-
Notifications
You must be signed in to change notification settings - Fork 55
/
wildcardbudget.py
1180 lines (953 loc) · 50.3 KB
/
wildcardbudget.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
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
"""
Functions related to computation of the log-likelihood.
"""
#***************************************************************************************************
# Copyright 2015, 2019 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
# Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights
# in this software.
# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
# in compliance with the License. You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0 or in the LICENSE file in the root pyGSTi directory.
#***************************************************************************************************
import numpy as _np
from pygsti import tools as _tools
from pygsti.baseobjs import NicelySerializable as _NicelySerializable
#pos = lambda x: x**2
pos = abs
class WildcardBudget(_NicelySerializable):
"""
A fixed wildcard budget.
Encapsulates a fixed amount of "wildcard budget" that allows each circuit
an amount "slack" in its outcomes probabilities. The way in which this
slack is computed - or "distributed", though it need not necessarily sum to
a fixed total - per circuit depends on each derived class's implementation
of the :meth:`circuit_budget` method. Goodness-of-fit quantities such as
the log-likelihood or chi2 can utilize a `WildcardBudget` object to compute
a value that shifts the circuit outcome probabilities within their allowed
slack (so `|p_used - p_actual| <= slack`) to achieve the best goodness of
fit. For example, see the `wildcard` argument of :func:`two_delta_logl_terms`.
This is a base class, which must be inherited from in order to obtain a
full functional wildcard budge (the `circuit_budget` method must be
implemented and usually `__init__` should accept more customized args).
Parameters
----------
w_vec : numpy.array
vector of wildcard budget components.
"""
def __init__(self, w_vec):
"""
Create a new WildcardBudget.
Parameters
----------
w_vec : numpy array
The "wildcard vector" which stores the parameters of this budget
which can be varied when trying to find an optimal budget (similar
to the parameters of a :class:`Model`).
"""
super().__init__()
self.wildcard_vector = w_vec
def to_vector(self):
"""
Get the parameters of this wildcard budget.
Returns
-------
numpy array
"""
return self.wildcard_vector
def from_vector(self, w_vec):
"""
Set the parameters of this wildcard budget.
Parameters
----------
w_vec : numpy array
A vector of parameter values.
Returns
-------
None
"""
self.wildcard_vector = w_vec
@property
def num_params(self):
"""
The number of parameters of this wildcard budget.
Returns
-------
int
"""
return len(self.wildcard_vector)
def circuit_budget(self, circuit):
"""
Get the amount of wildcard budget, or "outcome-probability-slack" for `circuit`.
Parameters
----------
circuit : Circuit
the circuit to get the budget for.
Returns
-------
float
"""
raise NotImplementedError("Derived classes must implement `circuit_budget`")
def circuit_budgets(self, circuits, precomp=None):
"""
Get the wildcard budgets for a list of circuits.
Parameters
----------
circuits : list
The list of circuits to act on.
precomp : numpy.ndarray, optional
A precomputed quantity that speeds up the computation of circuit
budgets. Given by :meth:`precompute_for_same_circuits`.
Returns
-------
numpy.ndarray
"""
# XXX is this supposed to do something?
# circuit_budgets = [self.circuit_budget(circ) for circ in circuits]
pass
@property
def description(self):
"""
A dictionary of quantities describing this budget.
Return the contents of this budget in a dictionary containing
(description, value) pairs for each element name.
Returns
-------
dict
"""
raise NotImplementedError("Derived classes must implement `description`")
#def compute_circuit_wildcard_budget(c, w_vec):
# #raise NotImplementedError("TODO!!!")
# #for now, assume w_vec is a length-1 vector
# return abs(w_vec[0]) * len(c)
def precompute_for_same_circuits(self, circuits):
"""
Compute a pre-computed quantity for speeding up circuit calculations.
This value can be passed to `update_probs` or `circuit_budgets` whenever this
same `circuits` list is passed to `update_probs` to speed things up.
Parameters
----------
circuits : list
A list of :class:`Circuit` objects.
Returns
-------
object
"""
raise NotImplementedError("Derived classes must implement `precompute_for_same_circuits`")
def slow_update_probs(self, probs_in, probs_out, freqs, layout, precomp=None):
"""
Updates `probs_in` to `probs_out` by applying this wildcard budget.
Update a set of circuit outcome probabilities, `probs_in`, into a
corresponding set, `probs_out`, which uses the slack alloted to each
outcome probability to match (as best as possible) the data frequencies
in `freqs`. In particular, it computes this best-match in a way that
maximizes the likelihood between `probs_out` and `freqs`. This method is
the core function of a :class:`WildcardBudget`.
Parameters
----------
probs_in : numpy array
The input probabilities, usually computed by a :class:`Model`.
probs_out : numpy array
The output probabilities: `probs_in`, adjusted according to the
slack allowed by this wildcard budget, in order to maximize
`logl(probs_out, freqs)`. Note that `probs_out` may be the same
array as `probs_in` for in-place updating.
freqs : numpy array
An array of frequencies corresponding to each of the
outcome probabilites in `probs_in` or `probs_out`.
layout : CircuitOutcomeProbabilityArrayLayout
The layout for `probs_in`, `probs_out`, and `freqs`, specifying how array
indices correspond to circuit outcomes, as well as the list of circuits.
precomp : numpy.ndarray, optional
A precomputed quantity for speeding up this calculation.
Returns
-------
None
"""
#Special case where f_k=0, since ratio is ill-defined. One might think
# we shouldn't don't bother wasting any TVD on these since the corresponding
# p_k doesn't enter the likelihood. ( => treat these components as if f_k == q_k (ratio = 1))
# BUT they *do* enter in poisson-picture logl...
# so set freqs very small so ratio is large (and probably not chosen)
for i, circ in enumerate(layout.circuits):
elInds = layout.indices_for_index(i)
qvec = probs_in[elInds]
fvec = freqs[elInds]
W = self.circuit_budget(circ)
#print("Circuit %d: %s" % (i, circ))
#print(" inds = ", elInds, "q = ", qvec, " f = ", fvec)
updated_qvec = update_circuit_probs(qvec, fvec, W)
_tools.matrixtools._fas(probs_out, (elInds,), updated_qvec)
return
def precompute_for_same_probs_freqs(self, probs_in, freqs, layout):
tol = 1e-8 # for checking equality - same as in update_probs
tvd_precomp = 0.5 * _np.abs(probs_in - freqs)
A_precomp = _np.logical_and(probs_in > freqs + tol, freqs > 0)
B_precomp = _np.logical_and(probs_in < freqs - tol, freqs > 0)
C_precomp = _np.logical_and(freqs - tol <= probs_in, probs_in <= freqs + tol) # freqs == probs
D_precomp = _np.logical_and(~C_precomp, freqs == 0) # probs_in != freqs and freqs == 0
circuits = layout.circuits
precomp_info = []
for i, circ in enumerate(circuits):
elInds = layout.indices_for_index(i)
fvec = freqs[elInds]
qvec = probs_in[elInds]
initialTVD = sum(tvd_precomp[elInds]) # 0.5 * sum(_np.abs(qvec - fvec))
A = A_precomp[elInds]
B = B_precomp[elInds]
C = C_precomp[elInds]
D = D_precomp[elInds]
sum_fA = float(_np.sum(fvec[A]))
sum_fB = float(_np.sum(fvec[B]))
sum_qA = float(_np.sum(qvec[A]))
sum_qB = float(_np.sum(qvec[B]))
sum_qC = float(_np.sum(qvec[C]))
sum_qD = float(_np.sum(qvec[D]))
min_qvec = _np.min(qvec)
# sort(abs(qvec[A] / fvec[A] - 1.0)) but abs and 1.0 irrelevant since ratio is always > 1
iA = sorted(zip(_np.nonzero(A)[0], qvec[A] / fvec[A]), key=lambda x: x[1])
# sort(abs(1.0 - qvec[B] / fvec[B])) but abs and 1.0 irrelevant since ratio is always < 1
iB = sorted(zip(_np.nonzero(B)[0], qvec[B] / fvec[B]), key=lambda x: -x[1])
precomp_info.append((A, B, C, D, sum_fA, sum_fB, sum_qA, sum_qB, sum_qC, sum_qD,
initialTVD, fvec, qvec, min_qvec, iA, iB))
return precomp_info
def update_probs(self, probs_in, probs_out, freqs, layout, precomp=None, probs_freqs_precomp=None,
return_deriv=False):
"""
Updates `probs_in` to `probs_out` by applying this wildcard budget.
Update a set of circuit outcome probabilities, `probs_in`, into a
corresponding set, `probs_out`, which uses the slack alloted to each
outcome probability to match (as best as possible) the data frequencies
in `freqs`. In particular, it computes this best-match in a way that
maximizes the likelihood between `probs_out` and `freqs`. This method is
the core function of a :class:`WildcardBudget`.
Parameters
----------
probs_in : numpy array
The input probabilities, usually computed by a :class:`Model`.
probs_out : numpy array
The output probabilities: `probs_in`, adjusted according to the
slack allowed by this wildcard budget, in order to maximize
`logl(probs_out, freqs)`. Note that `probs_out` may be the same
array as `probs_in` for in-place updating.
freqs : numpy array
An array of frequencies corresponding to each of the
outcome probabilites in `probs_in` or `probs_out`.
layout : CircuitOutcomeProbabilityArrayLayout
The layout for `probs_in`, `probs_out`, and `freqs`, specifying how array
indices correspond to circuit outcomes, as well as the list of circuits.
precomp : numpy.ndarray, optional
A precomputed quantity for speeding up this calculation.
probs_freqs_precomp : list, optional
A precomputed list of quantities re-used when calling `update_probs`
using the same `probs_in`, `freqs`, and `layout`. Generate by calling
:meth:`precompute_for_same_probs_freqs`.
return_deriv : bool, optional
When True, returns the derivative of each updated probability with
respect to its circuit budget as a numpy array. Useful for internal
methods.
Returns
-------
None
"""
#Note: special case where f_k=0, since ratio is ill-defined. One might think
# we shouldn't don't bother wasting any TVD on these since the corresponding
# p_k doesn't enter the likelihood. ( => treat these components as if f_k == q_k (ratio = 1))
# BUT they *do* enter in poisson-picture logl...
# so set freqs very small so ratio is large (and probably not chosen)
tol = 1e-8 # for checking equality
circuits = layout.circuits
circuit_budgets = self.circuit_budgets(circuits, precomp)
p_deriv = _np.empty(layout.num_elements, 'd')
if probs_freqs_precomp is None:
probs_freqs_precomp = self.precompute_for_same_probs_freqs(probs_in, freqs, layout)
for i, (circ, W, info) in enumerate(zip(circuits, circuit_budgets, probs_freqs_precomp)):
A, B, C, D, sum_fA, sum_fB, sum_qA, sum_qB, sum_qC, sum_qD, initialTVD, fvec, qvec, min_qvec, iA, iB = info
elInds = layout.indices_for_index(i)
if initialTVD <= W + tol: # TVD is already "in-budget" for this circuit - can adjust to fvec exactly
probs_out[elInds] = fvec # _tools.matrixtools._fas(probs_out, (elInds,), fvec)
if return_deriv: p_deriv[elInds] = 0.0
continue
if min_qvec < 0 or abs(1.0 - sum(qvec)) > tol: # note: this need to be the same tol
qvec, W = _adjust_qvec_to_be_nonnegative_and_unit_sum(qvec, W, min_qvec, circ, tol)
initialTVD = 0.5 * sum(_np.abs(qvec - fvec)) # update current TVD
if initialTVD <= W + tol: # TVD is "in-budget" for this circuit due to adjustment; leave as is
probs_out[elInds] = qvec
if return_deriv: p_deriv[elInds] = 0.0
continue
#recompute A-D b/c we've updated qvec
A = _np.logical_and(qvec > fvec, fvec > 0); sum_fA = sum(fvec[A]); sum_qA = sum(qvec[A])
B = _np.logical_and(qvec < fvec, fvec > 0); sum_fB = sum(fvec[B]); sum_qB = sum(qvec[B])
C = (qvec == fvec); sum_qC = sum(qvec[C])
D = _np.logical_and(qvec != fvec, fvec == 0); sum_qD = sum(qvec[D])
#update other values tht depend on qvec (same as in precompute_for_same_probs_freqs)
sum_qA = float(_np.sum(qvec[A]))
sum_qB = float(_np.sum(qvec[B]))
sum_qC = float(_np.sum(qvec[C]))
sum_qD = float(_np.sum(qvec[D]))
iA = sorted(zip(_np.nonzero(A)[0], qvec[A] / fvec[A]), key=lambda x: x[1])
iB = sorted(zip(_np.nonzero(B)[0], qvec[B] / fvec[B]), key=lambda x: -x[1])
indices_moved_to_C = []; alist_ptr = blist_ptr = 0
while alist_ptr < len(iA): # and sum_fA > 0
# if alist_ptr < len(iA): # always true when sum_fA > 0
jA, alphaA = iA[alist_ptr]
betaA = (1.0 - alphaA * sum_fA - sum_qC) / sum_fB
testA = min(alphaA - 1.0, 1.0 - betaA)
#if blist_ptr < len(iB): # also always true
assert(sum_fB > 0), 'sum_fB = %g <= 0! %s qvec=%s fvec=%s' % (sum_fB, str(circ), str(qvec), str(fvec))
# sum_fB should always be > 0 - otherwise there's nowhere to take probability from
jB, betaB = iB[blist_ptr]
alphaB = (1.0 - betaB * sum_fB - sum_qC) / sum_fA
testB = min(alphaB - 1.0, 1.0 - betaB)
#Note: pushedSD = 0.0
if testA < testB:
j, alpha_break, beta_break = jA, alphaA, betaA
TVD_at_breakpt = 0.5 * (sum_qA - alpha_break * sum_fA
+ beta_break * sum_fB - sum_qB
+ sum_qD) # - pushedSD) # compute_tvd
if TVD_at_breakpt <= W + tol: break # exit loop
# move j from A -> C
sum_qA -= qvec[j]; sum_qC += qvec[j]; sum_fA -= fvec[j]
alist_ptr += 1
else:
j, alpha_break, beta_break = jB, alphaB, betaB
TVD_at_breakpt = 0.5 * (sum_qA - alpha_break * sum_fA
+ beta_break * sum_fB - sum_qB
+ sum_qD) # - pushedSD) # compute_tvd
if TVD_at_breakpt <= W + tol: break # exit loop
# move j from B -> C
sum_qB -= qvec[j]; sum_qC += qvec[j]; sum_fB -= fvec[j]
blist_ptr += 1
indices_moved_to_C.append(j)
else: # if we didn't break due to TVD being small enough, continue to process with empty A-list:
while blist_ptr < len(iB): # now sum_fA == 0 => alist_ptr is maxed out
assert(sum_fB > 0) # otherwise there's nowhere to take probability from
j, beta_break = iB[blist_ptr]
pushedSD = 1.0 - beta_break * sum_fB - sum_qC # just used for TVD calc below
TVD_at_breakpt = 0.5 * (sum_qA + beta_break * sum_fB - sum_qB
+ sum_qD - pushedSD) # compute_tvd
if TVD_at_breakpt <= W + tol: break # exit loop
# move j from B -> C
sum_qB -= qvec[j]; sum_qC += qvec[j]; sum_fB -= fvec[j]
blist_ptr += 1
indices_moved_to_C.append(j)
else:
assert(False), "TVD should reach zero: qvec=%s, fvec=%s, W=%g" % (str(qvec), str(fvec), W)
#Now A,B,C are fixed to what they need to be for our given W
# test if len(A) > 0, make tol here *smaller* than that assigned to zero freqs above
if sum_fA > tol:
alpha = (sum_qA - sum_qB + sum_qD - 2 * W) / sum_fA if sum_fB == 0 else \
(sum_qA - sum_qB + sum_qD + 1.0 - sum_qC - 2 * W) / (2 * sum_fA) # compute_alpha
beta = _np.nan if sum_fB == 0 else (1.0 - alpha * sum_fA - sum_qC) / sum_fB # beta_fn
pushedSD = 0.0 # assume initially that we don't need to push any TVD into the "D" set
dalpha_dW = -2 / sum_fA if sum_fB == 0 else -1 / sum_fA
dbeta_dW = 0.0 if sum_fB == 0 else (- dalpha_dW * sum_fA) / sum_fB
dpushedSD_dW = 0.0
else: # fall back to this when len(A) == 0
beta = -(sum_qA - sum_qB + sum_qD + sum_qC - 1 - 2 * W) / (2 * sum_fB) if sum_fA == 0 else \
-(sum_qA - sum_qB + sum_qD - 1.0 + sum_qC - 2 * W) / (2 * sum_fB)
# compute_beta (assumes pushedSD can be >0)
#beta = -(sum_qA - sum_qB + sum_qD - 2 * W) / sum_fB # assumes pushedSD == 0
alpha = 0.0 # doesn't matter OLD: _alpha_fn(beta, A, B, C, qvec, fvec)
pushedSD = 1 - beta * sum_fB - sum_qC
dalpha_dW = 0.0
dbeta_dW = 2 / sum_fB if sum_fA == 0 else 1 / sum_fB
dpushedSD_dW = -dbeta_dW * sum_fB
#compute_pvec
pvec = fvec.copy()
pvec[A] = alpha * fvec[A]
pvec[B] = beta * fvec[B]
pvec[C] = qvec[C]
#indices_moved_to_C = [x[0] for x in sorted_indices_and_ratios[0:nMovedToC]]
pvec[indices_moved_to_C] = qvec[indices_moved_to_C]
pvec[D] = pushedSD * qvec[D] / sum_qD
probs_out[elInds] = pvec # _tools.matrixtools._fas(probs_out, (elInds,), pvec)
assert(W > 0 or min_qvec < 0 or _np.linalg.norm(qvec - pvec) < 1e-6), \
"Probability shouldn't be updated when W=0!" # don't check this when there are negative probs
#Check with other version (for debugging)
#check_pvec = update_circuit_probs(qvec.copy(), fvec.copy(), W)
#assert(_np.linalg.norm(check_pvec - pvec) < 1e-6)
if return_deriv:
p_deriv_wrt_W = _np.zeros(len(pvec), 'd')
p_deriv_wrt_W[A] = dalpha_dW * fvec[A]
p_deriv_wrt_W[B] = dbeta_dW * fvec[B]
p_deriv_wrt_W[indices_moved_to_C] = 0.0
p_deriv_wrt_W[D] = dpushedSD_dW * qvec[D] / sum_qD
p_deriv[elInds] = p_deriv_wrt_W
return p_deriv if return_deriv else None
def _to_nice_serialization(self):
state = super()._to_nice_serialization()
state.update({'wildcard_vector': list(self.wildcard_vector)})
return state
@classmethod
def _from_nice_serialization(cls, state): # memo holds already de-serialized objects
return cls(_np.array(state['wildcard_vector'], 'd'))
class PrimitiveOpsWildcardBudgetBase(WildcardBudget):
"""
A base class for wildcard budget objects that allocate wildcard error per "primitive operation".
The amount of wildcard error for a primitive operation gives the amount of "slack"
that is allocated per that particular operation.
Primitive operations are the components of circuit layers, and so
the wilcard budget for a circuit is just the sum of the wildcard errors
corresponding to each primitive operation in the circuit.
Parameters
----------
primitive_op_labels : iterable
A list of primitive-operation labels, e.g. `Label('Gx',(0,))`,
which give all the possible primitive ops (components of circuit
layers) that will appear in circuits.
wildcard_vector : numpy.ndarray
An initial wildcard vector of the parameter values of this budget.
idle_name : str, optional
The gate name to be used for the 1-qubit idle gate. If not `None`, then
circuit budgets are computed by considering layers of the circuit as being
"padded" with `1-qubit` idles gates on any empty lines.
"""
def __init__(self, primitive_op_labels, wildcard_vector, idle_name=None):
#if isinstance(primitive_op_labels, dict):
# assert(set(primitive_op_labels.values()) == set(range(len(set(primitive_op_labels.values())))))
# self.primOpLookup = primitive_op_labels
#else:
self.primitive_op_labels = primitive_op_labels
self.primitive_op_index = {lbl: i for i, lbl in enumerate(primitive_op_labels)}
self._idlename = idle_name
self.per_op_wildcard_vector = self._per_op_wildcard_error_from_vector(wildcard_vector)
super(PrimitiveOpsWildcardBudgetBase, self).__init__(wildcard_vector)
def _per_op_wildcard_error_from_vector(self, wildcard_vector):
"""
Returns an array of per-operation wildcard errors based on `wildcard_vector`,
with ordering corresponding to `self.primitive_op_labels`.
"""
raise NotImplementedError("Sub-classes need to implement this!")
def _per_op_wildcard_error_deriv_from_vector(self, wildcard_vector):
"""
Returns a MxN matrix, where M=(# of primitive ops) and N=(# of parameters),
such that its (i,j)-th element is the derivative of the wildcard error
for the i-th primitive op with respect to the j-th budget parameter.
"""
raise NotImplementedError("Sub-classes need to implement this!")
def from_vector(self, w_vec):
"""
Set the parameters of this wildcard budget.
Parameters
----------
w_vec : numpy array
A vector of parameter values.
Returns
-------
None
"""
super().from_vector(w_vec)
self.per_op_wildcard_vector = self._per_op_wildcard_error_from_vector(w_vec)
@property
def num_primitive_ops(self):
return len(self.primitive_op_labels)
@property
def wildcard_error_per_op(self):
return {lbl: val for lbl, val in zip(self.primitive_op_labels, self.per_op_wildcard_vector)}
def _to_nice_serialization(self):
state = super()._to_nice_serialization()
state.update({'primitive_op_labels': [str(lbl) for lbl in self.primitive_op_labels],
'idle_name': self._idlename,
})
return state
@classmethod
def _from_nice_serialization(cls, state): # memo holds already de-serialized objects
primitive_op_labels = cls._parse_primitive_op_labels(state['primitive_op_labels'])
return cls(primitive_op_labels, _np.array(state['wildcard_vector'], 'd'), state['idle_name'])
@classmethod
def _parse_primitive_op_labels(cls, label_strs):
from pygsti.circuits.circuitparser import parse_label as _parse_label
return [(_parse_label(lbl_str) if (lbl_str != 'SPAM') else 'SPAM')
for lbl_str in label_strs]
def circuit_budget(self, circuit):
"""
Get the amount of wildcard budget, or "outcome-probability-slack" for `circuit`.
Parameters
----------
circuit : Circuit
the circuit to get the budget for.
Returns
-------
float
"""
error_per_op = self.wildcard_error_per_op
def budget_for_label(lbl):
if lbl in error_per_op: # Note: includes len(lbl.components) == 0 case of (global) idle
return pos(error_per_op[lbl])
elif lbl.name in error_per_op:
return pos(error_per_op[lbl.name])
else:
assert(not lbl.is_simple()), "Simple label %s must be a primitive op of this WEB!" % str(lbl)
return sum([budget_for_label(component) for component in lbl.components])
budget = error_per_op.get('SPAM', 0)
layers = [circuit.layer_label(i) for i in range(circuit.depth)] if (self._idlename is None) \
else [circuit.layer_label_with_idles(i, idle_gate_name=self._idlename) for i in range(circuit.depth)]
for layer in layers:
budget += budget_for_label(layer)
return budget
def circuit_budgets(self, circuits, precomp=None):
"""
Get the wildcard budgets for a list of circuits.
Parameters
----------
circuits : list
The list of circuits to act on.
precomp : numpy.ndarray, optional
A precomputed quantity that speeds up the computation of circuit
budgets. Given by :meth:`precompute_for_same_circuits`.
Returns
-------
numpy.ndarray
"""
if precomp is None:
circuit_budgets = _np.array([self.circuit_budget(circ) for circ in circuits])
else:
Wvec = _np.abs(self.wildcard_vector)
circuit_budgets = _np.dot(precomp, Wvec)
return circuit_budgets
def precompute_for_same_circuits(self, circuits):
"""
Compute a pre-computed quantity for speeding up circuit calculations.
This value can be passed to `update_probs` or `circuit_budgets` whenever this
same `circuits` list is passed to `update_probs` to speed things up.
Parameters
----------
circuits : list
A list of :class:`Circuit` objects.
Returns
-------
object
"""
def budget_deriv_for_label(lbl):
if lbl in self.primitive_op_index: # Note: includes len(lbl.components) == 0 case of (global) idle
deriv = _np.zeros(self.num_primitive_ops, 'd')
deriv[self.primitive_op_index[lbl]] = 1.0
return deriv
elif lbl.name in self.primitive_op_index:
deriv = _np.zeros(self.num_primitive_ops, 'd')
deriv[self.primitive_op_index[lbl.name]] = 1.0
return deriv
else:
assert(not lbl.is_simple()), "Simple label %s must be a primitive op of this WEB!" % str(lbl)
return sum([budget_deriv_for_label(component) for component in lbl.components])
circuit_budget_matrix = _np.zeros((len(circuits), self.num_primitive_ops), 'd')
for i, circuit in enumerate(circuits):
layers = [circuit.layer_label(i) for i in range(circuit.depth)] if (self._idlename is None) \
else [circuit.layer_label_with_idles(i, idle_gate_name=self._idlename) for i in range(circuit.depth)]
for layer in layers:
circuit_budget_matrix[i, :] += budget_deriv_for_label(layer)
if 'SPAM' in self.primitive_op_index:
circuit_budget_matrix[:, self.primitive_op_index['SPAM']] = 1.0
dprimop_dwvec = self._per_op_wildcard_error_deriv_from_vector(self.wildcard_vector)
return _np.dot(circuit_budget_matrix, dprimop_dwvec)
@property
def description(self):
"""
A dictionary of quantities describing this budget.
Return the contents of this budget in a dictionary containing
(description, value) pairs for each element name.
Returns
-------
dict
Keys are primitive op labels and values are (description_string, value) tuples.
"""
wildcardDict = {}
error_per_op = self.wildcard_error_per_op
for lbl, val in error_per_op.items():
if lbl == "SPAM": continue # treated separately below
wildcardDict[lbl] = ('budget per each instance %s' % str(lbl), pos(val))
if 'SPAM' in error_per_op:
wildcardDict['SPAM'] = ('uniform per-circuit SPAM budget', pos(error_per_op['SPAM']))
return wildcardDict
def budget_for(self, op_label):
"""
Retrieve the budget amount correponding to primitive op `op_label`.
This is just the absolute value of this wildcard budget's parameter
that corresponds to `op_label`.
Parameters
----------
op_label : Label
The operation label to extract a budget for.
Returns
-------
float
"""
return pos(self.per_op_wildcard_vector[self.primitive_op_index[op_label]])
def __str__(self):
return "Wildcard budget: " + str(self.wildcard_error_per_op)
#For these helper functions, see Robin's notes
def _compute_tvd(a, b, d, alpha, beta, pushedD, q, f):
# TVD = 0.5 * (qA - alpha*SA + beta*SB - qB + qD - pushed_pd) = difference between p=[alpha|beta]*f and q
# (no contrib from set C)
pushed_pd = pushedD * q[d] / sum(q[d]) # vector that sums to pushedD and aligns with q[d]
ret = 0.5 * (sum(q[a] - alpha * f[a]) + sum(beta * f[b] - q[b]) + sum(q[d] - pushed_pd))
return ret
def _compute_alpha(a, b, c, d, tvd, q, f):
# beta = (1-alpha*SA - qC)/SB
# 2*tvd = qA - alpha*SA + [(1-alpha*SA - qC)/SB]*SB - qB + qD (pushedSD == 0 b/c A is nonempty if we call this fn)
# 2*tvd = qA - alpha(SA + SA) + (1-qC) - qB + qD
# alpha = [ qA-qB+qD + (1-qC) - 2*tvd ] / 2*SA
# But if SB == 0 then 2*tvd = qA - alpha*SA - qB + qD => alpha = (qA-qB+qD-2*tvd)/SA
# Note: no need to deal with pushedSD > 0 since this only occurs when alpha is irrelevant.
if sum(f[b]) == 0:
return (sum(q[a]) - sum(q[b]) + sum(q[d]) - 2 * tvd) / sum(f[a])
return (sum(q[a]) - sum(q[b]) + sum(q[d]) + 1.0 - sum(q[c]) - 2 * tvd) / (2 * sum(f[a]))
def _compute_beta(a, b, c, d, tvd, q, f):
# alpha = (1-beta*SB - qC)/SA
# 2*tvd = qA - [(1-beta*SB - qC)/SA]*SA + beta*SB - qB + qD (assume pushedD == 0)
# 2*tvd = qA - (1-qC) + beta(SB + SB) - qB + qD
# beta = -[ qA-qB+qD - (1-qC) - 2*tvd ] / 2*SB
# But if SA == 0 then some probability may be "pushed" into set D:
# 2*tvd = qA + (beta*SB - qB) + (qD - pushed_pD) and pushed_pD = 1 - beta * SB - qC, so
# 2*tvd = qA + (beta*SB - qB) + (qD - 1 + beta*SB + qC) = qA - qB + qD +qC -1 + 2*beta*SB
# => beta = -(qA-qB+qD+qC-1-2*tvd)/(2*SB)
if sum(f[a]) == 0:
return -(sum(q[a]) - sum(q[b]) + sum(q[d]) + sum(q[c]) - 1 - 2 * tvd) / (2 * sum(f[b]))
return -(sum(q[a]) - sum(q[b]) + sum(q[d]) - 1.0 + sum(q[c]) - 2 * tvd) / (2 * sum(f[b]))
def _compute_pvec(alpha, beta, pushedD, a, b, c, d, q, f):
p = f.copy()
#print("Fill pvec alpha=%g, beta=%g" % (alpha,beta))
#print("f = ",f, " a = ",a, "b=",b," c=",c)
p[a] = alpha * f[a]
p[b] = beta * f[b]
p[c] = q[c]
p[d] = pushedD * q[d] / sum(q[d])
return p
def _alpha_fn(beta, a, b, c, q, f, empty_val=1.0):
# Note: this function is for use before we shift "D" set of f == 0 probs, and assumes all probs in set D are 0
if len(a) == 0: return empty_val
return (1.0 - beta * sum(f[b]) - sum(q[c])) / sum(f[a])
def _beta_fn(alpha, a, b, c, q, f, empty_val=1.0):
# Note: this function is for use before we shift "D" set of f == 0 probs, and assumes all probs in set D are 0
# beta * SB = 1 - alpha * SA - qC => 1 = alpha*SA + beta*SB + qC (probs sum to 1)
# also though, beta must be > 0 so (alpha*SA + qC) < 1.0
if len(b) == 0: return empty_val
return (1.0 - alpha * sum(f[a]) - sum(q[c])) / sum(f[b])
def _pushedD_fn(beta, b, c, q, f): # The sum of additional TVD that gets "pushed" into set D
# 1 = alpha*SA + beta*SB + qC + pushedSD => 1 = beta*SB + qC + pushedSD (probs sum to 1)
return 1 - beta * sum(f[b]) - sum(q[c])
def _get_nextalpha_breakpoint(remaining_ratios):
j = None; best_test = 1e10 # sentinel
for jj, dct in remaining_ratios.items():
test = min(dct['alpha'] - 1.0 if (dct['alpha'] is not None) else 1e10,
1.0 - dct['beta'] if (dct['beta'] is not None) else 1e10)
if test < best_test:
best_test, j = test, jj
best_dct = remaining_ratios[j]
alpha = best_dct['alpha'] if (best_dct['alpha'] is not None) else 1.0
beta = best_dct['beta'] if (best_dct['beta'] is not None) else 1.0
return j, alpha, beta, best_dct['typ']
def _chk_sum(alpha, beta, fvec, A, B, C):
return alpha * sum(fvec[A]) + beta * sum(fvec[B]) + sum(fvec[C])
def _adjust_qvec_to_be_nonnegative_and_unit_sum(qvec, W, min_qvec, circ=None, tol=1e-6):
if min_qvec >= 0 and abs(1.0 - sum(qvec)) < tol:
return qvec, W # no change needed
if min_qvec < 0:
#Stopgap solution when a probability is negative: use wcbudget to move as
# much negative prob to zero as possible, while reducing all the positive
# probs. This seems reasonable but isn't provably the right thing to do!
qvec = qvec.copy() # make sure we don't mess with memory we shouldn't
neg_inds = _np.where(qvec < 0)[0]; neg_sum = sum(qvec[neg_inds])
pos_inds = _np.where(qvec > 0)[0]; pos_sum = sum(qvec[pos_inds]) # note: NOT >= (leave zeros alone)
if -neg_sum > pos_sum:
circ_str = circ.str if (circ is not None) else "circuit"
raise NotImplementedError(("Wildcard budget cannot be applied when the model predicts more "
"*negative* then positive probability! (%s predicts neg_sum=%.3g, "
"pos_sum=%.3g)") % (circ_str, neg_sum, pos_sum))
while _np.min(qvec) < 0 and not _np.isclose(W, 0):
add_to = _np.argmin(qvec)
subtract_from = _np.argmax(qvec)
amount = _np.min([qvec[subtract_from], -qvec[add_to], W])
qvec[add_to] += amount
qvec[subtract_from] -= amount
W -= amount
if abs(1.0 - sum(qvec)) > tol:
qvec = qvec.copy() # make sure we don't mess with memory we shouldn't
qvec /= sum(qvec)
return qvec, W
def update_circuit_probs(probs, freqs, circuit_budget, circuit=None):
qvec = probs
fvec = freqs
W = circuit_budget
debug = False
base_tol = 1e-8 # for checking for equality of qvec and fvec
tol = len(qvec) * base_tol # for checking if TVD is zero (e.g. when W==0 and TVD_at_breakpt is 1e-17)
initialTVD = 0.5 * sum(_np.abs(qvec - fvec))
if initialTVD <= W + tol: # TVD is already "in-budget" for this circuit - can adjust to fvec exactly
return fvec
qvec, W = _adjust_qvec_to_be_nonnegative_and_unit_sum(qvec, W, min(qvec), circuit, base_tol)
initialTVD = 0.5 * sum(_np.abs(qvec - fvec)) # update current TVD
if initialTVD <= W + tol: # TVD is "in-budget" for this circuit due to adjustment; leave as is
return qvec
#Note: must ensure that A,B,C,D are *disjoint*
fvec_equals_qvec = _np.logical_and(fvec - base_tol <= qvec, qvec <= fvec + base_tol) # fvec == qvec
A = _np.where(_np.logical_and(qvec > fvec + base_tol, fvec > 0))[0]
B = _np.where(_np.logical_and(qvec < fvec - base_tol, fvec > 0))[0]
C = _np.where(fvec_equals_qvec)[0]
D = _np.where(_np.logical_and(~fvec_equals_qvec, fvec == 0))[0]
if debug:
print(" budget = ", W, " A=", A, " B=", B, " C=", C, " D=", D)
ratio_vec = qvec / _np.where(fvec > 0, fvec, 1.0) # avoid divide-by-zero warning (on sets C & D)
ratio_vec[C] = _np.inf # below we work in order of ratios distance
ratio_vec[D] = _np.inf # from 1.0 - and we don't want exactly-1.0 ratios.
if debug: print(" Ratio vec = ", ratio_vec)
#OLD: remaining_indices = list(range(len(ratio_vec)))
# Set A: q > f != 0 alpha > 1.0 => p = alpha*f gets closer to q and p increases => logl increases
# Set B: q < f beta < 1.0 => p = beta*f gets closer to q and p decreases => logl decreases
# Set C: q = f requires no change (ever!)
# Set D: q > f = 0 p=0 initially can be added to (to reduce TVD) but other p's must
# decrease then: adding moves p closer to q and p increases => logl stays same
# See that working on Set A is preferable to Set D since logl increases in the former but
# stays the same in the latter. Once set A is exhausted, however, we should increase set D
# proportionally balance out movements from set B
ratios = {}
for j in A:
ratios[j] = {'alpha': ratio_vec[j],
'beta': _beta_fn(ratio_vec[j], A, B, C, qvec, fvec, None),
'typ': 'A'}
for j in B:
ratios[j] = {'beta': ratio_vec[j],
'alpha': _alpha_fn(ratio_vec[j], A, B, C, qvec, fvec, None),
'typ': 'B'}
while len(ratios) > 0:
# find best next element
j, alpha0, beta0, typ = _get_nextalpha_breakpoint(ratios)
if len(A) == 0: # no frequencies left to increase => qvec via alpha, so dump into pushedSD0
pushedSD0 = 1.0 - beta0 * sum(fvec[B]) - sum(qvec[C])
else:
pushedSD0 = 0.0
# will keep getting smaller with each iteration
TVD_at_breakpt = _compute_tvd(A, B, D, alpha0, beta0, pushedSD0, qvec, fvec)
#Note: does't matter if we move j from A or B -> C before calling this, as alpha0 is set so results is
#the same
if debug: print("break: j=", j, " alpha=", alpha0, " beta=",
beta0, " typ=", typ, " TVD = ", TVD_at_breakpt)
if TVD_at_breakpt <= W + tol:
break # exit loop
# move j from A/B -> C
if typ == 'A':
Alst = list(A); del Alst[Alst.index(j)]; A = _np.array(Alst, _np.int64)
Clst = list(C); Clst.append(j); C = _np.array(Clst, _np.int64) # move A -> C
else: # typ == 'B'
Blst = list(B); del Blst[Blst.index(j)]; B = _np.array(Blst, _np.int64)
Clst = list(C); Clst.append(j); C = _np.array(Clst, _np.int64) # move B -> C
#update ratios
del ratios[j]
for dct in ratios.values():
if dct['typ'] == 'A':
dct['beta'] = _beta_fn(dct['alpha'], A, B, C, qvec, fvec, None)
else: # dct['typ'] == 'B':
dct['alpha'] = _alpha_fn(dct['beta'], A, B, C, qvec, fvec, None)
else:
assert(False), "TVD should eventually reach zero: qvec=%s, fvec=%s, W=%g" % (str(qvec), str(fvec), W)
#Now A,B,C are fixed to what they need to be for our given W
if debug: print("Final A=", A, "B=", B, "C=", C, "W=", W, "qvec=", qvec, 'fvec=', fvec)
if len(A) > 0:
alpha = _compute_alpha(A, B, C, D, W, qvec, fvec)
beta = _beta_fn(alpha, A, B, C, qvec, fvec, _np.nan)
pushedSD = 0.0
else: # fall back to this when len(A) == 0
beta = _compute_beta(A, B, C, D, W, qvec, fvec)
alpha = 0.0 # doesn't matter OLD: _alpha_fn(beta, A, B, C, qvec, fvec)
pushedSD = _pushedD_fn(beta, B, C, qvec, fvec)
if debug:
print("Computed final alpha,beta = ", alpha, beta)
print("CHECK SUM = ", _chk_sum(alpha, beta, fvec, A, B, C))
print("DB: probs_in = ", qvec)
updated_qvec = _compute_pvec(alpha, beta, pushedSD, A, B, C, D, qvec, fvec)
if debug:
print("DB: probs_out = ", updated_qvec)
#print("TVD = ",compute_tvd(A,B,alpha,beta_fn(alpha,A,B,C,fvec),qvec,fvec))
compTVD = _compute_tvd(A, B, D, alpha, beta, pushedSD, qvec, fvec)
#print("compare: ",W,compTVD)
assert(abs(W - compTVD) < 1e-3), "TVD mismatch!"
#assert(_np.isclose(W, compTVD)), "TVD mismatch!"
return updated_qvec
class PrimitiveOpsWildcardBudget(PrimitiveOpsWildcardBudgetBase):
"""
A wildcard budget containing one parameter per "primitive operation".
A parameter's absolute value gives the amount of "slack", or
"wildcard budget" that is allocated per that particular primitive
operation.
Primitive operations are the components of circuit layers, and so
the wilcard budget for a circuit is just the sum of the (abs vals of)
the parameters corresponding to each primitive operation in the circuit.
Parameters
----------
primitive_op_labels : iterable or dict
A list of primitive-operation labels, e.g. `Label('Gx',(0,))`,
which give all the possible primitive ops (components of circuit
layers) that will appear in circuits. Each one of these operations
will be assigned it's own independent element in the wilcard-vector.
A dictionary can be given whose keys are Labels and whose values are
0-based parameter indices. In the non-dictionary case, each label gets
it's own parameter. Dictionaries allow multiple labels to be associated
with the *same* wildcard budget parameter,
e.g. `{Label('Gx',(0,)): 0, Label('Gy',(0,)): 0}`.
If `'SPAM'` is included as a primitive op, this value correspond to a
uniform "SPAM budget" added to each circuit.
start_budget : float or dict, optional
An initial value to set all the parameters to (if a float), or a
dictionary mapping primitive operation labels to initial values.
"""
def __init__(self, primitive_op_labels, start_budget=0.0, idle_name=None):
"""
Create a new PrimitiveOpsWildcardBudget.
Parameters
----------
primitive_op_labels : iterable or dict
A list of primitive-operation labels, e.g. `Label('Gx',(0,))`,
which give all the possible primitive ops (components of circuit
layers) that will appear in circuits. Each one of these operations
will be assigned it's own independent element in the wilcard-vector.
A dictionary can be given whose keys are Labels and whose values are
0-based parameter indices. In the non-dictionary case, each label gets
it's own parameter. Dictionaries allow multiple labels to be associated