qecp 0.2.7

Quantum Error Correction Playground for Surface Code Research
Documentation
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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
//! build customized noise model by giving a name
//!

use super::clap::ValueEnum;
use super::code_builder::*;
use super::noise_model::*;
use super::simulator::*;
use super::types::*;
use super::util_macros::*;
use crate::serde::{Deserialize, Serialize};
#[cfg(feature = "python_binding")]
use pyo3::prelude::*;
use std::collections::BTreeSet;
use std::sync::Arc;

/// commonly used noise models
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, ValueEnum, Serialize, Deserialize, Debug)]
#[cfg_attr(feature = "python_binding", pyclass)]
pub enum NoiseModelBuilder {
    /// add data qubit errors and measurement errors individually
    Phenomenological,
    /// same as phenomenological, but with half unfixed stabilizers
    PhenomenologicalInit,
    /// tailored surface code with Bell state initialization (logical |+> state) to fix 3/4 of all stabilizers
    TailoredScBellInitPhenomenological,
    TailoredScBellInitCircuit,
    /// arXiv:2104.09539v1 Sec.IV.A
    GenericBiasedWithBiasedCX,
    /// arXiv:2104.09539v1 Sec.IV.A
    GenericBiasedWithStandardCX,
    /// 100% erasure errors only on the data qubits before the gates happen and on the ancilla qubits before the measurement
    ErasureOnlyPhenomenological,
    /// errors happen at 4 stages in each measurement round (although removed errors happening at initialization and measurement stage, measurement errors can still occur when curtain error applies on the ancilla after the last gate)
    OnlyGateErrorCircuitLevel,
    /// mixed erasure error and Pauli errors only on the data qubits before the gates happen and on the ancilla qubits before the measurement
    MixedPhenomenological,
    /// Fault-tolerant weighted union-find decoding on the toric code
    DepolarizingNoise,
    /// the noise model in stim: after_clifford_depolarization, before_round_data_depolarization, before_measure_flip_probability, after_reset_flip_probability;
    /// see https://github.com/quantumlib/Stim/blob/main/doc/python_api_reference_vDev.md#stim.Circuit.generated
    StimNoiseModel,
}

#[cfg(feature = "python_binding")]
#[pymethods]
impl NoiseModelBuilder {
    #[pyo3(name = "apply", signature = (simulator, noise_model, p, noise_model_configuration=None, bias_eta=0.5, pe=0.))]
    fn trait_apply(
        &self,
        simulator: &mut Simulator,
        noise_model: &mut NoiseModel,
        p: f64,
        noise_model_configuration: Option<PyObject>,
        bias_eta: f64,
        pe: f64,
    ) {
        let noise_model_configuration = noise_model_configuration
            .map(|v| crate::util::pyobject_to_json(v))
            .unwrap_or(json!({}));
        self.apply(simulator, noise_model, &noise_model_configuration, p, bias_eta, pe)
    }
}

impl NoiseModelBuilder {
    /// apply noise model
    pub fn apply(
        &self,
        simulator: &mut Simulator,
        noise_model: &mut NoiseModel,
        noise_model_configuration: &serde_json::Value,
        p: f64,
        bias_eta: f64,
        pe: f64,
    ) {
        // commonly used biased qubit error node
        let px = p / (1. + bias_eta) / 2.;
        let py = px;
        let pz = p - 2. * px;
        let mut biased_node = NoiseModelNode::new();
        biased_node.pauli_error_rates.error_rate_X = px;
        biased_node.pauli_error_rates.error_rate_Y = py;
        biased_node.pauli_error_rates.error_rate_Z = pz;
        biased_node.erasure_error_rate = pe;
        let biased_node = Arc::new(biased_node);
        // commonly used pure measurement error node
        let mut pm = p;
        if let Some(value) = noise_model_configuration.get("measurement_error_rate") {
            pm = value.as_f64().expect("measurement_error_rate must be `f64`");
        }
        let mut pure_measurement_node = NoiseModelNode::new();
        pure_measurement_node.pauli_error_rates.error_rate_Y = pm; // Y error will cause pure measurement error for StabX (X basis), StabZ (Z basis), StabY (X basis)
        let pure_measurement_node = Arc::new(pure_measurement_node);
        // commonly used noiseless error node
        let noiseless_node = Arc::new(NoiseModelNode::new());
        // noise model builder
        match self {
            Self::Phenomenological => {
                let simulator = &*simulator; // force simulator to be immutable, to avoid unexpected changes
                assert!(px + py + pz <= 1. && px >= 0. && py >= 0. && pz >= 0.);
                assert!(pe == 0.); // phenomenological noise model doesn't support erasure errors
                if simulator.measurement_cycles == 1 {
                    eprintln!("[warning] setting error rates of unknown code, no perfect measurement protection is enabled");
                }
                simulator_iter_real!(simulator, position, node, {
                    noise_model.set_node(position, Some(noiseless_node.clone())); // clear existing noise model
                    if position.t >= simulator.height - simulator.measurement_cycles {
                        // no error at the final perfect measurement round
                        continue;
                    }
                    if position.t % simulator.measurement_cycles == 0 && node.qubit_type == QubitType::Data {
                        noise_model.set_node(position, Some(biased_node.clone()));
                    }
                    if (position.t + 1) % simulator.measurement_cycles == 0 && node.qubit_type != QubitType::Data {
                        // measurement error must happen before measurement round
                        noise_model.set_node(position, Some(pure_measurement_node.clone()));
                    }
                });
            }
            NoiseModelBuilder::PhenomenologicalInit => {
                // let (noisy_measurements, _, _) = match simulator.code_type {
                //     CodeType::RotatedTailoredCode{ noisy_measurements, dp, dn } => { (noisy_measurements, dp, dn) }
                //     _ => unimplemented!("tailored surface code with Bell state initialization is only implemented for open-boundary rotated tailored surface code")
                // };
                let (noisy_measurements, _, _) = match simulator.code_type {
                    CodeType::RotatedTailoredCode => { (simulator.code_size.noisy_measurements, simulator.code_size.di, simulator.code_size.dj) }
                    _ => unimplemented!("tailored surface code with Bell state initialization is only implemented for open-boundary rotated tailored surface code")
                };
                assert!(noisy_measurements > 0, "to simulate bell initialization, noisy measurement must be set +1 (e.g. set noisy measurement 1 is equivalent to 0 noisy measurements)");
                assert!(simulator.measurement_cycles > 1);
                // change all stabilizers at the first round as virtual
                simulator_iter_mut!(simulator, position, node, t => simulator.measurement_cycles, {
                    if node.qubit_type != QubitType::Data {
                        assert!(node.gate_type.is_measurement());
                        assert!(node.gate_type.is_single_qubit_gate());
                        // since no peer, just set myself as virtual is ok
                        node.is_virtual = true;
                        noise_model.set_node(position, Some(noiseless_node.clone()));  // clear existing noise model
                    }
                });
                let simulator = &*simulator; // force simulator to be immutable, to avoid unexpected changes
                assert!(px + py + pz <= 1. && px >= 0. && py >= 0. && pz >= 0.);
                assert!(pe == 0.); // phenomenological error model doesn't support erasure errors
                if simulator.measurement_cycles == 1 {
                    eprintln!("[warning] setting error rates of unknown code, no perfect measurement protection is enabled");
                }
                // create an error model that is always 50% change of measurement error
                let mut messed_measurement_node = NoiseModelNode::new();
                messed_measurement_node.pauli_error_rates.error_rate_Y = 0.5; // Y error will cause pure measurement error for StabX (X basis), StabZ (Z basis), StabY (X basis)
                let messed_measurement_node = Arc::new(messed_measurement_node);
                simulator_iter_real!(simulator, position, node, {
                    noise_model.set_node(position, Some(noiseless_node.clone())); // clear existing noise model
                    if position.t == simulator.measurement_cycles - 1 && node.qubit_type == QubitType::StabY {
                        noise_model.set_node(position, Some(messed_measurement_node.clone()))
                    } else if position.t >= simulator.measurement_cycles {
                        // no error before the first round
                        if position.t < simulator.height - simulator.measurement_cycles {
                            // no error at the final perfect measurement round
                            if position.t % simulator.measurement_cycles == 0 && node.qubit_type == QubitType::Data {
                                noise_model.set_node(position, Some(biased_node.clone()));
                            }
                            if (position.t + 1) % simulator.measurement_cycles == 0 && node.qubit_type != QubitType::Data {
                                // measurement error must happen before measurement round
                                noise_model.set_node(position, Some(pure_measurement_node.clone()));
                            }
                        }
                    }
                });
            }
            NoiseModelBuilder::TailoredScBellInitPhenomenological => {
                let (noisy_measurements, dp, dn) = match simulator.code_type {
                    CodeType::RotatedTailoredCode => { (simulator.code_size.noisy_measurements, simulator.code_size.di, simulator.code_size.dj) }
                    _ => unimplemented!("tailored surface code with Bell state initialization is only implemented for open-boundary rotated tailored surface code")
                };
                assert!(noisy_measurements > 0, "to simulate bell initialization, noisy measurement must be set +1 (e.g. set noisy measurement 1 is equivalent to 0 noisy measurements)");
                assert!(simulator.measurement_cycles > 1);
                // change all stabilizers at the first round as virtual
                simulator_iter_mut!(simulator, position, node, t => simulator.measurement_cycles, {
                    if node.qubit_type != QubitType::Data {
                        assert!(node.gate_type.is_measurement());
                        assert!(node.gate_type.is_single_qubit_gate());
                        // since no peer, just set myself as virtual is ok
                        node.is_virtual = true;
                        noise_model.set_node(position, Some(noiseless_node.clone()));  // clear existing noise model
                    }
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                });
                let simulator = &*simulator; // force simulator to be immutable, to avoid unexpected changes
                assert!(px + py + pz <= 1. && px >= 0. && py >= 0. && pz >= 0.);
                assert!(pe == 0.); // phenomenological noise model doesn't support erasure errors
                if simulator.measurement_cycles == 1 {
                    eprintln!("[warning] setting error rates of unknown code, no perfect measurement protection is enabled");
                }
                // create an noise model that is always 50% change of measurement error
                let mut messed_measurement_node = NoiseModelNode::new();
                messed_measurement_node.pauli_error_rates.error_rate_Y = 0.5; // Y error will cause pure measurement error for StabX (X basis), StabZ (Z basis), StabY (X basis)
                let messed_measurement_node = Arc::new(messed_measurement_node);
                simulator_iter_real!(simulator, position, node, {
                    noise_model.set_node(position, Some(noiseless_node.clone())); // clear existing noise model
                    if position.t == simulator.measurement_cycles - 1 {
                        for i in 0..((dn + 1) / 2 - 1) {
                            for j in 0..(dp + 1) / 2 {
                                // println!("{:?} {:?} {:?}", position.t, 3 + 2*i + 2*j, dn-1 - 2*i + 2*j);
                                noise_model.set_node(
                                    &pos!(position.t, 3 + 2 * i + 2 * j, dn - 1 - 2 * i + 2 * j),
                                    Some(messed_measurement_node.clone()),
                                );
                            }
                        }
                    } else if position.t >= simulator.measurement_cycles {
                        // no error before the first round
                        if position.t < simulator.height - simulator.measurement_cycles {
                            // no error at the final perfect measurement round
                            if position.t % simulator.measurement_cycles == 0 && node.qubit_type == QubitType::Data {
                                noise_model.set_node(position, Some(biased_node.clone()));
                            }
                            if (position.t + 1) % simulator.measurement_cycles == 0 && node.qubit_type != QubitType::Data {
                                // measurement error must happen before measurement round
                                noise_model.set_node(position, Some(pure_measurement_node.clone()));
                            }
                        }
                    }
                });
            }
            Self::GenericBiasedWithBiasedCX | Self::GenericBiasedWithStandardCX => {
                // (here) FIRST qubit: anc; SECOND: data, due to circuit design
                let mut initialization_error_rate = p; // by default initialization error rate is the same as p
                let mut measurement_error_rate = p;
                let mut config_cloned = noise_model_configuration.clone();
                let config = config_cloned
                    .as_object_mut()
                    .expect("noise_model_configuration must be JSON object");
                if let Some(value) = config.remove("initialization_error_rate") {
                    initialization_error_rate = value.as_f64().expect("f64")
                }
                if let Some(value) = config.remove("measurement_error_rate") {
                    measurement_error_rate = value.as_f64().expect("f64");
                }
                if !config.is_empty() {
                    panic!("unknown keys: {:?}", config.keys().collect::<Vec<&String>>());
                }
                // normal biased node
                let mut normal_biased_node = NoiseModelNode::new();
                normal_biased_node.pauli_error_rates.error_rate_X = initialization_error_rate / bias_eta;
                normal_biased_node.pauli_error_rates.error_rate_Z = initialization_error_rate;
                normal_biased_node.pauli_error_rates.error_rate_Y = initialization_error_rate / bias_eta;
                let normal_biased_node = Arc::new(normal_biased_node);
                // CZ gate node
                let mut cphase_node = NoiseModelNode::new();
                cphase_node.correlated_pauli_error_rates =
                    Some(CorrelatedPauliErrorRates::default_with_probability(p / bias_eta));
                cphase_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZI = p;
                cphase_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_IZ = p;
                let cphase_node = Arc::new(cphase_node);
                // CZ gate with measurement error
                let mut cphase_measurement_error_node: NoiseModelNode = (*cphase_node).clone();
                cphase_measurement_error_node.pauli_error_rates.error_rate_X = measurement_error_rate / bias_eta;
                cphase_measurement_error_node.pauli_error_rates.error_rate_Z = measurement_error_rate;
                cphase_measurement_error_node.pauli_error_rates.error_rate_Y = measurement_error_rate / bias_eta;
                let cphase_measurement_error_node = Arc::new(cphase_measurement_error_node);
                // CX gate node
                let mut cx_node = NoiseModelNode::new();
                cx_node.correlated_pauli_error_rates =
                    Some(CorrelatedPauliErrorRates::default_with_probability(p / bias_eta));
                cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZI = p;
                match self {
                    Self::GenericBiasedWithStandardCX => {
                        cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_IZ = 0.375 * p;
                        cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZZ = 0.375 * p;
                        cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_IY = 0.125 * p;
                        cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZY = 0.125 * p;
                    }
                    Self::GenericBiasedWithBiasedCX => {
                        cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_IZ = 0.5 * p;
                        cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZZ = 0.5 * p;
                    }
                    _ => {}
                }
                let cx_node = Arc::new(cx_node);
                // CX gate with measurement error
                let mut cx_measurement_error_node: NoiseModelNode = (*cx_node).clone();
                cx_measurement_error_node.pauli_error_rates.error_rate_X = measurement_error_rate / bias_eta;
                cx_measurement_error_node.pauli_error_rates.error_rate_Z = measurement_error_rate;
                cx_measurement_error_node.pauli_error_rates.error_rate_Y = measurement_error_rate / bias_eta;
                let cx_measurement_error_node = Arc::new(cx_measurement_error_node);
                // iterate over all nodes
                simulator_iter_real!(simulator, position, node, {
                    // first clear error rate
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                    if position.t >= simulator.height - simulator.measurement_cycles {
                        // no error on the top, as a perfect measurement round
                        continue;
                    }
                    // do different things for each stage
                    match position.t % simulator.measurement_cycles {
                        1 => {
                            // initialization
                            noise_model.set_node(position, Some(normal_biased_node.clone()));
                        }
                        0 => { // measurement
                             // do nothing
                        }
                        _ => {
                            let has_measurement_error = position.t % simulator.measurement_cycles
                                == simulator.measurement_cycles - 1
                                && node.qubit_type != QubitType::Data;
                            match node.gate_type {
                                GateType::CZGate => {
                                    if node.qubit_type != QubitType::Data {
                                        // this is ancilla
                                        // better check whether peer is indeed data qubit, but it's hard here due to Rust's borrow check
                                        noise_model.set_node(
                                            position,
                                            Some(if has_measurement_error {
                                                cphase_measurement_error_node.clone()
                                            } else {
                                                cphase_node.clone()
                                            }),
                                        );
                                    }
                                }
                                GateType::CXGateControl => {
                                    // this is ancilla in XZZX code, see arXiv:2104.09539v1
                                    noise_model.set_node(
                                        position,
                                        Some(if has_measurement_error {
                                            cx_measurement_error_node.clone()
                                        } else {
                                            cx_node.clone()
                                        }),
                                    );
                                }
                                _ => {}
                            }
                        }
                    }
                });
            }
            Self::TailoredScBellInitCircuit => {
                let CodeSize { noisy_measurements, di: dp, dj: _dn } = match simulator.code_type {
                    CodeType::RotatedTailoredCodeBellInit => { simulator.code_size.clone() }
                    _ => unimplemented!("tailored surface code with Bell state initialization is only implemented for open-boundary rotated tailored surface code")
                };
                assert!(noisy_measurements > 0, "to simulate bell initialization, noisy measurement must be set +1 (e.g. set noisy measurement 1 is equivalent to 0 noisy measurements)");
                assert!(simulator.measurement_cycles > 1);
                // a bunch of function for determining qubit type during init, copied from code_builder.rs
                let (di, dj) = (dp, dp);
                let is_real = |i: usize, j: usize| -> bool {
                    let is_real_dj = |pi, pj| pi + pj < dj || (pi + pj == dj && pi % 2 == 0 && pi > 0);
                    let is_real_di = |pi, pj| pi + pj < di || (pi + pj == di && pj % 2 == 0 && pj > 0);
                    if i <= dj && j <= dj {
                        is_real_dj(dj - i, dj - j)
                    } else if i >= di && j >= di {
                        is_real_dj(i - di, j - di)
                    } else if i >= dj && j <= di {
                        is_real_di(i - dj, di - j)
                    } else if i <= di && j >= dj {
                        is_real_di(di - i, j - dj)
                    } else {
                        unreachable!()
                    }
                };
                // some criteria for bell init
                let is_bell_init_anc = |i: usize, j: usize| -> bool {
                    is_real(i, j) && i < j + dj - 3 && ((i % 4 == 1 && j % 4 == 0) || (i % 4 == 3 && j % 4 == 2))
                };
                let is_bell_init_top = |i: usize, j: usize| -> bool {
                    is_real(i, j) && i < j + dj - 1 && ((i % 4 == 0 && j % 4 == 0) || (i % 4 == 2 && j % 4 == 2))
                };
                let is_bell_init_left = |i: usize, j: usize| -> bool {
                    is_real(i, j) && i < j + dj - 1 && ((i % 4 == 1 && j % 4 == 3) || (i % 4 == 3 && j % 4 == 1))
                };
                let is_bell_init_right = |i: usize, j: usize| -> bool {
                    is_real(i, j) && i < j + dj - 1 && ((i % 4 == 1 && j % 4 == 1) || (i % 4 == 3 && j % 4 == 3))
                };
                let is_bell_init_bot = |i: usize, j: usize| -> bool {
                    is_real(i, j) && i < j + dj - 1 && ((i % 4 == 2 && j % 4 == 0) || (i % 4 == 0 && j % 4 == 2))
                };
                let is_bell_init_unfixed = |i: usize, j: usize| -> bool {
                    is_real(i, j) && ((i % 4 == 3 && j % 4 == 0) || (i % 4 == 1 && j % 4 == 2))
                };

                ////Error nodes for XY code
                let initialization_error_rate = p;
                // normal bias nodes
                let mut normal_biased_node = NoiseModelNode::new();
                normal_biased_node.pauli_error_rates.error_rate_X = initialization_error_rate / bias_eta;
                normal_biased_node.pauli_error_rates.error_rate_Z = initialization_error_rate;
                normal_biased_node.pauli_error_rates.error_rate_Y = initialization_error_rate / bias_eta;
                let normal_biased_node = Arc::new(normal_biased_node);

                // normal bias + cx node (for init)
                let mut normal_biased_with_cx_node = (*normal_biased_node).clone();
                normal_biased_with_cx_node.correlated_pauli_error_rates =
                    Some(CorrelatedPauliErrorRates::default_with_probability(p / bias_eta));
                normal_biased_with_cx_node
                    .correlated_pauli_error_rates
                    .as_mut()
                    .unwrap()
                    .error_rate_ZI = p;
                normal_biased_with_cx_node
                    .correlated_pauli_error_rates
                    .as_mut()
                    .unwrap()
                    .error_rate_IZ = 0.5 * p;
                normal_biased_with_cx_node
                    .correlated_pauli_error_rates
                    .as_mut()
                    .unwrap()
                    .error_rate_ZZ = 0.5 * p;
                let normal_biased_with_cx_node = Arc::new(normal_biased_with_cx_node);

                // biased CX gate node; CX & CY have same noise model if using bias-preserving gate
                let mut cx_node = NoiseModelNode::new();
                cx_node.correlated_pauli_error_rates =
                    Some(CorrelatedPauliErrorRates::default_with_probability(p / bias_eta));
                cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZI = p;
                cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_IZ = 0.5 * p;
                cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZZ = 0.5 * p;
                let cx_node = Arc::new(cx_node);

                // reversed CX gate node, for convinience
                let mut rev_cx_node = NoiseModelNode::new();
                rev_cx_node.correlated_pauli_error_rates =
                    Some(CorrelatedPauliErrorRates::default_with_probability(p / bias_eta));
                rev_cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_IZ = p;
                rev_cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZI = 0.5 * p;
                rev_cx_node.correlated_pauli_error_rates.as_mut().unwrap().error_rate_ZZ = 0.5 * p;
                let rev_cx_node = Arc::new(rev_cx_node);

                // CX gate with measurement error
                let mut cx_measurement_error_node: NoiseModelNode = (*cx_node).clone();
                cx_measurement_error_node.pauli_error_rates.error_rate_X = initialization_error_rate / bias_eta;
                cx_measurement_error_node.pauli_error_rates.error_rate_Z = initialization_error_rate;
                cx_measurement_error_node.pauli_error_rates.error_rate_Y = initialization_error_rate / bias_eta;
                let cx_measurement_error_node = Arc::new(cx_measurement_error_node);

                let simulator = &*simulator; // force simulator to be immutable, to avoid unexpected changes
                assert!(px + py + pz <= 1. && px >= 0. && py >= 0. && pz >= 0.);
                assert!(pe == 0.); // phenomenological noise model doesn't support erasure errors
                if simulator.measurement_cycles == 1 {
                    eprintln!("[warning] setting error rates of unknown code, no perfect measurement protection is enabled");
                }
                // create an noise model that is always 50% change of measurement error
                let mut messed_measurement_node = NoiseModelNode::new();
                messed_measurement_node.pauli_error_rates.error_rate_Z = 0.5; // Z error will cause pure measurement error for unfixed stabilizer(Y)
                let messed_measurement_node = Arc::new(messed_measurement_node);

                simulator_iter_real!(simulator, position, node, {
                    noise_model.set_node(position, Some(noiseless_node.clone())); // clear existing noise model
                    if position.t > 0 && position.t <= simulator.measurement_cycles {
                        // first measurement_cycle is empty, used to set a perfect measurement
                        let (i, j) = (position.i, position.j);
                        assert!(is_real(i, j), "sim_iter_real should iter over real right?");
                        match position.t {
                            1 => {
                                // if is_bell_init_anc: normal+cx
                                // else: normal
                                if is_bell_init_anc(i, j) && is_bell_init_top(i - 1, j) {
                                    noise_model.set_node(position, Some(normal_biased_with_cx_node.clone()));
                                } else {
                                    noise_model.set_node(position, Some(normal_biased_node.clone()));
                                }
                            }
                            2 => {
                                // if is_bell_init_anc: cx
                                if is_bell_init_anc(i, j) && is_bell_init_left(i, j - 1) {
                                    noise_model.set_node(position, Some(cx_node.clone()));
                                }
                            }
                            3 => {
                                // if is_bell_init_anc: cx
                                if is_bell_init_anc(i, j) && is_bell_init_right(i, j + 1) {
                                    noise_model.set_node(position, Some(cx_node.clone()));
                                }
                            }
                            4 => {
                                // if is_bell_init_anc: cx
                                if is_bell_init_anc(i, j) && is_bell_init_bot(i + 1, j) {
                                    noise_model.set_node(position, Some(cx_node.clone()));
                                }
                            }
                            5 => {
                                // if is_bell_init_anc: rev_cx
                                if is_bell_init_anc(i, j) && is_bell_init_bot(i + 1, j) {
                                    noise_model.set_node(position, Some(rev_cx_node.clone()));
                                }
                            }
                            0 => {
                                // if is_bell_init_anc: cx
                                // if is_bell_init_unfixed: z
                                if is_bell_init_anc(i, j) && is_bell_init_bot(i + 1, j) {
                                    noise_model.set_node(position, Some(cx_measurement_error_node.clone()));
                                }
                                if is_bell_init_unfixed(i, j) {
                                    noise_model.set_node(position, Some(messed_measurement_node.clone()));
                                }
                            }
                            _ => {
                                //nothing
                            }
                        }
                    } else if position.t < simulator.height - simulator.measurement_cycles {
                        // no error before the first round and at final round
                        // do different things for each stage
                        match position.t % simulator.measurement_cycles {
                            1 => {
                                // pauli error on qubits
                                noise_model.set_node(position, Some(normal_biased_node.clone()));
                            }
                            0 => { // measurement
                                 // do nothing
                            }
                            _ => {
                                // gate things
                                let has_measurement_error = position.t % simulator.measurement_cycles
                                    == simulator.measurement_cycles - 1
                                    && node.qubit_type != QubitType::Data; // && position.t < (noisy_measurements - 2) * simulator.measurement_cycles - 2;
                                                                           // println!("position.t: {:?}; err: {:?}", position.t, has_measurement_error);
                                if (node.gate_type == GateType::CXGateControl || node.gate_type == GateType::CYGateControl)
                                    && node.qubit_type != QubitType::Data
                                {
                                    //an ancilla
                                    noise_model.set_node(
                                        position,
                                        Some(if has_measurement_error {
                                            cx_measurement_error_node.clone()
                                        } else {
                                            cx_node.clone()
                                        }),
                                    )
                                }
                            }
                        }
                    }
                });
            }
            Self::ErasureOnlyPhenomenological => {
                assert_eq!(p, 0., "pauli error should be 0 in this noise model");
                let mut erasure_node = NoiseModelNode::new();
                // erasure node must have some non-zero pauli error rate for the decoder to work properly
                erasure_node.pauli_error_rates.error_rate_X = 1e-300; // f64::MIN_POSITIVE ~= 2.22e-308
                erasure_node.pauli_error_rates.error_rate_Z = 1e-300;
                erasure_node.pauli_error_rates.error_rate_Y = 1e-300;
                erasure_node.erasure_error_rate = pe;
                let erasure_node = Arc::new(erasure_node);
                // iterate over all nodes
                simulator_iter_real!(simulator, position, node, {
                    // first clear error rate
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                    if position.t >= simulator.height - simulator.measurement_cycles {
                        // no error on the top, as a perfect measurement round
                        continue;
                    }
                    if position.t % simulator.measurement_cycles == 0 {
                        // add data qubit erasure at the beginning
                        if node.qubit_type == QubitType::Data {
                            noise_model.set_node(position, Some(erasure_node.clone()));
                        }
                    } else if position.t % simulator.measurement_cycles == simulator.measurement_cycles - 1 {
                        // the round before measurement, add erasures
                        if node.qubit_type != QubitType::Data {
                            noise_model.set_node(position, Some(erasure_node.clone()));
                        }
                    }
                });
            }
            Self::MixedPhenomenological => {
                let mut noise_node = biased_node.as_ref().clone();
                // erasure node must have some non-zero pauli error rate for the decoder to work properly
                if p == 0. && pe != 0. {
                    noise_node.pauli_error_rates.error_rate_X = 1e-300; // f64::MIN_POSITIVE ~= 2.22e-308
                    noise_node.pauli_error_rates.error_rate_Z = 1e-300;
                    noise_node.pauli_error_rates.error_rate_Y = 1e-300;
                }
                let noise_node = Arc::new(noise_node);
                // iterate over all nodes
                simulator_iter_real!(simulator, position, node, {
                    // first clear error rate
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                    if position.t >= simulator.height - simulator.measurement_cycles {
                        // no error on the top, as a perfect measurement round
                        continue;
                    }
                    if position.t % simulator.measurement_cycles == 0 {
                        // add data qubit erasure at the beginning
                        if node.qubit_type == QubitType::Data {
                            noise_model.set_node(position, Some(noise_node.clone()));
                        }
                    } else if position.t % simulator.measurement_cycles == simulator.measurement_cycles - 1 {
                        // the round before measurement, add erasures
                        if node.qubit_type != QubitType::Data {
                            noise_model.set_node(position, Some(noise_node.clone()));
                        }
                    }
                });
            }
            Self::OnlyGateErrorCircuitLevel => {
                assert_eq!(bias_eta, 0.5, "bias not supported yet, please use the default value 0.5");
                let mut initialization_error_rate = 0.;
                let mut measurement_error_rate = 0.;
                let mut use_correlated_erasure = false;
                let mut use_correlated_pauli = false;
                let mut before_pauli_bug_fix = false;
                let mut erasure_delay_cycle = 0;
                let mut config_cloned = noise_model_configuration.clone();
                let config = config_cloned
                    .as_object_mut()
                    .expect("noise_model_configuration must be JSON object");
                if let Some(value) = config.remove("initialization_error_rate") {
                    initialization_error_rate = value.as_f64().expect("f64");
                }
                if let Some(value) = config.remove("measurement_error_rate") {
                    measurement_error_rate = value.as_f64().expect("f64");
                }
                if let Some(value) = config.remove("use_correlated_erasure") {
                    use_correlated_erasure = value.as_bool().expect("bool");
                }
                if let Some(value) = config.remove("use_correlated_pauli") {
                    use_correlated_pauli = value.as_bool().expect("bool");
                }
                if let Some(value) = config.remove("before_pauli_bug_fix") {
                    before_pauli_bug_fix = value.as_bool().expect("bool");
                }
                if let Some(value) = config.remove("erasure_delay_cycle") {
                    // erasures that are not corrected immediately, instead an erasure may stay
                    // for `delay_cycle` cycles and all qubits that are related will be effected.
                    erasure_delay_cycle = value.as_u64().expect("u64") as usize;
                }
                if !config.is_empty() {
                    panic!("unknown keys: {:?}", config.keys().collect::<Vec<&String>>());
                }
                // initialization node
                let mut initialization_node = NoiseModelNode::new();
                initialization_node.pauli_error_rates.error_rate_X = initialization_error_rate / 3.;
                initialization_node.pauli_error_rates.error_rate_Z = initialization_error_rate / 3.;
                initialization_node.pauli_error_rates.error_rate_Y = initialization_error_rate / 3.;
                if erasure_delay_cycle > 0 {
                    initialization_node.erasure_error_rate = 1e-300;
                }
                let initialization_node = Arc::new(initialization_node);
                // noiseless node
                let mut erasure_noiseless_node = noiseless_node.clone();
                if erasure_delay_cycle > 0 {
                    // otherwise erasure graph will not contain enough information
                    let mut erasure_noiseless = NoiseModelNode::new();
                    erasure_noiseless.erasure_error_rate = 1e-300;
                    erasure_noiseless_node = Arc::new(erasure_noiseless);
                }
                // iterate over all nodes
                simulator_iter_real!(simulator, position, node, {
                    // first clear error rate
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                    if position.t >= simulator.height - simulator.measurement_cycles {
                        // no error on the top, as a perfect measurement round
                        continue;
                    }
                    noise_model.set_node(position, Some(erasure_noiseless_node.clone()));
                    // do different things for each stage
                    match position.t % simulator.measurement_cycles {
                        1 => {
                            // initialization
                            if node.qubit_type != QubitType::Data {
                                noise_model.set_node(position, Some(initialization_node.clone()));
                            }
                        }
                        0 => { // measurement
                             // do nothing
                        }
                        _ => {
                            // errors everywhere
                            let mut this_position_use_correlated_pauli = false;
                            let mut error_node = NoiseModelNode::new(); // it's perfectly fine to instantiate an error node for each node: just memory inefficient at large code distances
                            if use_correlated_pauli
                                && node.gate_type.is_two_qubit_gate()
                                && node.qubit_type != QubitType::Data
                            {
                                // this is ancilla
                                this_position_use_correlated_pauli = use_correlated_pauli;
                            }

                            if erasure_delay_cycle > 0 {
                                error_node.erasure_error_rate = 1e-300; // single erasure exists, but just never triggered; for decoders
                                let mut erased_qubits = BTreeSet::new();
                                if use_correlated_erasure {
                                    if node.gate_type.is_two_qubit_gate() && node.qubit_type != QubitType::Data {
                                        let gate_peer = node.gate_peer.as_ref().unwrap();
                                        erased_qubits.insert((position.i, position.j));
                                        erased_qubits.insert((gate_peer.i, gate_peer.j));
                                    }
                                } else {
                                    erased_qubits.insert((position.i, position.j));
                                }
                                if !erased_qubits.is_empty() {
                                    let mut erasures = SparseErasures::new();
                                    let t = position.t;
                                    for dt in 0..erasure_delay_cycle + 1 {
                                        for &(i, j) in erased_qubits.iter() {
                                            erasures.insert_erasure(&pos!(t + dt, i, j));
                                        }
                                        if dt == erasure_delay_cycle {
                                            break;
                                        }
                                        // calculate what are the effected qubits in the next round
                                        let nt = t + dt + 1;
                                        if nt >= simulator.height - simulator.measurement_cycles {
                                            break;
                                        }
                                        let mut next_erased_qubits = BTreeSet::new();
                                        for &(i, j) in erased_qubits.iter() {
                                            let next_node = simulator.get_node_unwrap(&pos!(nt, i, j));
                                            if !next_node.gate_type.is_initialization() {
                                                next_erased_qubits.insert((i, j));
                                            }
                                            if next_node.gate_type.is_two_qubit_gate() && !next_node.is_peer_virtual {
                                                let gate_peer = next_node.gate_peer.as_ref().unwrap();
                                                next_erased_qubits.insert((gate_peer.i, gate_peer.j));
                                            }
                                        }
                                        erased_qubits = next_erased_qubits;
                                    }
                                    noise_model.additional_noise.push(AdditionalNoise {
                                        probability: pe,
                                        pauli_errors: SparseErrorPattern::new(),
                                        erasures,
                                    })
                                }
                            } else if use_correlated_erasure
                                && node.gate_type.is_two_qubit_gate()
                                && node.qubit_type != QubitType::Data
                            {
                                // this is ancilla
                                // better check whether peer is indeed data qubit, but it's hard here due to Rust's borrow check
                                let mut correlated_erasure_error_rates =
                                    CorrelatedErasureErrorRates::default_with_probability(0.);
                                correlated_erasure_error_rates.error_rate_EE = pe;
                                correlated_erasure_error_rates.sanity_check();
                                error_node.correlated_erasure_error_rates = Some(correlated_erasure_error_rates);
                            } else {
                                error_node.erasure_error_rate = pe;
                            }

                            // this bug is hard to find without visualization tool...
                            // so I develop such a tool at https://qec.wuyue98.cn/NoiseModelViewer2D.html
                            // to compare: (in url, %20 is space, %22 is double quote)
                            //     https://qec.wuyue98.cn/NoiseModelViewer2D.html?p=0.01&pe=0.05&parameters=--code_type%20StandardXZZXCode%20--noise_model%20only-gate-error-circuit-level%20--noise_model_configuration%20%27{"use_correlated_pauli":true,"use_correlated_erasure":true}%27
                            //     https://qec.wuyue98.cn/NoiseModelViewer2D.html?p=0.01&pe=0.05&parameters=--code_type%20StandardXZZXCode%20--noise_model%20only-gate-error-circuit-level%20--noise_model_configuration%20%27{"use_correlated_pauli":true,"use_correlated_erasure":true,"before_pauli_bug_fix":true}%27
                            let mut px_py_pz = if before_pauli_bug_fix {
                                if this_position_use_correlated_pauli {
                                    (0., 0., 0.)
                                } else {
                                    (p / 3., p / 3., p / 3.)
                                }
                            } else if use_correlated_pauli {
                                (0., 0., 0.)
                            } else {
                                (p / 3., p / 3., p / 3.)
                            };
                            if position.t % simulator.measurement_cycles == simulator.measurement_cycles - 1
                                && node.qubit_type != QubitType::Data
                            {
                                // add additional measurement error
                                // whether it's X axis measurement or Z axis measurement, the additional error rate is always `measurement_error_rate`
                                px_py_pz = ErrorType::combine_probability(
                                    px_py_pz,
                                    (
                                        measurement_error_rate / 2.,
                                        measurement_error_rate / 2.,
                                        measurement_error_rate / 2.,
                                    ),
                                );
                            }
                            let (px, py, pz) = px_py_pz;
                            error_node.pauli_error_rates.error_rate_X = px;
                            error_node.pauli_error_rates.error_rate_Y = py;
                            error_node.pauli_error_rates.error_rate_Z = pz;
                            if pe > 0. {
                                // need to set minimum pauli error when this is subject to erasure
                                if error_node.pauli_error_rates.error_rate_X == 0. {
                                    error_node.pauli_error_rates.error_rate_X = 1e-300;
                                    // f64::MIN_POSITIVE ~= 2.22e-308
                                }
                                if error_node.pauli_error_rates.error_rate_Y == 0. {
                                    error_node.pauli_error_rates.error_rate_Y = 1e-300;
                                    // f64::MIN_POSITIVE ~= 2.22e-308
                                }
                                if error_node.pauli_error_rates.error_rate_Z == 0. {
                                    error_node.pauli_error_rates.error_rate_Z = 1e-300;
                                    // f64::MIN_POSITIVE ~= 2.22e-308
                                }
                            }
                            if this_position_use_correlated_pauli {
                                let correlated_pauli_error_rates =
                                    CorrelatedPauliErrorRates::default_with_probability(p / 15.); // 15 possible errors equally probable
                                correlated_pauli_error_rates.sanity_check();
                                error_node.correlated_pauli_error_rates = Some(correlated_pauli_error_rates);
                            }
                            noise_model.set_node(position, Some(Arc::new(error_node)));
                        }
                    }
                });
            }
            Self::StimNoiseModel => {
                let mut after_clifford_depolarization = p;
                let mut before_round_data_depolarization = p;
                let mut before_measure_flip_probability = p;
                let mut after_reset_flip_probability = p;
                let mut config_cloned = noise_model_configuration.clone();
                let config = config_cloned
                    .as_object_mut()
                    .expect("noise_model_configuration must be JSON object");
                if let Some(value) = config.remove("after_clifford_depolarization") {
                    after_clifford_depolarization = value.as_f64().expect("f64")
                }
                if let Some(value) = config.remove("before_round_data_depolarization") {
                    before_round_data_depolarization = value.as_f64().expect("f64");
                }
                if let Some(value) = config.remove("before_measure_flip_probability") {
                    before_measure_flip_probability = value.as_f64().expect("f64")
                }
                if let Some(value) = config.remove("after_reset_flip_probability") {
                    after_reset_flip_probability = value.as_f64().expect("f64")
                }
                if !config.is_empty() {
                    panic!("unknown keys: {:?}", config.keys().collect::<Vec<&String>>());
                }
                // correlated depolarize_2 node
                let mut depolarize_2_node = NoiseModelNode::new();
                let correlated_pauli_error_rates =
                    CorrelatedPauliErrorRates::default_with_probability(after_clifford_depolarization / 15.); // 15 possible errors equally probable
                correlated_pauli_error_rates.sanity_check();
                depolarize_2_node.correlated_pauli_error_rates = Some(correlated_pauli_error_rates);
                let depolarize_2_node = Arc::new(depolarize_2_node);
                // data qubit before round depolarization node
                let mut data_qubit_depolarize_node = NoiseModelNode::new();
                data_qubit_depolarize_node.pauli_error_rates.error_rate_X = before_round_data_depolarization / 3.;
                data_qubit_depolarize_node.pauli_error_rates.error_rate_Y = before_round_data_depolarization / 3.;
                data_qubit_depolarize_node.pauli_error_rates.error_rate_Z = before_round_data_depolarization / 3.;
                let data_qubit_depolarize_node = Arc::new(data_qubit_depolarize_node);
                // measurement flip node: whatever basis is the stabilizer, there is always `before_measure_flip_probability` probability to be flipped
                let mut measure_flip_node = NoiseModelNode::new();
                measure_flip_node.pauli_error_rates.error_rate_X = before_measure_flip_probability / 2.;
                measure_flip_node.pauli_error_rates.error_rate_Y = before_measure_flip_probability / 2.;
                measure_flip_node.pauli_error_rates.error_rate_Z = before_measure_flip_probability / 2.;
                let measure_flip_node = Arc::new(measure_flip_node);
                // reset flip node: whatever basis is the stabilizer, there is always `after_reset_flip_probability` probability to be flipped
                let mut reset_flip_node = NoiseModelNode::new();
                reset_flip_node.pauli_error_rates.error_rate_X = after_reset_flip_probability / 2.;
                reset_flip_node.pauli_error_rates.error_rate_Y = after_reset_flip_probability / 2.;
                reset_flip_node.pauli_error_rates.error_rate_Z = after_reset_flip_probability / 2.;
                let reset_flip_node = Arc::new(reset_flip_node);
                // iterate over all nodes
                simulator_iter_real!(simulator, position, node, {
                    // first clear error rate
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                    if position.t >= simulator.height - simulator.measurement_cycles {
                        // no error on the top, as a perfect measurement round
                        continue;
                    }
                    // do different things for each stage
                    match position.t % simulator.measurement_cycles {
                        1 => {
                            // initialization
                            if node.qubit_type != QubitType::Data {
                                noise_model.set_node(position, Some(reset_flip_node.clone()));
                            } else {
                                noise_model.set_node(position, Some(data_qubit_depolarize_node.clone()));
                            }
                        }
                        0 => { // measurement
                             // do nothing; measurement errors need to be added before this round...
                        }
                        _ => {
                            let mut error_node = noiseless_node.clone();
                            if node.gate_type.is_two_qubit_gate()
                                && node.qubit_type == QubitType::Data
                                && !node.is_peer_virtual
                            {
                                // this is data qubit with actual 2-qubit gate
                                error_node = depolarize_2_node.clone();
                            }
                            if position.t % simulator.measurement_cycles == simulator.measurement_cycles - 1 {
                                if node.qubit_type != QubitType::Data {
                                    error_node = measure_flip_node.clone();
                                } else if position.t == simulator.height - simulator.measurement_cycles - 2 {
                                    let mut new_error_node = error_node.as_ref().clone();
                                    new_error_node.pauli_error_rates = data_qubit_depolarize_node.pauli_error_rates.clone();
                                    error_node = Arc::new(new_error_node);
                                }
                            }
                            noise_model.set_node(position, Some(error_node));
                        }
                    }
                });
            }
            Self::DepolarizingNoise => {
                let mut config_cloned = noise_model_configuration.clone();
                let config = config_cloned
                    .as_object_mut()
                    .expect("noise_model_configuration must be JSON object");
                if !config.is_empty() {
                    panic!("unknown keys: {:?}", config.keys().collect::<Vec<&String>>());
                }
                // depolarizing node
                let mut depolarizing_node = NoiseModelNode::new();
                depolarizing_node.pauli_error_rates.error_rate_X = p / 3.;
                depolarizing_node.pauli_error_rates.error_rate_Z = p / 3.;
                depolarizing_node.pauli_error_rates.error_rate_Y = p / 3.;
                let depolarizing_node = Arc::new(depolarizing_node);
                // double depolarizing node
                let mut double_depolarizing_node = NoiseModelNode::new();
                double_depolarizing_node.pauli_error_rates.error_rate_X = 2. * p / 3.;
                double_depolarizing_node.pauli_error_rates.error_rate_Z = 2. * p / 3.;
                double_depolarizing_node.pauli_error_rates.error_rate_Y = 2. * p / 3.;
                let double_depolarizing_node = Arc::new(double_depolarizing_node);
                // two qubit depolarizing node
                let mut correlated_depolarizing_node = NoiseModelNode::new();
                let correlated_pauli_error_rates = CorrelatedPauliErrorRates::default_with_probability(p / 15.); // 15 possible errors equally probable
                correlated_depolarizing_node.correlated_pauli_error_rates = Some(correlated_pauli_error_rates);
                let correlated_depolarizing_node = Arc::new(correlated_depolarizing_node);
                // iterate over all nodes
                simulator_iter_real!(simulator, position, node, {
                    // first clear error rate
                    noise_model.set_node(position, Some(noiseless_node.clone()));
                    if position.t == 0 || position.t >= simulator.height - simulator.measurement_cycles {
                        // no error on the top, as a perfect measurement round
                        continue;
                    }
                    // do different things for each stage
                    match position.t % simulator.measurement_cycles {
                        1 => {
                            // initialization
                            noise_model.set_node(position, Some(depolarizing_node.clone()));
                        }
                        0 => {
                            // measurement
                            // do nothing
                            if node.qubit_type == QubitType::Data {
                                noise_model.set_node(position, Some(depolarizing_node.clone()));
                            }
                        }
                        _ => {
                            if node.is_peer_virtual || node.gate_peer.is_none() {
                                if position.t % simulator.measurement_cycles == simulator.measurement_cycles - 1
                                    && node.qubit_type != QubitType::Data
                                {
                                    noise_model.set_node(position, Some(double_depolarizing_node.clone()));
                                } else {
                                    noise_model.set_node(position, Some(depolarizing_node.clone()));
                                }
                            } else {
                                if node.qubit_type == QubitType::Data {
                                    noise_model.set_node(position, Some(correlated_depolarizing_node.clone()));
                                }
                                if position.t % simulator.measurement_cycles == simulator.measurement_cycles - 1
                                    && node.qubit_type != QubitType::Data
                                {
                                    noise_model.set_node(position, Some(depolarizing_node.clone()));
                                    // measurement error
                                }
                            }
                        }
                    }
                });
            }
        }
    }

    /// check as strictly as possible, given the user specified json noise model description
    pub fn apply_noise_model_modifier(
        simulator: &mut Simulator,
        noise_model: &mut NoiseModel,
        modifier: &serde_json::Value,
    ) -> Result<(), String> {
        if modifier.get("code_type").ok_or("missing field: code_type")? != &json!(simulator.code_type) {
            return Err("mismatch: code_type".to_string());
        }
        if modifier.get("height").ok_or("missing field: height")? != &json!(simulator.height) {
            return Err("mismatch: height".to_string());
        }
        if modifier.get("vertical").ok_or("missing field: vertical")? != &json!(simulator.vertical) {
            return Err("mismatch: vertical".to_string());
        }
        if modifier.get("horizontal").ok_or("missing field: horizontal")? != &json!(simulator.horizontal) {
            return Err("mismatch: horizontal".to_string());
        }
        // iterate nodes
        let nodes = modifier
            .get("nodes")
            .ok_or("missing field: nodes".to_string())?
            .as_array()
            .ok_or("format error: nodes".to_string())?;
        if simulator.nodes.len() != nodes.len() {
            return Err("mismatch: nodes.len()".to_string());
        }
        for (t, nodes_t) in nodes.iter().enumerate() {
            let nodes_row_0 = nodes_t.as_array().ok_or(format!("format error: nodes[{}]", t))?;
            if nodes_row_0.len() != simulator.nodes[t].len() {
                return Err(format!("mimsatch: nodes[{}].len()", t));
            }
            for (i, nodes_i) in nodes_row_0.iter().enumerate() {
                let nodes_row_1 = nodes_i.as_array().ok_or(format!("format error: nodes[{}][{}]", t, i))?;
                if nodes_row_1.len() != simulator.nodes[t][i].len() {
                    return Err(format!("mismatch: nodes[{}][{}].len()", t, i));
                }
                for (j, node) in nodes_row_1.iter().enumerate() {
                    if node.is_null() != simulator.nodes[t][i][j].is_none() {
                        return Err(format!("mismatch: nodes[{}][{}][{}].is_none", t, i, j));
                    }
                    if !node.is_null() {
                        let self_node = simulator.nodes[t][i][j].as_mut().unwrap(); // already checked existance
                        if node.get("position").ok_or("missing field: position".to_string())? != &json!(pos!(t, i, j)) {
                            return Err(format!("mismatch position [{}][{}][{}]", t, i, j));
                        }
                        if node.get("qubit_type").ok_or("missing field: qubit_type".to_string())?
                            != &json!(self_node.qubit_type)
                        {
                            return Err(format!("mismatch [{}][{}][{}]: qubit_type", t, i, j));
                        }
                        if node.get("gate_type").ok_or("missing field: gate_type".to_string())?
                            != &json!(self_node.gate_type)
                        {
                            return Err(format!("mismatch [{}][{}][{}]: gate_type", t, i, j));
                        }
                        if node.get("gate_peer").ok_or("missing field: gate_peer".to_string())?
                            != &json!(self_node.gate_peer)
                        {
                            return Err(format!("mismatch [{}][{}][{}]: gate_peer", t, i, j));
                        }
                        // TODO: user can modify the 'is_virtual' attribute to manually discard a measurement event
                        let is_virtual = node
                            .get("is_virtual")
                            .ok_or("missing field: is_virtual".to_string())?
                            .as_bool()
                            .ok_or("wrong field: is_virtual".to_string())?;
                        let is_peer_virtual = node
                            .get("is_peer_virtual")
                            .ok_or("missing field: is_peer_virtual".to_string())?
                            .as_bool()
                            .ok_or("wrong field: is_peer_virtual".to_string())?;
                        assert_eq!(
                            is_virtual, self_node.is_virtual,
                            "is_virtual modification not implemented, needs sanity check"
                        );
                        assert_eq!(
                            is_peer_virtual, self_node.is_peer_virtual,
                            "is_peer_virtual modification not implemented, needs sanity check"
                        );
                        // then copy error rate data
                        let noise_model_node = node
                            .get("noise_model")
                            .ok_or("missing field: noise_model".to_string())?
                            .clone();
                        let noise_model_node: NoiseModelNode =
                            serde_json::from_value(noise_model_node).map_err(|e| format!("{:?}", e))?;
                        noise_model.set_node(&pos!(t, i, j), Some(Arc::new(noise_model_node)));
                    }
                }
            }
        }
        Ok(())
    }
}

impl std::str::FromStr for NoiseModelBuilder {
    type Err = String;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        for variant in Self::value_variants() {
            if variant.to_possible_value().unwrap().matches(s, false) {
                return Ok(*variant);
            }
        }
        Err(format!("Invalid variant: {}", s))
    }
}

#[cfg(feature = "python_binding")]
#[pyfunction]
pub(crate) fn register(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
    m.add_class::<NoiseModelBuilder>()?;
    Ok(())
}