
'T': T,
'PHASE': PHASE,
'RX': RX,
'RY': RY,
'RZ': RZ,
'CNOT': CNOT,
'CCNOT': CCNOT,
'CPHASE00': CPHASE00,
'CPHASE01': CPHASE01,
'CPHASE10': CPHASE10,
'CPHASE': CPHASE,
'SWAP': SWAP,
'CSWAP': CSWAP,
'ISWAP': ISWAP,
'PSWAP': PSWAP,
'BARENCO': BARENCO,
'CZ': CZ
}
stabilizer_gate_matrix = {
'I': I,
'X': X,
'Y': Y,
'Z': Z,
'H': H,
'CNOT': CNOT,
'S': S,
'CZ': CZ
}
# noisy gates
def relaxation(p):
"""
Return the amplitude damping Kraus operators
"""
k0 = np.array([[1.0, 0.0], [0.0, np.sqrt(1 - p)]])
k1 = np.array([[0.0, np.sqrt(p)], [0.0, 0.0]])
return [k0, k1]
def dephasing(p):
"""
Return the phase damping Kraus operators
"""
k0 = np.eye(2)*np.sqrt(1 - p/2)
k1 = np.sqrt(p/2) * Z
return [k0, k1]
def depolarizing(p):
"""
Return the phase damping Kraus operators
"""
k0 = np.sqrt(1.0 - p)*I
k1 = np.sqrt(p/3.0)*X
k2 = np.sqrt(p/3.0)*Y
k3 = np.sqrt(p/3.0)*Z
return [k0, k1, k2, k3]
def phase_flip(p):
"""
Return the phase flip kraus operators
"""
k0 = np.sqrt(1 - p)*I
k1 = np.sqrt(p)*Z
return [k0, k1]
def bit_flip(p):
"""
Return the phase flip kraus operators
"""
k0 = np.sqrt(1 - p)*I
k1 = np.sqrt(p)*X
return [k0, k1]
def bitphase_flip(p):
"""
Return the phase flip kraus operators
"""
k0 = np.sqrt(1 - p)*I
k1 = np.sqrt(p)*Y
return [k0, k1]
noise_gates = {'relaxation': relaxation,
'dephasing': dephasing,
'depolarizing': depolarizing,
'phase_flip': phase_flip,
'bit_flip': bit_flip,
'bitphase_flip': bitphase_flip}