/
test_basistools.py
283 lines (235 loc) · 12 KB
/
test_basistools.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
import numpy as np
import scipy
from pygsti.baseobjs.basis import Basis
import pygsti.tools.basistools as bt
from ..util import BaseCase
class BasisToolsTester(BaseCase):
def test_basis_element_labels(self):
basisnames = ['gm', 'std', 'pp']
# One dimensional gm
self.assertEqual([''], bt.basis_element_labels('gm', 1))
# Two dimensional
expectedLabels = [
['I', 'X', 'Y', 'Z'],
['(0,0)', '(0,1)', '(1,0)', '(1,1)'],
['I', 'X', 'Y', 'Z']
]
labels = [bt.basis_element_labels(basisname, 4) for basisname in basisnames]
self.assertEqual(labels, expectedLabels)
with self.assertRaises(AssertionError):
bt.basis_element_labels('asdklfasdf', 4)
# Non power of two for pp labels:
with self.assertRaises(ValueError):
label = bt.basis_element_labels('pp', 9)
# Single list arg for pp labels
self.assertEqual(bt.basis_element_labels('pp', 4), ['I', 'X', 'Y', 'Z'])
# Four dimensional+
expectedLabels = [
['I', 'X_{0,1}', 'X_{0,2}', 'X_{0,3}', 'X_{1,2}', 'X_{1,3}', 'X_{2,3}', 'Y_{0,1}', 'Y_{0,2}', 'Y_{0,3}',
'Y_{1,2}', 'Y_{1,3}', 'Y_{2,3}', 'Z_{1}', 'Z_{2}', 'Z_{3}'],
['(0,0)', '(0,1)', '(0,2)', '(0,3)', '(1,0)', '(1,1)', '(1,2)', '(1,3)', '(2,0)', '(2,1)', '(2,2)', '(2,3)',
'(3,0)', '(3,1)', '(3,2)', '(3,3)'],
['II', 'IX', 'IY', 'IZ', 'XI', 'XX', 'XY', 'XZ', 'YI', 'YX', 'YY', 'YZ', 'ZI', 'ZX', 'ZY', 'ZZ']
]
labels = [bt.basis_element_labels(basisname, 16) for basisname in basisnames]
self.assertEqual(expectedLabels, labels)
def test_basis_longname(self):
longnames = {bt.basis_longname(b) for b in {'gm', 'std', 'PP', 'pp', 'qt'}}
self.assertEqual(longnames, {'Gell-Mann basis', 'Matrix-unit basis', 'Pauli-Product basis', 'Normalized Pauli-Product basis', 'Qutrit basis'})
with self.assertRaises(KeyError):
bt.basis_longname('not a basis')
def test_expand_contract(self):
# matrix that operates on 2x2 density matrices, but only on the 0-th and 3-rd
# elements which correspond to the diagonals of the 2x2 density matrix.
mxInStdBasis = np.array([[1,0,0,2],
[0,0,0,0],
[0,0,0,0],
[3,0,0,4]], 'd')
# Reduce to a matrix operating on a density matrix space with 2 1x1 blocks (hence [1,1])
begin = Basis.cast('std', [1, 1])
end = Basis.cast('std', 4)
mxInReducedBasis = bt.resize_std_mx(mxInStdBasis, 'contract', end, begin)
#mxInReducedBasis = bt.change_basis(mxInStdBasis, begin, end)
notReallyContracted = bt.change_basis(mxInStdBasis, 'std', 'std') # 4
correctAnswer = np.array([[ 1.0, 2.0],
[ 3.0, 4.0]])
self.assertArraysAlmostEqual(mxInReducedBasis, correctAnswer)
self.assertArraysAlmostEqual(notReallyContracted, mxInStdBasis)
expandedMx = bt.resize_std_mx(mxInReducedBasis, 'expand', begin, end)
#expandedMx = bt.change_basis(mxInReducedBasis, end, begin)
expandedMxAgain = bt.change_basis(expandedMx, 'std', 'std') # , 4)
self.assertArraysAlmostEqual(expandedMx, mxInStdBasis)
self.assertArraysAlmostEqual(expandedMxAgain, mxInStdBasis)
def test_transforms(self):
mxStd = np.array([[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]], 'complex')
vecStd = np.array([1,0,0,0], 'complex')
change = bt.change_basis
mxGM = change(mxStd, 'std', 'gm')
mxStd2 = change(mxGM, 'gm', 'std')
self.assertArraysAlmostEqual(mxStd, mxStd2)
vecGM = change(vecStd, 'std', 'gm')
vecStd2 = change(vecGM, 'gm', 'std')
self.assertArraysAlmostEqual(vecStd, vecStd2)
mxPP = change(mxStd, 'std', 'pp')
mxStd2 = change(mxPP, 'pp', 'std')
self.assertArraysAlmostEqual(mxStd, mxStd2)
vecPP = change(vecStd, 'std', 'pp')
vecStd2 = change(vecPP, 'pp', 'std')
self.assertArraysAlmostEqual(vecStd, vecStd2)
mxPP2 = change(mxGM, 'gm', 'pp')
self.assertArraysAlmostEqual(mxPP, mxPP2)
vecPP2 = change(vecGM, 'gm', 'pp')
self.assertArraysAlmostEqual(vecPP, vecPP2)
mxGM2 = change(mxPP, 'pp', 'gm')
self.assertArraysAlmostEqual(mxGM, mxGM2)
vecGM2 = change(vecPP, 'pp', 'gm')
self.assertArraysAlmostEqual(vecGM, vecGM2)
non_herm_mxStd = np.array([[1,0,2,3j],
[0,1,0,2],
[0,0,1,0],
[0,0,0,1]], 'complex')
non_herm_vecStd = np.array([1,0,2,3j], 'complex') # ~ non-herm 2x2 density mx
rank3tensor = np.ones((4, 4, 4), 'd')
with self.assertRaises(ValueError):
change(non_herm_mxStd, 'std', 'gm') # will result in gm mx with *imag* part
with self.assertRaises(ValueError):
change(non_herm_vecStd, 'std', 'gm') # will result in gm vec with *imag* part
with self.assertRaises(ValueError):
change(non_herm_mxStd, 'std', 'pp') # will result in pp mx with *imag* part
with self.assertRaises(ValueError):
change(non_herm_vecStd, 'std', 'pp') # will result in pp vec with *imag* part
with self.assertRaises(ValueError):
change(rank3tensor, 'std', 'gm') # only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'gm', 'std') # only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'std', 'pp') # only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'pp', 'std') # only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'gm', 'pp') # only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'pp', 'gm') # only convert rank 1 & 2 objects
densityMx = np.array([[1, 0], [0, -1]], 'complex')
gmVec = bt.stdmx_to_gmvec(densityMx)
ppVec = bt.stdmx_to_ppvec(densityMx)
stdVec = bt.stdmx_to_stdvec(densityMx)
self.assertArraysAlmostEqual(gmVec, np.array([[0], [0], [0], [np.sqrt(2)]], 'd'))
self.assertArraysAlmostEqual(ppVec, np.array([[0], [0], [0], [np.sqrt(2)]], 'd'))
self.assertArraysAlmostEqual(stdVec, np.array([[1], [0], [0], [-1]], 'complex'))
mxFromGM = bt.gmvec_to_stdmx(gmVec)
mxFromPP = bt.ppvec_to_stdmx(ppVec)
mxFromStd = bt.stdvec_to_stdmx(stdVec)
self.assertArraysAlmostEqual(mxFromGM, densityMx)
self.assertArraysAlmostEqual(mxFromPP, densityMx)
self.assertArraysAlmostEqual(mxFromStd, densityMx)
def test_few_qubit_fns(self):
state_vec = np.array([1, 0], 'complex')
dmVec = bt.state_to_pauli_density_vec(state_vec)
self.assertArraysAlmostEqual(dmVec, np.array([[0.70710678], [0], [0], [0.70710678]], 'complex'))
stdMx = np.array([[1, 0], [0, 0]], 'complex') # density matrix
pauliVec = bt.stdmx_to_ppvec(stdMx)
self.assertArraysAlmostEqual(pauliVec, np.array([[0.70710678], [0], [0], [0.70710678]], 'complex'))
stdMx2 = bt.ppvec_to_stdmx(pauliVec)
self.assertArraysAlmostEqual(stdMx, stdMx2)
def test_vec_to_stdmx(self):
vec = np.zeros(shape=(4,))
for b in {'gm', 'pp', 'std'}:
bt.vec_to_stdmx(vec, b)
with self.assertRaises(AssertionError):
bt.vec_to_stdmx(vec, 'akdfj;ladskf')
def test_auto_expand(self):
comp = Basis.cast([('std', 4,), ('std', 1)])
std = Basis.cast('std', 9)
mxStd = np.identity(5)
test = bt.resize_std_mx(mxStd, 'expand', comp, std)
# Intermediate test
mxInter = np.identity(9)
mxInter[2,2] = mxInter[5,5] = mxInter[6,6] = mxInter[7,7] = 0
self.assertArraysAlmostEqual(test, mxInter)
test2 = bt.resize_std_mx(test, 'contract', std, comp)
self.assertArraysAlmostEqual(test2, mxStd)
def test_flexible_change_basis(self):
comp = Basis.cast([('gm', 4,), ('gm', 1)])
std = Basis.cast('std', 9)
mx = np.identity(5)
test = bt.flexible_change_basis(mx, comp, std)
self.assertEqual(test.shape[0], comp.elsize)
test2 = bt.flexible_change_basis(test, std, comp)
self.assertArraysAlmostEqual(test2, mx)
def test_change_between_composites(self):
a = Basis.cast('std', [4, 1])
b = Basis.cast('gm', [4, 1])
mxStd = np.identity(5)
test = bt.change_basis(mxStd, a, b)
self.assertEqual(test.shape, mxStd.shape)
test2 = bt.change_basis(test, b, a)
self.assertArraysAlmostEqual(test2, mxStd)
def test_general(self):
std = Basis.cast('std', 4)
std4 = Basis.cast('std', 16)
std2x2 = Basis.cast([('std', 4), ('std', 4)])
gm = Basis.cast('gm', 4)
from_basis, to_basis = bt.create_basis_pair(np.identity(4, 'd'), "std", "gm")
from_basis, to_basis = bt.create_basis_pair(np.identity(4, 'd'), std, "gm")
from_basis, to_basis = bt.create_basis_pair(np.identity(4, 'd'), "std", gm)
mx = np.array([
[1, 0, 0, 1],
[0, 1, 2, 0],
[0, 2, 1, 0],
[1, 0, 0, 1]
])
bt.change_basis(mx, 'std', 'gm') # shortname lookup
bt.change_basis(mx, std, gm) # object
bt.change_basis(mx, std, 'gm') # combination
bt.flexible_change_basis(mx, std, gm) # same dimension
I2x2 = np.identity(8, 'd')
I4 = bt.flexible_change_basis(I2x2, std2x2, std4)
self.assertArraysAlmostEqual(bt.flexible_change_basis(I4, std4, std2x2), I2x2)
with self.assertRaises(AssertionError):
bt.change_basis(mx, std, std4) # basis size mismatch
mxInStdBasis = np.array([[1,0,0,2],
[0,0,0,0],
[0,0,0,0],
[3,0,0,4]], 'd')
begin = Basis.cast('std', [1, 1])
end = Basis.cast('std', 4)
mxInReducedBasis = bt.resize_std_mx(mxInStdBasis, 'contract', end, begin)
original = bt.resize_std_mx(mxInReducedBasis, 'expand', begin, end)
self.assertArraysAlmostEqual(mxInStdBasis, original)
def test_sparse_lindblad_bases(self):
sparsePP = Basis.cast("pp", 16, sparse=True)
mxs = sparsePP.elements
#for lbl, mx in zip(sparsePP.labels, mxs):
# print("{}: {} matrix with {} nonzero entries (of {} total)".format(
# lbl, mx.shape, mx.nnz, mx.shape[0] * mx.shape[1]
# ))
# print(mx.toarray())
#print("{} basis elements".format(len(sparsePP)))
self.assertEqual(len(sparsePP), 16)
densePP = Basis.cast("pp", 16, sparse=False)
for smx, dmx in zip(sparsePP.elements, densePP.elements):
self.assertArraysAlmostEqual(smx.toarray(), dmx)
M = np.ones((16, 16), 'd')
v = np.ones(16, 'd')
S = scipy.sparse.identity(16, 'd', 'csr')
#print("Test types after basis change by sparse basis:")
Mout = bt.change_basis(M, sparsePP, 'std')
vout = bt.change_basis(v, sparsePP, 'std')
Sout = bt.change_basis(S, sparsePP, 'std')
#print("{} -> {}".format(type(M), type(Mout)))
#print("{} -> {}".format(type(v), type(vout)))
#print("{} -> {}".format(type(S), type(Sout)))
self.assertIsInstance(Mout, np.ndarray)
self.assertIsInstance(vout, np.ndarray)
self.assertIsInstance(Sout, scipy.sparse.csr_matrix)
Mdout = bt.change_basis(M, densePP, 'std')
vdout = bt.change_basis(v, densePP, 'std')
Sdout = bt.change_basis(S, densePP, 'std')
self.assertIsInstance(Sdout, np.ndarray)
self.assertArraysAlmostEqual(Mout, Mdout)
self.assertArraysAlmostEqual(vout, vdout)
self.assertArraysAlmostEqual(Sout, Sdout)