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In [1]:

    
%load_ext autoreload
%autoreload 2
%matplotlib inline

from matplotlib import pyplot as plt
from cvxopt import matrix, solvers
solvers.options['show_progress'] = False
import numpy as np
import pandas as pd
import scipy as sp
import seaborn as sns
np.set_printoptions(precision=3, linewidth=120)
from copy import copy
from tqdm import *
from drift_qec.Q import *









    



/Users/yan/.miniconda/lib/python2.7/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
  warnings.warn(self.msg_depr % (key, alt_key))



In [56]:

    
D = 0.25 * np.pi
L = SENSOR(D, D, D)
np.round(np.dot(np.linalg.inv(np.dot(L.T, L)), L.T), 2)









    Out[56]:





array([[ 0.22,  0.22, -0.11,  0.22, -0.11,  0.22,  0.56, -0.11, -0.11],
       [-1.  ,  1.  ,  0.  ,  0.  , -0.  ,  0.  ,  0.  , -0.  , -0.  ],
       [ 0.  ,  0.  , -0.  , -1.  ,  0.  ,  1.  ,  0.  , -0.  , -0.  ],
       [ 0.22,  0.22, -0.11, -0.11,  0.56, -0.11, -0.11,  0.22,  0.22],
       [ 0.  ,  0.  , -0.  , -0.  ,  0.  , -0.  ,  0.  , -1.  ,  1.  ],
       [-0.11, -0.11,  0.56,  0.22, -0.11,  0.22, -0.11,  0.22,  0.22]])



In [46]:

    
channel = Channel(kx=0.7, ky=0.2, kz=0.1,
                  Q=np.linalg.qr(np.random.randn(3,3))[0],
                  n=N, d1=D0, d2=D0, d3=D0)



In [47]:

    
channel.sample_data()









    Out[47]:





array([ 0.246,  0.369,  0.385,  0.246,  0.369,  0.385,  0.245,  0.369,  0.386])



In [48]:

    
channel.d1









    Out[48]:





0.001



In [28]:

    
p = 0.01
D0 = 0.001
N = 100000*int(2.0*np.log(1.0/D0))
T = np.arange(1000)
N_TRIALS = 10
RECORDS = []
for trial in tqdm(range(N_TRIALS)):
    channel = Channel(kx=0.7, ky=0.2, kz=0.1,
                      Q=np.linalg.qr(np.random.randn(3,3))[0],
                      n=N, d1=D0, d2=D0, d3=D0)
    for t in T:
        channel.update()
        QAhat = np.linalg.svd(channel.Ahat)[0]
        Qhat, phat = np.linalg.svd(channel.Mhat)[0:2]
        maxidx = np.argmax(phat)
        RECORDS.append({"t": t,
                        "d": channel.d1,

                        "C_Mhat":     np.linalg.norm(channel.C-channel.Mhat),
                        "Mhat_Ahat":  np.linalg.norm(channel.Ahat-channel.Mhat),
                        "Ahat_M":     np.linalg.norm(channel.C-channel.Ahat),

                        "Q_Qhat":     np.linalg.norm(channel.Q - Qhat),
                        "Qhat_QAhat": np.linalg.norm(Qhat - QAhat),
                        "QAhat_Q":    np.linalg.norm(QAhat - channel.Q),

                        "q_qhat":     np.linalg.norm(channel.Q[maxidx, :] - Qhat[maxidx, :]),
                        "qhat_qahat": np.linalg.norm(Qhat[maxidx, :] - QAhat[maxidx, :]),
                        "qahat_q":    np.linalg.norm(QAhat[maxidx, :] - channel.Q[maxidx, :]),

                        "c11_m11": np.abs(channel.C[0,0] - channel.Mhat[0,0]),
                        "c22_m22": np.abs(channel.C[1,1] - channel.Mhat[1,1]),
                        "c33_m33": np.abs(channel.C[2,2] - channel.Mhat[2,2]),
                        "c12_m12": np.abs(channel.C[0,1] - channel.Mhat[0,1]),
                        "c13_m13": np.abs(channel.C[0,2] - channel.Mhat[0,2]),
                        "c23_m23": np.abs(channel.C[1,2] - channel.Mhat[1,2]),

                        "c11_a11": np.abs(channel.C[0,0] - channel.Ahat[0,0]),
                        "c22_a22": np.abs(channel.C[1,1] - channel.Ahat[1,1]),
                        "c33_a33": np.abs(channel.C[2,2] - channel.Ahat[2,2]),
                        "c12_a12": np.abs(channel.C[0,1] - channel.Ahat[0,1]),
                        "c13_a13": np.abs(channel.C[0,2] - channel.Ahat[0,2]),
                        "c23_a23": np.abs(channel.C[1,2] - channel.Ahat[1,2])
                    })
#         Dt = np.min([np.max([p ** 2, D0 ** (0.5 * (t-1.0))]), p])
#         channel.d1 = Dt
#         channel.d2 = Dt
#         channel.d3 = Dt

df = pd.DataFrame(RECORDS)
df.to_csv("decayd.csv")

df = pd.read_csv("decayd.csv", index_col=0)
cols = ['t', 'd',
 'Ahat_M',   'C_Mhat', 'Mhat_Ahat',
 'QAhat_Q',  'Q_Qhat', 'Qhat_QAhat',
 'q_qhat',  'qahat_q', 'qhat_qahat',
 'c11_a11', 'c22_a22', 'c33_a33',
 'c12_a12', 'c13_a13', 'c23_a23',
 'c11_m11', 'c22_m22', 'c33_m33',
 'c12_m12', 'c13_m13', 'c23_m23']
df = df[cols]

data = df.groupby("t").mean()

data.head(20)









    









    Out[28]:






  
    
      
      d
      Ahat_M
      C_Mhat
      Mhat_Ahat
      QAhat_Q
      Q_Qhat
      Qhat_QAhat
      q_qhat
      qahat_q
      qhat_qahat
      ...
      c33_a33
      c12_a12
      c13_a13
      c23_a23
      c11_m11
      c22_m22
      c33_m33
      c12_m12
      c13_m13
      c23_m23
    
    
      t
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
  
  
    
      0
      0.001
      0.856097
      0.397823
      0.534651
      2.153633
      1.576445
      1.648528e+00
      0.778999
      0.918448
      7.503898e-01
      ...
      0.000260
      0.294267
      0.283177
      0.322673
      0.037303
      0.058476
      0.060600
      0.138075
      0.090212
      0.132265
    
    
      1
      0.001
      0.689876
      0.416234
      0.339095
      1.524648
      1.338668
      4.000000e-01
      0.655964
      0.731545
      1.865678e-01
      ...
      0.124545
      0.138459
      0.318044
      0.190008
      0.095779
      0.132363
      0.078380
      0.105957
      0.152799
      0.131035
    
    
      2
      0.001
      0.492848
      0.343687
      0.199378
      1.470296
      1.018224
      7.656854e-01
      0.508148
      0.623668
      2.855040e-01
      ...
      0.111471
      0.103261
      0.220855
      0.133846
      0.114396
      0.088002
      0.073980
      0.099685
      0.122349
      0.104535
    
    
      3
      0.001
      0.392786
      0.289429
      0.125303
      1.458464
      1.268026
      2.828427e-01
      0.650023
      0.672146
      6.527244e-02
      ...
      0.104729
      0.145256
      0.153994
      0.063169
      0.057579
      0.074815
      0.069986
      0.118783
      0.095273
      0.056184
    
    
      4
      0.001
      0.389038
      0.299547
      0.111624
      1.290502
      1.530748
      2.828427e-01
      0.826290
      0.647828
      1.936177e-01
      ...
      0.077567
      0.125963
      0.151868
      0.084259
      0.053309
      0.073797
      0.050784
      0.104484
      0.103472
      0.073245
    
    
      5
      0.001
      0.396708
      0.327582
      0.089309
      1.699970
      1.713517
      7.656854e-01
      0.924800
      0.911026
      2.510307e-01
      ...
      0.074335
      0.145475
      0.126729
      0.104506
      0.057550
      0.071215
      0.055555
      0.126268
      0.099475
      0.092104
    
    
      6
      0.001
      0.397654
      0.343978
      0.070353
      1.755925
      1.780143
      4.828427e-01
      0.933974
      0.931750
      2.328676e-01
      ...
      0.065907
      0.146662
      0.142178
      0.083133
      0.084116
      0.085323
      0.052312
      0.132857
      0.111086
      0.081948
    
    
      7
      0.001
      0.363489
      0.318806
      0.052786
      1.460414
      1.296280
      2.000000e-01
      0.618839
      0.696655
      8.094137e-02
      ...
      0.057591
      0.119055
      0.133950
      0.070331
      0.089144
      0.092722
      0.043625
      0.113594
      0.104660
      0.074966
    
    
      8
      0.001
      0.329324
      0.292753
      0.043670
      1.667449
      1.667449
      1.272141e-15
      0.884274
      0.884274
      4.503386e-16
      ...
      0.064940
      0.112817
      0.117720
      0.068373
      0.071125
      0.076195
      0.054935
      0.108686
      0.091264
      0.070921
    
    
      9
      0.001
      0.285165
      0.260381
      0.030890
      1.257366
      1.257366
      6.954504e-16
      0.586650
      0.586650
      3.791452e-16
      ...
      0.062188
      0.092892
      0.117270
      0.056234
      0.063199
      0.073538
      0.054634
      0.090447
      0.098348
      0.058915
    
    
      10
      0.001
      0.280181
      0.256330
      0.032644
      1.120917
      1.120917
      5.686337e-16
      0.551553
      0.551553
      3.087056e-16
      ...
      0.060798
      0.093403
      0.111426
      0.055723
      0.065196
      0.072052
      0.049875
      0.090072
      0.094658
      0.056021
    
    
      11
      0.001
      0.270442
      0.251271
      0.026331
      1.092129
      1.092129
      5.832931e-16
      0.535773
      0.535773
      3.024130e-16
      ...
      0.071189
      0.083119
      0.102492
      0.054768
      0.069054
      0.075201
      0.062016
      0.080578
      0.090286
      0.054111
    
    
      12
      0.001
      0.272722
      0.260583
      0.017961
      1.573661
      1.573661
      7.723548e-16
      0.860436
      0.860436
      4.428572e-16
      ...
      0.070876
      0.086116
      0.094675
      0.060767
      0.077430
      0.080386
      0.065543
      0.084178
      0.086085
      0.058622
    
    
      13
      0.001
      0.240874
      0.231855
      0.014054
      1.297091
      1.297091
      5.680424e-16
      0.728938
      0.728938
      3.918803e-16
      ...
      0.058281
      0.072255
      0.080973
      0.060641
      0.075015
      0.062271
      0.053188
      0.071580
      0.074156
      0.059342
    
    
      14
      0.001
      0.228499
      0.217800
      0.016514
      1.292254
      1.292254
      6.235812e-16
      0.733632
      0.733632
      3.202068e-16
      ...
      0.057819
      0.072048
      0.077743
      0.060554
      0.064170
      0.058100
      0.050960
      0.069839
      0.069910
      0.060365
    
    
      15
      0.001
      0.226133
      0.220316
      0.009189
      1.251510
      1.251510
      5.845645e-16
      0.733736
      0.733736
      3.450215e-16
      ...
      0.046235
      0.071547
      0.080614
      0.051037
      0.063813
      0.061969
      0.042648
      0.070665
      0.075863
      0.050906
    
    
      16
      0.001
      0.237374
      0.229404
      0.012378
      1.247807
      1.247807
      5.615974e-16
      0.627951
      0.627951
      3.502303e-16
      ...
      0.052356
      0.076138
      0.078765
      0.058288
      0.071931
      0.064517
      0.047449
      0.075091
      0.072447
      0.057872
    
    
      17
      0.001
      0.217837
      0.211715
      0.010002
      0.759947
      0.759947
      6.834218e-16
      0.443084
      0.443084
      3.860493e-16
      ...
      0.044880
      0.073938
      0.071497
      0.051963
      0.059587
      0.053435
      0.041205
      0.072887
      0.066112
      0.052133
    
    
      18
      0.001
      0.220208
      0.209443
      0.015330
      0.966665
      0.966665
      9.531940e-16
      0.478997
      0.478997
      3.706317e-16
      ...
      0.053611
      0.080192
      0.074547
      0.046108
      0.053177
      0.058037
      0.046907
      0.076213
      0.068482
      0.045196
    
    
      19
      0.001
      0.220329
      0.211520
      0.011462
      0.711764
      0.711764
      7.946863e-16
      0.442580
      0.442580
      4.584795e-16
      ...
      0.053765
      0.073294
      0.075590
      0.049785
      0.059939
      0.063352
      0.048045
      0.069521
      0.072163
      0.048131
    
  

20 rows × 22 columns



In [45]:

    
fig, axs = plt.subplots(8, 3, figsize=(12,28),
                        sharey=True, sharex=True)
PAL = sns.color_palette("BuGn_r", len(df["d"].unique()))
axs[0,0].set_ylim([1e-2, 1e1])

for idx, (col, y) in enumerate(data.drop("d", axis=1).iteritems()):
    axs[int(idx/3), idx%3].loglog((y.index.values+1)*N, y.values, c = PAL[0])
    axs[int(idx/3), idx%3].set_title(col)



In [ ]:

	d	Ahat_M	C_Mhat	Mhat_Ahat	QAhat_Q	Q_Qhat	Qhat_QAhat	q_qhat	qahat_q	qhat_qahat	...	c33_a33	c12_a12	c13_a13	c23_a23	c11_m11	c22_m22	c33_m33	c12_m12	c13_m13	c23_m23
t
0	0.001	0.856097	0.397823	0.534651	2.153633	1.576445	1.648528e+00	0.778999	0.918448	7.503898e-01	...	0.000260	0.294267	0.283177	0.322673	0.037303	0.058476	0.060600	0.138075	0.090212	0.132265
1	0.001	0.689876	0.416234	0.339095	1.524648	1.338668	4.000000e-01	0.655964	0.731545	1.865678e-01	...	0.124545	0.138459	0.318044	0.190008	0.095779	0.132363	0.078380	0.105957	0.152799	0.131035
2	0.001	0.492848	0.343687	0.199378	1.470296	1.018224	7.656854e-01	0.508148	0.623668	2.855040e-01	...	0.111471	0.103261	0.220855	0.133846	0.114396	0.088002	0.073980	0.099685	0.122349	0.104535
3	0.001	0.392786	0.289429	0.125303	1.458464	1.268026	2.828427e-01	0.650023	0.672146	6.527244e-02	...	0.104729	0.145256	0.153994	0.063169	0.057579	0.074815	0.069986	0.118783	0.095273	0.056184
4	0.001	0.389038	0.299547	0.111624	1.290502	1.530748	2.828427e-01	0.826290	0.647828	1.936177e-01	...	0.077567	0.125963	0.151868	0.084259	0.053309	0.073797	0.050784	0.104484	0.103472	0.073245
5	0.001	0.396708	0.327582	0.089309	1.699970	1.713517	7.656854e-01	0.924800	0.911026	2.510307e-01	...	0.074335	0.145475	0.126729	0.104506	0.057550	0.071215	0.055555	0.126268	0.099475	0.092104
6	0.001	0.397654	0.343978	0.070353	1.755925	1.780143	4.828427e-01	0.933974	0.931750	2.328676e-01	...	0.065907	0.146662	0.142178	0.083133	0.084116	0.085323	0.052312	0.132857	0.111086	0.081948
7	0.001	0.363489	0.318806	0.052786	1.460414	1.296280	2.000000e-01	0.618839	0.696655	8.094137e-02	...	0.057591	0.119055	0.133950	0.070331	0.089144	0.092722	0.043625	0.113594	0.104660	0.074966
8	0.001	0.329324	0.292753	0.043670	1.667449	1.667449	1.272141e-15	0.884274	0.884274	4.503386e-16	...	0.064940	0.112817	0.117720	0.068373	0.071125	0.076195	0.054935	0.108686	0.091264	0.070921
9	0.001	0.285165	0.260381	0.030890	1.257366	1.257366	6.954504e-16	0.586650	0.586650	3.791452e-16	...	0.062188	0.092892	0.117270	0.056234	0.063199	0.073538	0.054634	0.090447	0.098348	0.058915
10	0.001	0.280181	0.256330	0.032644	1.120917	1.120917	5.686337e-16	0.551553	0.551553	3.087056e-16	...	0.060798	0.093403	0.111426	0.055723	0.065196	0.072052	0.049875	0.090072	0.094658	0.056021
11	0.001	0.270442	0.251271	0.026331	1.092129	1.092129	5.832931e-16	0.535773	0.535773	3.024130e-16	...	0.071189	0.083119	0.102492	0.054768	0.069054	0.075201	0.062016	0.080578	0.090286	0.054111
12	0.001	0.272722	0.260583	0.017961	1.573661	1.573661	7.723548e-16	0.860436	0.860436	4.428572e-16	...	0.070876	0.086116	0.094675	0.060767	0.077430	0.080386	0.065543	0.084178	0.086085	0.058622
13	0.001	0.240874	0.231855	0.014054	1.297091	1.297091	5.680424e-16	0.728938	0.728938	3.918803e-16	...	0.058281	0.072255	0.080973	0.060641	0.075015	0.062271	0.053188	0.071580	0.074156	0.059342
14	0.001	0.228499	0.217800	0.016514	1.292254	1.292254	6.235812e-16	0.733632	0.733632	3.202068e-16	...	0.057819	0.072048	0.077743	0.060554	0.064170	0.058100	0.050960	0.069839	0.069910	0.060365
15	0.001	0.226133	0.220316	0.009189	1.251510	1.251510	5.845645e-16	0.733736	0.733736	3.450215e-16	...	0.046235	0.071547	0.080614	0.051037	0.063813	0.061969	0.042648	0.070665	0.075863	0.050906
16	0.001	0.237374	0.229404	0.012378	1.247807	1.247807	5.615974e-16	0.627951	0.627951	3.502303e-16	...	0.052356	0.076138	0.078765	0.058288	0.071931	0.064517	0.047449	0.075091	0.072447	0.057872
17	0.001	0.217837	0.211715	0.010002	0.759947	0.759947	6.834218e-16	0.443084	0.443084	3.860493e-16	...	0.044880	0.073938	0.071497	0.051963	0.059587	0.053435	0.041205	0.072887	0.066112	0.052133
18	0.001	0.220208	0.209443	0.015330	0.966665	0.966665	9.531940e-16	0.478997	0.478997	3.706317e-16	...	0.053611	0.080192	0.074547	0.046108	0.053177	0.058037	0.046907	0.076213	0.068482	0.045196
19	0.001	0.220329	0.211520	0.011462	0.711764	0.711764	7.946863e-16	0.442580	0.442580	4.584795e-16	...	0.053765	0.073294	0.075590	0.049785	0.059939	0.063352	0.048045	0.069521	0.072163	0.048131