-
Notifications
You must be signed in to change notification settings - Fork 8
/
Copy pathtest.nb
3243 lines (3181 loc) · 172 KB
/
test.nb
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
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 9.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
NotebookDataLength[ 176238, 3235]
NotebookOptionsPosition[ 171692, 3145]
NotebookOutlinePosition[ 172183, 3163]
CellTagsIndexPosition[ 172140, 3160]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.602010574079318*^9,
3.602010577038896*^9}},ExpressionUUID->"39b6a9e7-da96-489d-a993-\
0e82c0f92d55"],
Cell[BoxData[
RowBox[{"Needs", "[", "\"\<Quantum`\>\"", "]"}]], "Input",
CellChangeTimes->{{3.538747820968527*^9, 3.538747820972623*^9}},
CellLabel->"In[1]:=",ExpressionUUID->"0a7cacb0-3e86-4e7c-8ea0-8257c8b86660"],
Cell[CellGroupData[{
Cell["Check Partial trace", "Subsection",
CellChangeTimes->{{3.545497852142183*^9,
3.545497856859102*^9}},ExpressionUUID->"973b70e6-97d9-4748-84e0-\
638a3d6455a0"],
Cell[BoxData[{
RowBox[{
RowBox[{"QubitsA", "=", "3"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"QubitsB", "=", "4"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Psi]AB", "=",
RowBox[{"RandomState", "[",
SuperscriptBox["2",
RowBox[{"QubitsA", "+", "QubitsB"}]], "]"}]}], ";"}], "\n",
RowBox[{
RowBox[{"Export", "[",
RowBox[{"\"\</tmp/psiab.dat\>\"", ",",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Re", "[", "#", "]"}], ",",
RowBox[{"Im", "[", "#", "]"}]}], "}"}], "&"}], "/@", "\[Psi]AB"}]}],
"]"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Rho]A", "=",
RowBox[{"PartialTrace", "[",
RowBox[{"\[Psi]AB", ",",
RowBox[{
RowBox[{"Power", "[",
RowBox[{"2", ",", "QubitsA"}], "]"}], "-", "1"}]}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Export", "[",
RowBox[{"\"\</tmp/rhoa.dat\>\"", ",",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Re", "[", "#", "]"}], ",",
RowBox[{"Im", "[", "#", "]"}]}], "}"}], "&"}], "/@",
RowBox[{"Flatten", "[", "\[Rho]A", "]"}]}]}], "]"}], ";"}]}], "Input",
CellChangeTimes->{{3.538747831100922*^9, 3.538747866616877*^9}, {
3.538747914720241*^9, 3.538747923456869*^9}, {3.538747973776409*^9,
3.538747973848289*^9}, {3.53874847999379*^9, 3.538748482064971*^9},
3.538748534960989*^9},ExpressionUUID->"0801007a-7909-4bac-9ec7-\
470ac179e873"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"MatrixForm", "[", "\[Rho]A", "]"}]], "Input",
CellChangeTimes->{{3.538748562835455*^9,
3.538748566276944*^9}},ExpressionUUID->"6220a72a-05a7-4ddb-af8e-\
140bb175b206"],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{
RowBox[{"0.11000585999087152`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.01834571235414916`"}], "+",
RowBox[{"0.012021094305255359`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.011232926641687502`"}], "+",
RowBox[{"0.03384717769144092`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.021269051235115473`", "\[VeryThinSpace]", "+",
RowBox[{"0.0017001838746707192`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.038764893989220506`", "\[VeryThinSpace]", "+",
RowBox[{"0.018671689433634273`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.025734638867717777`"}], "+",
RowBox[{"0.007615486471300276`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.024184191539296875`"}], "+",
RowBox[{"0.0013567702427337192`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.003998607048463117`", "\[VeryThinSpace]", "-",
RowBox[{"0.010316181840707588`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{
RowBox[{"-", "0.01834571235414916`"}], "-",
RowBox[{"0.012021094305255359`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.18579393370513603`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.025245758382598567`", "\[VeryThinSpace]", "+",
RowBox[{"0.00846892790706261`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.015323441334415112`", "\[VeryThinSpace]", "-",
RowBox[{"0.044367735403007244`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.02484346352807356`"}], "-",
RowBox[{"0.02173856823817581`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.0015367953768008736`", "\[VeryThinSpace]", "+",
RowBox[{"0.0014066976933946214`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.020624403271417444`"}], "+",
RowBox[{"0.002672674078880644`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.001856947172997479`", "\[VeryThinSpace]", "-",
RowBox[{"0.021274433883242617`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{
RowBox[{"-", "0.011232926641687502`"}], "-",
RowBox[{"0.03384717769144092`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.025245758382598567`", "\[VeryThinSpace]", "-",
RowBox[{"0.00846892790706261`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.12838663077112986`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.02821408540100035`", "\[VeryThinSpace]", "+",
RowBox[{"0.0009737489642304472`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.00613611133164272`"}], "-",
RowBox[{"0.008585098601315039`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.015491809785782379`"}], "+",
RowBox[{"0.03056715501516006`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.001851147757740459`"}], "-",
RowBox[{"0.05277767499687224`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.005066161644445653`"}], "-",
RowBox[{"0.01160429318013774`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{"0.021269051235115473`", "\[VeryThinSpace]", "-",
RowBox[{"0.0017001838746707192`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.015323441334415112`", "\[VeryThinSpace]", "+",
RowBox[{"0.044367735403007244`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.02821408540100035`", "\[VeryThinSpace]", "-",
RowBox[{"0.0009737489642304472`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.13153389235577387`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.0265138775224821`", "\[VeryThinSpace]", "-",
RowBox[{"0.002397175701850003`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.007487122772526455`"}], "+",
RowBox[{"0.005538381281314238`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.03840181154681774`"}], "-",
RowBox[{"0.01801051129128832`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.019251776134117642`", "\[VeryThinSpace]", "+",
RowBox[{"0.0021370740073395475`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{"0.038764893989220506`", "\[VeryThinSpace]", "-",
RowBox[{"0.018671689433634273`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.02484346352807356`"}], "+",
RowBox[{"0.02173856823817581`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.00613611133164272`"}], "+",
RowBox[{"0.008585098601315039`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.0265138775224821`", "\[VeryThinSpace]", "+",
RowBox[{"0.002397175701850003`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.09091549599167995`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.00795306868880066`", "\[VeryThinSpace]", "-",
RowBox[{"0.0025189148154666947`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.004885787867829679`"}], "+",
RowBox[{"0.01372645174059724`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.019619546442867654`"}], "-",
RowBox[{"0.010143367555500021`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{
RowBox[{"-", "0.025734638867717777`"}], "-",
RowBox[{"0.007615486471300276`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.0015367953768008736`", "\[VeryThinSpace]", "-",
RowBox[{"0.0014066976933946214`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.015491809785782379`"}], "-",
RowBox[{"0.03056715501516006`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.007487122772526455`"}], "-",
RowBox[{"0.005538381281314238`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.00795306868880066`", "\[VeryThinSpace]", "+",
RowBox[{"0.0025189148154666947`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.07308667434105466`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.0036120826646832698`"}], "+",
RowBox[{"0.006548021077002173`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.014974456244112597`", "\[VeryThinSpace]", "+",
RowBox[{"0.009589666019330171`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{
RowBox[{"-", "0.024184191539296875`"}], "-",
RowBox[{"0.0013567702427337192`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.020624403271417444`"}], "-",
RowBox[{"0.002672674078880644`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.001851147757740459`"}], "+",
RowBox[{"0.05277767499687224`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.03840181154681774`"}], "+",
RowBox[{"0.01801051129128832`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.004885787867829679`"}], "-",
RowBox[{"0.01372645174059724`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.0036120826646832698`"}], "-",
RowBox[{"0.006548021077002173`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.1453667635456839`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.016317275233881046`"}], "-",
RowBox[{"0.0057564712717112325`", " ", "\[ImaginaryI]"}]}]},
{
RowBox[{"0.003998607048463117`", "\[VeryThinSpace]", "+",
RowBox[{"0.010316181840707588`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.001856947172997479`", "\[VeryThinSpace]", "+",
RowBox[{"0.021274433883242617`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.005066161644445653`"}], "+",
RowBox[{"0.01160429318013774`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.019251776134117642`", "\[VeryThinSpace]", "-",
RowBox[{"0.0021370740073395475`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.019619546442867654`"}], "+",
RowBox[{"0.010143367555500021`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.014974456244112597`", "\[VeryThinSpace]", "-",
RowBox[{"0.009589666019330171`", " ", "\[ImaginaryI]"}]}],
RowBox[{
RowBox[{"-", "0.016317275233881046`"}], "+",
RowBox[{"0.0057564712717112325`", " ", "\[ImaginaryI]"}]}],
RowBox[{"0.1349107492986701`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{
3.538748566655211*^9},ExpressionUUID->"09d15b70-f5dd-441d-be04-\
dc8d5cb73493"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"\[Rho]", "=",
RowBox[{"Proyector", "[",
RowBox[{"Bell", "[", "]"}], "]"}]}], ";"}]], "Input",
CellChangeTimes->{{3.540133177744213*^9, 3.540133187184167*^9},
3.540133406254364*^9},ExpressionUUID->"1d1fa9e3-6d4e-41f1-ab8b-\
157e59e39b50"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"Tr", "[",
RowBox[{"\[Rho]", ".",
RowBox[{"Pauli", "[",
RowBox[{"{",
RowBox[{"3", ",", "3"}], "}"}], "]"}]}], "]"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Tr", "[",
RowBox[{"\[Rho]", ".",
RowBox[{"Pauli", "[",
RowBox[{"{",
RowBox[{"3", ",", "0"}], "}"}], "]"}]}], "]"}],
RowBox[{"Tr", "[",
RowBox[{"\[Rho]", ".",
RowBox[{"Pauli", "[",
RowBox[{"{",
RowBox[{"0", ",", "3"}], "}"}], "]"}]}], "]"}]}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Tr", "[",
RowBox[{
RowBox[{"PartialTrace", "[",
RowBox[{"\[Rho]", ",", "1"}], "]"}], ".",
RowBox[{"Pauli", "[", "3", "]"}]}], "]"}],
RowBox[{"Tr", "[",
RowBox[{
RowBox[{"PartialTrace", "[",
RowBox[{"\[Rho]", ",", "2"}], "]"}], ".",
RowBox[{"Pauli", "[", "3", "]"}]}], "]"}]}]}], "}"}]], "Input",
CellChangeTimes->{{3.540133230821565*^9, 3.540133323893314*^9}, {
3.540133408181304*^9,
3.540133413397975*^9}},ExpressionUUID->"202866be-e6cc-4012-9579-\
18483046e2a9"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"1", ",", "0", ",", "0"}], "}"}]], "Output",
CellChangeTimes->{{3.540133236445473*^9, 3.540133258515633*^9},
3.54013328939081*^9, 3.540133324452503*^9,
3.5401334137158*^9},ExpressionUUID->"4eaf7bc0-b111-41d4-b8b4-8aa0c144c085"]
}, Open ]]
}, Closed]],
Cell[CellGroupData[{
Cell["Check Explicit form of control something", "Subsection",
CellChangeTimes->{{3.545497852142183*^9,
3.545497873688997*^9}},ExpressionUUID->"418ba52e-db6a-493d-867b-\
97a69dc38102"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"u", "=",
RowBox[{"Eigenvectors", "[",
RowBox[{"RandomHermitianMatrix", "[", "1", "]"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"Norm", "[",
RowBox[{
RowBox[{"u", ".",
RowBox[{"Dagger", "[", "u", "]"}]}], "-",
RowBox[{"IdentityMatrix", "[", "2", "]"}]}], "]"}]}], "Input",
CellChangeTimes->{{3.545497916595086*^9,
3.545497955918573*^9}},ExpressionUUID->"0edeaf2a-3076-4db2-b7f0-\
b74ae13e6ae8"],
Cell[BoxData["5.745107445142144`*^-17"], "Output",
CellChangeTimes->{{3.545497919809196*^9, 3.545497956202712*^9},
3.545498033012881*^9},ExpressionUUID->"027b5ad0-b31e-49ef-a129-\
d54d41a71ca6"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"Gate", "=",
RowBox[{
RowBox[{"ApplyGate", "[",
RowBox[{"u", ",", "#", ",", "0"}], "]"}], "&"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"Norm", "[",
RowBox[{
RowBox[{"GetMatrixForm", "[",
RowBox[{"Gate", ",", "1"}], "]"}], "-", "u"}], "]"}]}], "Input",
CellChangeTimes->{{3.545496979169893*^9, 3.545496989645781*^9}, {
3.545497896022177*^9, 3.545497902292827*^9}, {3.545497961653671*^9,
3.545497978494422*^9}, {3.545498035942087*^9,
3.545498042765626*^9}},ExpressionUUID->"14bbe3e5-f897-422d-bf35-\
f45127202754"],
Cell[BoxData["0.`"], "Output",
CellChangeTimes->{{3.545496986479849*^9, 3.545496990281323*^9},
3.545497890577238*^9, {3.54549796734464*^9, 3.545497978784978*^9}, {
3.545498034104744*^9,
3.545498043065291*^9}},ExpressionUUID->"0bd8604c-2966-4116-b327-\
a0fa9240a679"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"Gate", "=",
RowBox[{
RowBox[{"ApplyControlGate", "[",
RowBox[{"u", ",", "#", ",", "1", ",", "0"}], "]"}], "&"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"GetMatrixForm", "[",
RowBox[{"Gate", ",", "2"}], "]"}]}], "Input",
CellChangeTimes->{{3.545497087429511*^9, 3.545497088933531*^9},
3.545498049974932*^9},ExpressionUUID->"996fead1-fdde-4a8b-9982-\
31b26041d26f"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"0.`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",",
RowBox[{
RowBox[{"-", "0.24982067693830146`"}], "-",
RowBox[{"0.2294529227159971`", " ", "\[ImaginaryI]"}]}], ",",
RowBox[{"0.`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",",
RowBox[{"0.9407130198052834`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"0.`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",",
RowBox[{"0.6928276490566231`", "\[VeryThinSpace]", "+",
RowBox[{"0.636341759068072`", " ", "\[ImaginaryI]"}]}], ",",
RowBox[{"0.`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}], ",",
RowBox[{"0.3392034999359891`", "\[VeryThinSpace]", "+",
RowBox[{"0.`", " ", "\[ImaginaryI]"}]}]}], "}"}]}], "}"}]], "Output",
CellChangeTimes->{3.545497089249213*^9,
3.545498050593193*^9},ExpressionUUID->"b6174748-b011-4cd5-a159-\
f539145cad14"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Revisar si la eigenbase de un operador hermitico es completa", \
"Subsection",
CellChangeTimes->{{3.545497852142183*^9, 3.545497873688997*^9}, {
3.676728684676694*^9, 3.676728685052701*^9}, {3.676729038783243*^9,
3.676729050923374*^9}},ExpressionUUID->"f5092f14-2b2e-4a7d-bcea-\
f4fea86c8209"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"n", "=", "8"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"u", "=",
RowBox[{"Eigenvectors", "[",
RowBox[{"RandomHermitianMatrix", "[", "n", "]"}], "]"}]}], ";"}], "\n",
RowBox[{"Norm", "[",
RowBox[{
RowBox[{"Chop", "[",
RowBox[{"Total", "[",
RowBox[{"Proyector", "/@", "u"}], "]"}], "]"}], "-",
RowBox[{"IdentityMatrix", "[",
RowBox[{"Power", "[",
RowBox[{"2", ",", "n"}], "]"}], "]"}]}], "]"}]}], "Input",
CellChangeTimes->{{3.545497916595086*^9, 3.545497955918573*^9}, {
3.6767287165775423`*^9, 3.676728731298813*^9}, {3.6767287904104548`*^9,
3.676728798691527*^9}, {3.67672890102919*^9, 3.676728925983629*^9},
3.676729016111479*^9},ExpressionUUID->"d304b3b4-e992-4856-8650-\
f9acb5706702"],
Cell[BoxData["1.532107773982716`*^-14"], "Output",
CellChangeTimes->{{3.676728830701149*^9, 3.676728923142787*^9}, {
3.6767289921429663`*^9,
3.676729017959408*^9}},ExpressionUUID->"aa1f800b-327d-4528-9571-\
fec1404cddea"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Bloch", "Subsection",
CellChangeTimes->{{3.545497852142183*^9, 3.545497873688997*^9}, {
3.669057399160322*^9,
3.669057399752334*^9}},ExpressionUUID->"7d6faaf0-5eaa-4a8d-99ea-\
33f991aaa5da"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Pauli", "[", "1", "]"}]], "Input",
CellChangeTimes->{{3.6690574221551657`*^9,
3.6690574237955103`*^9}},ExpressionUUID->"2e532e2e-011b-48f9-b08e-\
dbfcdc3dbbee"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}]}], "}"}]], "Output",
CellChangeTimes->{
3.6690574240841427`*^9},ExpressionUUID->"3110c917-ec86-4572-8cb8-\
83795682b864"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"n", "=",
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Cos", "[", "\[Phi]", "]"}],
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Sin", "[", "\[Phi]", "]"}],
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", "\[IndentingNewLine]",
RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "}"}]}]], "Input",
CellChangeTimes->{{3.66905743242937*^9, 3.669057458144*^9}, {
3.669058540390566*^9,
3.669058565061545*^9}},ExpressionUUID->"fc9c57d5-e457-4e46-b026-\
35c142882f75"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Cos", "[", "\[Phi]", "]"}], " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",",
RowBox[{
RowBox[{"Sin", "[", "\[Theta]", "]"}], " ",
RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",",
RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "}"}]], "Output",
CellChangeTimes->{{3.6690585584957523`*^9,
3.669058566110401*^9}},ExpressionUUID->"0396f813-fe05-4ce4-92ca-\
69fe8b335317"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Simplify", "[",
RowBox[{"n", ".", "n"}], "]"}]], "Input",
CellChangeTimes->{{3.669058559460783*^9,
3.6690585711782913`*^9}},ExpressionUUID->"aeccbbcc-ff9a-4367-ad94-\
9c982566f970"],
Cell[BoxData["1"], "Output",
CellChangeTimes->{
3.669058571640833*^9},ExpressionUUID->"86fb1b53-f311-41dc-9279-\
1836a3465852"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"s", "=",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"Pauli", "[", "i", "]"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "3"}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.669058577452042*^9,
3.669058595969521*^9}},ExpressionUUID->"e47a3f20-d6ec-481a-b448-\
dab09afb4d43"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"-", "\[ImaginaryI]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[ImaginaryI]", ",", "0"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"-", "1"}]}], "}"}]}], "}"}]}], "}"}]], "Output",
CellChangeTimes->{{3.6690585824004393`*^9,
3.669058596329625*^9}},ExpressionUUID->"fe6afba1-2b0a-469a-8797-\
659f416fcbb8"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"n", ".", "s"}]], "Input",
CellChangeTimes->{{3.669058597055706*^9,
3.669058598065691*^9}},ExpressionUUID->"6f7400f3-835c-47e3-b7f4-\
7a288aa823c0"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Cos", "[", "\[Theta]", "]"}], ",",
RowBox[{
RowBox[{
RowBox[{"Cos", "[", "\[Phi]", "]"}], " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "-",
RowBox[{"\[ImaginaryI]", " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}], " ",
RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"Cos", "[", "\[Phi]", "]"}], " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "+",
RowBox[{"\[ImaginaryI]", " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}], " ",
RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}], ",",
RowBox[{"-",
RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], "}"}]}], "}"}]], "Output",
CellChangeTimes->{
3.669058598646183*^9},ExpressionUUID->"42277b59-e44f-46b8-8a60-\
76a21843a550"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{"(",
RowBox[{"n", ".", "s"}], ")"}], ".",
RowBox[{"{",
RowBox[{
RowBox[{"Cos", "[",
RowBox[{"\[Theta]", "/", "2"}], "]"}], ",",
RowBox[{
RowBox[{"Sin", "[",
RowBox[{"\[Theta]", "/", "2"}], "]"}],
RowBox[{"Exp", "[",
RowBox[{"\[ImaginaryI]", " ", "\[Phi]"}], "]"}]}]}], "}"}]}],
"]"}]], "Input",
CellChangeTimes->{{3.669058609399434*^9,
3.669058640375184*^9}},ExpressionUUID->"5fbde004-7bf2-4b47-8fbe-\
8eea8c71722d"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"Cos", "[",
FractionBox["\[Theta]", "2"], "]"}], ",",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{"\[ImaginaryI]", " ", "\[Phi]"}]], " ",
RowBox[{"Sin", "[",
FractionBox["\[Theta]", "2"], "]"}]}]}], "}"}]], "Output",
CellChangeTimes->{{3.6690586355323877`*^9,
3.669058640639069*^9}},ExpressionUUID->"20c69554-08c1-4374-a839-\
fac87ba5ed1a"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{
RowBox[{"Sin", "[",
RowBox[{"\[Theta]", "/", "2"}], "]"}],
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "+",
RowBox[{
RowBox[{"Cos", "[",
RowBox[{"\[Theta]", "/", "2"}], "]"}],
RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], "]"}]], "Input",
CellChangeTimes->{{3.6690588837464237`*^9,
3.669058902436757*^9}},ExpressionUUID->"0892cfbe-3c82-4091-aecb-\
acbf86f77edb"],
Cell[BoxData[
RowBox[{"Cos", "[",
FractionBox["\[Theta]", "2"], "]"}]], "Output",
CellChangeTimes->{
3.669058902610284*^9},ExpressionUUID->"a5140163-adaa-454d-904b-\
02240fcec692"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Bloch sphere transformation", "Section",
CellChangeTimes->{{3.822601493307344*^9,
3.8226015001177387`*^9}},ExpressionUUID->"a7c51199-c3ad-44bd-997b-\
814f4a670d1d"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"BlochSphTransformation", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "0.3"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",",
RowBox[{"1", "/", "2"}], ",",
RowBox[{"1", "/", "2"}]}], "}"}]}], "}"}], "]"}]], "Input",
CellChangeTimes->{{3.822601501369956*^9, 3.822601524750877*^9}},
CellLabel->"In[2]:=",ExpressionUUID->"067b73f7-1fc5-4b74-b162-14ae48ddf818"],
Cell[BoxData[
StyleBox[
Graphics3DBox[{{GraphicsComplex3DBox[CompressedData["
1:eJxlnHd0lFW3xgMJVbwEAUUTJGjo3I+OEbgMAkbhYghFQEFAih9NpINSJYBS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"], {
{RGBColor[1, 1, 0], Opacity[0.25], EdgeForm[None],
StyleBox[GraphicsGroup3DBox[
TagBox[{Polygon3DBox[CompressedData["
1:eJxN13V0FUcUx/H3Xh4uwQkSpIdSnEASIEiCuyY4hQIHCwTX0GLB3d0tuFOg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"]], Polygon3DBox[CompressedData["
1:eJxNmnn8j1UWx7/f5/nKklZkmSbZo0UoZItEUihZs/tZQ4jJmjVSmklUEs1U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