File size: 17,745 Bytes
6a86ad5
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
from sympy.external import import_module
from sympy.core.mul import Mul
from sympy.core.numbers import Integer
from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.gate import (X, Y, Z, H, CNOT,
        IdentityGate, CGate, PhaseGate, TGate)
from sympy.physics.quantum.identitysearch import (generate_gate_rules,
        generate_equivalent_ids, GateIdentity, bfs_identity_search,
        is_scalar_sparse_matrix,
        is_scalar_nonsparse_matrix, is_degenerate, is_reducible)
from sympy.testing.pytest import skip


def create_gate_sequence(qubit=0):
    gates = (X(qubit), Y(qubit), Z(qubit), H(qubit))
    return gates


def test_generate_gate_rules_1():
    # Test with tuples
    (x, y, z, h) = create_gate_sequence()
    ph = PhaseGate(0)
    cgate_t = CGate(0, TGate(1))

    assert generate_gate_rules((x,)) == {((x,), ())}

    gate_rules = {((x, x), ()),
                      ((x,), (x,))}
    assert generate_gate_rules((x, x)) == gate_rules

    gate_rules = {((x, y, x), ()),
                      ((y, x, x), ()),
                      ((x, x, y), ()),
                      ((y, x), (x,)),
                      ((x, y), (x,)),
                      ((y,), (x, x))}
    assert generate_gate_rules((x, y, x)) == gate_rules

    gate_rules = {((x, y, z), ()), ((y, z, x), ()), ((z, x, y), ()),
                      ((), (x, z, y)), ((), (y, x, z)), ((), (z, y, x)),
                      ((x,), (z, y)), ((y, z), (x,)), ((y,), (x, z)),
                      ((z, x), (y,)), ((z,), (y, x)), ((x, y), (z,))}
    actual = generate_gate_rules((x, y, z))
    assert actual == gate_rules

    gate_rules = {
        ((), (h, z, y, x)), ((), (x, h, z, y)), ((), (y, x, h, z)),
         ((), (z, y, x, h)), ((h,), (z, y, x)), ((x,), (h, z, y)),
         ((y,), (x, h, z)), ((z,), (y, x, h)), ((h, x), (z, y)),
         ((x, y), (h, z)), ((y, z), (x, h)), ((z, h), (y, x)),
         ((h, x, y), (z,)), ((x, y, z), (h,)), ((y, z, h), (x,)),
         ((z, h, x), (y,)), ((h, x, y, z), ()), ((x, y, z, h), ()),
         ((y, z, h, x), ()), ((z, h, x, y), ())}
    actual = generate_gate_rules((x, y, z, h))
    assert actual == gate_rules

    gate_rules = {((), (cgate_t**(-1), ph**(-1), x)),
                      ((), (ph**(-1), x, cgate_t**(-1))),
                      ((), (x, cgate_t**(-1), ph**(-1))),
                      ((cgate_t,), (ph**(-1), x)),
                      ((ph,), (x, cgate_t**(-1))),
                      ((x,), (cgate_t**(-1), ph**(-1))),
                      ((cgate_t, x), (ph**(-1),)),
                      ((ph, cgate_t), (x,)),
                      ((x, ph), (cgate_t**(-1),)),
                      ((cgate_t, x, ph), ()),
                      ((ph, cgate_t, x), ()),
                      ((x, ph, cgate_t), ())}
    actual = generate_gate_rules((x, ph, cgate_t))
    assert actual == gate_rules

    gate_rules = {(Integer(1), cgate_t**(-1)*ph**(-1)*x),
                      (Integer(1), ph**(-1)*x*cgate_t**(-1)),
                      (Integer(1), x*cgate_t**(-1)*ph**(-1)),
                      (cgate_t, ph**(-1)*x),
                      (ph, x*cgate_t**(-1)),
                      (x, cgate_t**(-1)*ph**(-1)),
                      (cgate_t*x, ph**(-1)),
                      (ph*cgate_t, x),
                      (x*ph, cgate_t**(-1)),
                      (cgate_t*x*ph, Integer(1)),
                      (ph*cgate_t*x, Integer(1)),
                      (x*ph*cgate_t, Integer(1))}
    actual = generate_gate_rules((x, ph, cgate_t), return_as_muls=True)
    assert actual == gate_rules


def test_generate_gate_rules_2():
    # Test with Muls
    (x, y, z, h) = create_gate_sequence()
    ph = PhaseGate(0)
    cgate_t = CGate(0, TGate(1))

    # Note: 1 (type int) is not the same as 1 (type One)
    expected = {(x, Integer(1))}
    assert generate_gate_rules((x,), return_as_muls=True) == expected

    expected = {(Integer(1), Integer(1))}
    assert generate_gate_rules(x*x, return_as_muls=True) == expected

    expected = {((), ())}
    assert generate_gate_rules(x*x, return_as_muls=False) == expected

    gate_rules = {(x*y*x, Integer(1)),
                      (y, Integer(1)),
                      (y*x, x),
                      (x*y, x)}
    assert generate_gate_rules(x*y*x, return_as_muls=True) == gate_rules

    gate_rules = {(x*y*z, Integer(1)),
                      (y*z*x, Integer(1)),
                      (z*x*y, Integer(1)),
                      (Integer(1), x*z*y),
                      (Integer(1), y*x*z),
                      (Integer(1), z*y*x),
                      (x, z*y),
                      (y*z, x),
                      (y, x*z),
                      (z*x, y),
                      (z, y*x),
                      (x*y, z)}
    actual = generate_gate_rules(x*y*z, return_as_muls=True)
    assert actual == gate_rules

    gate_rules = {(Integer(1), h*z*y*x),
                      (Integer(1), x*h*z*y),
                      (Integer(1), y*x*h*z),
                      (Integer(1), z*y*x*h),
                      (h, z*y*x), (x, h*z*y),
                      (y, x*h*z), (z, y*x*h),
                      (h*x, z*y), (z*h, y*x),
                      (x*y, h*z), (y*z, x*h),
                      (h*x*y, z), (x*y*z, h),
                      (y*z*h, x), (z*h*x, y),
                      (h*x*y*z, Integer(1)),
                      (x*y*z*h, Integer(1)),
                      (y*z*h*x, Integer(1)),
                      (z*h*x*y, Integer(1))}
    actual = generate_gate_rules(x*y*z*h, return_as_muls=True)
    assert actual == gate_rules

    gate_rules = {(Integer(1), cgate_t**(-1)*ph**(-1)*x),
                      (Integer(1), ph**(-1)*x*cgate_t**(-1)),
                      (Integer(1), x*cgate_t**(-1)*ph**(-1)),
                      (cgate_t, ph**(-1)*x),
                      (ph, x*cgate_t**(-1)),
                      (x, cgate_t**(-1)*ph**(-1)),
                      (cgate_t*x, ph**(-1)),
                      (ph*cgate_t, x),
                      (x*ph, cgate_t**(-1)),
                      (cgate_t*x*ph, Integer(1)),
                      (ph*cgate_t*x, Integer(1)),
                      (x*ph*cgate_t, Integer(1))}
    actual = generate_gate_rules(x*ph*cgate_t, return_as_muls=True)
    assert actual == gate_rules

    gate_rules = {((), (cgate_t**(-1), ph**(-1), x)),
                      ((), (ph**(-1), x, cgate_t**(-1))),
                      ((), (x, cgate_t**(-1), ph**(-1))),
                      ((cgate_t,), (ph**(-1), x)),
                      ((ph,), (x, cgate_t**(-1))),
                      ((x,), (cgate_t**(-1), ph**(-1))),
                      ((cgate_t, x), (ph**(-1),)),
                      ((ph, cgate_t), (x,)),
                      ((x, ph), (cgate_t**(-1),)),
                      ((cgate_t, x, ph), ()),
                      ((ph, cgate_t, x), ()),
                      ((x, ph, cgate_t), ())}
    actual = generate_gate_rules(x*ph*cgate_t)
    assert actual == gate_rules


def test_generate_equivalent_ids_1():
    # Test with tuples
    (x, y, z, h) = create_gate_sequence()

    assert generate_equivalent_ids((x,)) == {(x,)}
    assert generate_equivalent_ids((x, x)) == {(x, x)}
    assert generate_equivalent_ids((x, y)) == {(x, y), (y, x)}

    gate_seq = (x, y, z)
    gate_ids = {(x, y, z), (y, z, x), (z, x, y), (z, y, x),
                    (y, x, z), (x, z, y)}
    assert generate_equivalent_ids(gate_seq) == gate_ids

    gate_ids = {Mul(x, y, z), Mul(y, z, x), Mul(z, x, y),
                    Mul(z, y, x), Mul(y, x, z), Mul(x, z, y)}
    assert generate_equivalent_ids(gate_seq, return_as_muls=True) == gate_ids

    gate_seq = (x, y, z, h)
    gate_ids = {(x, y, z, h), (y, z, h, x),
                    (h, x, y, z), (h, z, y, x),
                    (z, y, x, h), (y, x, h, z),
                    (z, h, x, y), (x, h, z, y)}
    assert generate_equivalent_ids(gate_seq) == gate_ids

    gate_seq = (x, y, x, y)
    gate_ids = {(x, y, x, y), (y, x, y, x)}
    assert generate_equivalent_ids(gate_seq) == gate_ids

    cgate_y = CGate((1,), y)
    gate_seq = (y, cgate_y, y, cgate_y)
    gate_ids = {(y, cgate_y, y, cgate_y), (cgate_y, y, cgate_y, y)}
    assert generate_equivalent_ids(gate_seq) == gate_ids

    cnot = CNOT(1, 0)
    cgate_z = CGate((0,), Z(1))
    gate_seq = (cnot, h, cgate_z, h)
    gate_ids = {(cnot, h, cgate_z, h), (h, cgate_z, h, cnot),
                    (h, cnot, h, cgate_z), (cgate_z, h, cnot, h)}
    assert generate_equivalent_ids(gate_seq) == gate_ids


def test_generate_equivalent_ids_2():
    # Test with Muls
    (x, y, z, h) = create_gate_sequence()

    assert generate_equivalent_ids((x,), return_as_muls=True) == {x}

    gate_ids = {Integer(1)}
    assert generate_equivalent_ids(x*x, return_as_muls=True) == gate_ids

    gate_ids = {x*y, y*x}
    assert generate_equivalent_ids(x*y, return_as_muls=True) == gate_ids

    gate_ids = {(x, y), (y, x)}
    assert generate_equivalent_ids(x*y) == gate_ids

    circuit = Mul(*(x, y, z))
    gate_ids = {x*y*z, y*z*x, z*x*y, z*y*x,
                    y*x*z, x*z*y}
    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids

    circuit = Mul(*(x, y, z, h))
    gate_ids = {x*y*z*h, y*z*h*x,
                    h*x*y*z, h*z*y*x,
                    z*y*x*h, y*x*h*z,
                    z*h*x*y, x*h*z*y}
    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids

    circuit = Mul(*(x, y, x, y))
    gate_ids = {x*y*x*y, y*x*y*x}
    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids

    cgate_y = CGate((1,), y)
    circuit = Mul(*(y, cgate_y, y, cgate_y))
    gate_ids = {y*cgate_y*y*cgate_y, cgate_y*y*cgate_y*y}
    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids

    cnot = CNOT(1, 0)
    cgate_z = CGate((0,), Z(1))
    circuit = Mul(*(cnot, h, cgate_z, h))
    gate_ids = {cnot*h*cgate_z*h, h*cgate_z*h*cnot,
                    h*cnot*h*cgate_z, cgate_z*h*cnot*h}
    assert generate_equivalent_ids(circuit, return_as_muls=True) == gate_ids


def test_is_scalar_nonsparse_matrix():
    numqubits = 2
    id_only = False

    id_gate = (IdentityGate(1),)
    actual = is_scalar_nonsparse_matrix(id_gate, numqubits, id_only)
    assert actual is True

    x0 = X(0)
    xx_circuit = (x0, x0)
    actual = is_scalar_nonsparse_matrix(xx_circuit, numqubits, id_only)
    assert actual is True

    x1 = X(1)
    y1 = Y(1)
    xy_circuit = (x1, y1)
    actual = is_scalar_nonsparse_matrix(xy_circuit, numqubits, id_only)
    assert actual is False

    z1 = Z(1)
    xyz_circuit = (x1, y1, z1)
    actual = is_scalar_nonsparse_matrix(xyz_circuit, numqubits, id_only)
    assert actual is True

    cnot = CNOT(1, 0)
    cnot_circuit = (cnot, cnot)
    actual = is_scalar_nonsparse_matrix(cnot_circuit, numqubits, id_only)
    assert actual is True

    h = H(0)
    hh_circuit = (h, h)
    actual = is_scalar_nonsparse_matrix(hh_circuit, numqubits, id_only)
    assert actual is True

    h1 = H(1)
    xhzh_circuit = (x1, h1, z1, h1)
    actual = is_scalar_nonsparse_matrix(xhzh_circuit, numqubits, id_only)
    assert actual is True

    id_only = True
    actual = is_scalar_nonsparse_matrix(xhzh_circuit, numqubits, id_only)
    assert actual is True
    actual = is_scalar_nonsparse_matrix(xyz_circuit, numqubits, id_only)
    assert actual is False
    actual = is_scalar_nonsparse_matrix(cnot_circuit, numqubits, id_only)
    assert actual is True
    actual = is_scalar_nonsparse_matrix(hh_circuit, numqubits, id_only)
    assert actual is True


def test_is_scalar_sparse_matrix():
    np = import_module('numpy')
    if not np:
        skip("numpy not installed.")

    scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
    if not scipy:
        skip("scipy not installed.")

    numqubits = 2
    id_only = False

    id_gate = (IdentityGate(1),)
    assert is_scalar_sparse_matrix(id_gate, numqubits, id_only) is True

    x0 = X(0)
    xx_circuit = (x0, x0)
    assert is_scalar_sparse_matrix(xx_circuit, numqubits, id_only) is True

    x1 = X(1)
    y1 = Y(1)
    xy_circuit = (x1, y1)
    assert is_scalar_sparse_matrix(xy_circuit, numqubits, id_only) is False

    z1 = Z(1)
    xyz_circuit = (x1, y1, z1)
    assert is_scalar_sparse_matrix(xyz_circuit, numqubits, id_only) is True

    cnot = CNOT(1, 0)
    cnot_circuit = (cnot, cnot)
    assert is_scalar_sparse_matrix(cnot_circuit, numqubits, id_only) is True

    h = H(0)
    hh_circuit = (h, h)
    assert is_scalar_sparse_matrix(hh_circuit, numqubits, id_only) is True

    # NOTE:
    # The elements of the sparse matrix for the following circuit
    # is actually 1.0000000000000002+0.0j.
    h1 = H(1)
    xhzh_circuit = (x1, h1, z1, h1)
    assert is_scalar_sparse_matrix(xhzh_circuit, numqubits, id_only) is True

    id_only = True
    assert is_scalar_sparse_matrix(xhzh_circuit, numqubits, id_only) is True
    assert is_scalar_sparse_matrix(xyz_circuit, numqubits, id_only) is False
    assert is_scalar_sparse_matrix(cnot_circuit, numqubits, id_only) is True
    assert is_scalar_sparse_matrix(hh_circuit, numqubits, id_only) is True


def test_is_degenerate():
    (x, y, z, h) = create_gate_sequence()

    gate_id = GateIdentity(x, y, z)
    ids = {gate_id}

    another_id = (z, y, x)
    assert is_degenerate(ids, another_id) is True


def test_is_reducible():
    nqubits = 2
    (x, y, z, h) = create_gate_sequence()

    circuit = (x, y, y)
    assert is_reducible(circuit, nqubits, 1, 3) is True

    circuit = (x, y, x)
    assert is_reducible(circuit, nqubits, 1, 3) is False

    circuit = (x, y, y, x)
    assert is_reducible(circuit, nqubits, 0, 4) is True

    circuit = (x, y, y, x)
    assert is_reducible(circuit, nqubits, 1, 3) is True

    circuit = (x, y, z, y, y)
    assert is_reducible(circuit, nqubits, 1, 5) is True


def test_bfs_identity_search():
    assert bfs_identity_search([], 1) == set()

    (x, y, z, h) = create_gate_sequence()

    gate_list = [x]
    id_set = {GateIdentity(x, x)}
    assert bfs_identity_search(gate_list, 1, max_depth=2) == id_set

    # Set should not contain degenerate quantum circuits
    gate_list = [x, y, z]
    id_set = {GateIdentity(x, x),
                  GateIdentity(y, y),
                  GateIdentity(z, z),
                  GateIdentity(x, y, z)}
    assert bfs_identity_search(gate_list, 1) == id_set

    id_set = {GateIdentity(x, x),
                  GateIdentity(y, y),
                  GateIdentity(z, z),
                  GateIdentity(x, y, z),
                  GateIdentity(x, y, x, y),
                  GateIdentity(x, z, x, z),
                  GateIdentity(y, z, y, z)}
    assert bfs_identity_search(gate_list, 1, max_depth=4) == id_set
    assert bfs_identity_search(gate_list, 1, max_depth=5) == id_set

    gate_list = [x, y, z, h]
    id_set = {GateIdentity(x, x),
                  GateIdentity(y, y),
                  GateIdentity(z, z),
                  GateIdentity(h, h),
                  GateIdentity(x, y, z),
                  GateIdentity(x, y, x, y),
                  GateIdentity(x, z, x, z),
                  GateIdentity(x, h, z, h),
                  GateIdentity(y, z, y, z),
                  GateIdentity(y, h, y, h)}
    assert bfs_identity_search(gate_list, 1) == id_set

    id_set = {GateIdentity(x, x),
                  GateIdentity(y, y),
                  GateIdentity(z, z),
                  GateIdentity(h, h)}
    assert id_set == bfs_identity_search(gate_list, 1, max_depth=3,
                                         identity_only=True)

    id_set = {GateIdentity(x, x),
                  GateIdentity(y, y),
                  GateIdentity(z, z),
                  GateIdentity(h, h),
                  GateIdentity(x, y, z),
                  GateIdentity(x, y, x, y),
                  GateIdentity(x, z, x, z),
                  GateIdentity(x, h, z, h),
                  GateIdentity(y, z, y, z),
                  GateIdentity(y, h, y, h),
                  GateIdentity(x, y, h, x, h),
                  GateIdentity(x, z, h, y, h),
                  GateIdentity(y, z, h, z, h)}
    assert bfs_identity_search(gate_list, 1, max_depth=5) == id_set

    id_set = {GateIdentity(x, x),
                  GateIdentity(y, y),
                  GateIdentity(z, z),
                  GateIdentity(h, h),
                  GateIdentity(x, h, z, h)}
    assert id_set == bfs_identity_search(gate_list, 1, max_depth=4,
                                         identity_only=True)

    cnot = CNOT(1, 0)
    gate_list = [x, cnot]
    id_set = {GateIdentity(x, x),
                  GateIdentity(cnot, cnot),
                  GateIdentity(x, cnot, x, cnot)}
    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set

    cgate_x = CGate((1,), x)
    gate_list = [x, cgate_x]
    id_set = {GateIdentity(x, x),
                  GateIdentity(cgate_x, cgate_x),
                  GateIdentity(x, cgate_x, x, cgate_x)}
    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set

    cgate_z = CGate((0,), Z(1))
    gate_list = [cnot, cgate_z, h]
    id_set = {GateIdentity(h, h),
                  GateIdentity(cgate_z, cgate_z),
                  GateIdentity(cnot, cnot),
                  GateIdentity(cnot, h, cgate_z, h)}
    assert bfs_identity_search(gate_list, 2, max_depth=4) == id_set

    s = PhaseGate(0)
    t = TGate(0)
    gate_list = [s, t]
    id_set = {GateIdentity(s, s, s, s)}
    assert bfs_identity_search(gate_list, 1, max_depth=4) == id_set


def test_bfs_identity_search_xfail():
    s = PhaseGate(0)
    t = TGate(0)
    gate_list = [Dagger(s), t]
    id_set = {GateIdentity(Dagger(s), t, t)}
    assert bfs_identity_search(gate_list, 1, max_depth=3) == id_set