What additional options are available in CDR?#

In addition to the four necessary ingredients shown in How do I use CDR?, there are additional parameters in CDR.

One option is how many circuits are in the training set (default is 10). This can be changed as follows.

import warnings
warnings.filterwarnings("ignore")

import numpy as np

import cirq
from mitiq import cdr, Observable, PauliString
from mitiq.interface.mitiq_cirq import compute_density_matrix

a, b = cirq.LineQubit.range(2)
circuit = cirq.Circuit(
    cirq.H.on(a), # Clifford
    cirq.H.on(b), # Clifford
    cirq.rz(1.75).on(a),
    cirq.rz(2.31).on(b),
    cirq.CNOT.on(a, b),  # Clifford
    cirq.rz(-1.17).on(b),
    cirq.rz(3.23).on(a),
    cirq.rx(np.pi / 2).on(a),  # Clifford
    cirq.rx(np.pi / 2).on(b),  # Clifford
)
circuit = 5 * circuit

obs = Observable(PauliString("ZZ"), PauliString("X", coeff=-1.75))

def simulate(circuit: cirq.Circuit) -> np.ndarray:
    return compute_density_matrix(circuit, noise_level=(0.0,))

cdr.execute_with_cdr(
    circuit,
    compute_density_matrix,
    observable=obs,
    simulator=simulate,
    seed=0,
    num_training_circuits=20,
).real
before: [array([[ 0.834364  +1.0323221e-08j, -0.02658513+7.5414695e-02j,
        -0.00364555+6.0732979e-02j, -0.02219004-5.2193210e-02j],
       [-0.02658516-7.5414769e-02j,  0.05705505-2.1024118e-08j,
         0.00668314-6.3313493e-03j, -0.00279339+1.8779658e-03j],
       [-0.00364545-6.0733065e-02j,  0.00668317+6.3313707e-03j,
         0.05266568+2.8994888e-08j, -0.00493391+3.6680887e-03j],
       [-0.02219001+5.2193295e-02j, -0.00279342-1.8778936e-03j,
        -0.00493392-3.6681308e-03j,  0.05591451+1.8027587e-08j]],
      dtype=complex64), array([[ 7.1660799e-01-3.5965368e-08j, -8.3556734e-03-1.3385539e-02j,
         2.5589150e-01+1.3633078e-02j,  3.7273150e-03+7.3546119e-02j],
       [-8.3556883e-03+1.3385480e-02j,  5.8574304e-02+5.7533378e-09j,
        -5.5822060e-03+9.0991631e-03j,  1.3058417e-04-4.4034827e-03j],
       [ 2.5589141e-01-1.3633034e-02j, -5.5820667e-03-9.0992358e-03j,
         1.6270992e-01-1.6828688e-08j,  2.2262981e-04+2.8643413e-02j],
       [ 3.7273646e-03-7.3546134e-02j,  1.3057362e-04+4.4034994e-03j,
         2.2268484e-04-2.8643426e-02j,  6.2106416e-02-2.3732520e-08j]],
      dtype=complex64), array([[ 7.4048907e-01+1.8855184e-08j, -2.1953665e-02+1.1273532e-02j,
        -2.9282912e-03+3.9611671e-02j,  5.5836681e-03-2.4743517e-01j],
       [-2.1953728e-02-1.1273518e-02j,  5.4185554e-02+1.5268474e-08j,
        -7.1597297e-04-9.2425884e-04j, -6.7050784e-04+5.6728683e-03j],
       [-2.9282991e-03-3.9611753e-02j, -7.1596610e-04+9.2425878e-04j,
         6.2404253e-02+6.9703909e-09j, -1.6231678e-02+2.6380932e-03j],
       [ 5.5836407e-03+2.4743514e-01j, -6.7050033e-04-5.6728502e-03j,
        -1.6231660e-02-2.6380033e-03j,  1.4291985e-01-4.0162721e-08j]],
      dtype=complex64), array([[ 8.3592302e-01+5.0096631e-08j, -7.6393145e-03+1.3242954e-02j,
        -1.4859510e-03+1.6235875e-02j,  5.7167518e-03+1.0907008e-02j],
       [-7.6393150e-03-1.3242988e-02j,  5.4499924e-02-5.4536851e-09j,
        -1.2350495e-03+2.6152572e-03j,  7.4324000e-04-4.2930958e-03j],
       [-1.4859207e-03-1.6235912e-02j, -1.2350403e-03-2.6152385e-03j,
         5.9418790e-02+8.8374597e-09j, -2.2007222e-03+1.0756132e-03j],
       [ 5.7167322e-03-1.0907005e-02j,  7.4328354e-04+4.2930897e-03j,
        -2.2007665e-03-1.0755820e-03j,  5.0156984e-02-3.7880753e-08j]],
      dtype=complex64), array([[ 8.2866400e-01+7.0039299e-09j, -3.6428056e-03+1.2763038e-02j,
        -1.2833637e-03+8.3762661e-02j,  5.2158656e-03+4.5568284e-02j],
       [-3.6427514e-03-1.2763045e-02j,  5.3567640e-02-1.8636115e-09j,
        -4.0607515e-04+2.1665290e-03j,  9.3983137e-04-3.6913259e-03j],
       [-1.2835386e-03-8.3762631e-02j, -4.0618569e-04-2.1665269e-03j,
         6.4742200e-02-7.4532931e-09j,  1.8096166e-03+4.9312162e-04j],
       [ 5.2157920e-03-4.5568250e-02j,  9.3983428e-04+3.6913010e-03j,
         1.8095622e-03-4.9314549e-04j,  5.3024836e-02+3.2289922e-08j]],
      dtype=complex64), array([[ 0.7326348 +2.12773568e-08j, -0.00684327+2.67736137e-01j,
        -0.06178094+1.29675865e-02j,  0.00481563-1.05993813e-02j],
       [-0.00684327-2.67736107e-01j,  0.15350677+1.07310365e-08j,
         0.0028221 +1.89366471e-02j, -0.00641869-7.72016589e-03j],
       [-0.06178089-1.29675167e-02j,  0.00282208-1.89366825e-02j,
         0.06340896-4.75860560e-08j, -0.00272749+2.74218200e-03j],
       [ 0.00481561+1.05993431e-02j, -0.00641874+7.72020454e-03j,
        -0.00272752-2.74215243e-03j,  0.05044794+3.54846819e-08j]],
      dtype=complex64), array([[ 0.6552759 +3.7215276e-08j,  0.07901978+3.3942494e-03j,
         0.00138213-2.1167463e-01j,  0.00859066-2.1127746e-01j],
       [ 0.07901983-3.3943122e-03j,  0.06158101+1.8403304e-08j,
        -0.00186687-3.2321818e-02j,  0.00355495-3.3479635e-02j],
       [ 0.00138205+2.1167460e-01j, -0.00186682+3.2321751e-02j,
         0.14896268-2.2165104e-08j,  0.07551191+5.4452540e-03j],
       [ 0.00859062+2.1127743e-01j,  0.00355499+3.3479657e-02j,
         0.07551188-5.4452540e-03j,  0.13417916-3.6511569e-09j]],
      dtype=complex64), array([[ 0.69177073+6.7061094e-08j, -0.13663831+8.7493164e-03j,
         0.24736083+1.6792776e-02j, -0.04588495+1.0166333e-02j],
       [-0.13663831-8.7493397e-03j,  0.08818609+7.0349313e-09j,
        -0.05514681-5.1882747e-03j,  0.01236551-6.1934441e-03j],
       [ 0.24736083-1.6792670e-02j, -0.05514686+5.1882202e-03j,
         0.15973139-6.7952088e-09j, -0.02114664+7.5427103e-03j],
       [-0.04588495-1.0166289e-02j,  0.01236551+6.1933687e-03j,
        -0.02114664-7.5427196e-03j,  0.06031048-3.3773201e-08j]],
      dtype=complex64), array([[ 8.2866400e-01+7.0039299e-09j, -3.6428056e-03+1.2763038e-02j,
        -1.2833637e-03+8.3762661e-02j,  5.2158656e-03+4.5568284e-02j],
       [-3.6427514e-03-1.2763045e-02j,  5.3567640e-02-1.8636115e-09j,
        -4.0607515e-04+2.1665290e-03j,  9.3983137e-04-3.6913259e-03j],
       [-1.2835386e-03-8.3762631e-02j, -4.0618569e-04-2.1665269e-03j,
         6.4742200e-02-7.4532931e-09j,  1.8096166e-03+4.9312162e-04j],
       [ 5.2157920e-03-4.5568250e-02j,  9.3983428e-04+3.6913010e-03j,
         1.8095622e-03-4.9314549e-04j,  5.3024836e-02+3.2289922e-08j]],
      dtype=complex64), array([[ 8.0584228e-01+1.36807330e-08j, -7.6748347e-03-1.29124910e-01j,
        -1.8121132e-03-1.57404523e-02j,  1.3633000e-02+1.36094745e-02j],
       [-7.6748021e-03+1.29124925e-01j,  8.2166970e-02-1.00660369e-08j,
         3.3087966e-03+6.23110868e-03j,  4.2409802e-04-1.32682885e-03j],
       [-1.8121297e-03+1.57404132e-02j,  3.3088136e-03-6.23109471e-03j,
         6.1252434e-02-1.84793727e-08j, -2.2653728e-03+2.16471730e-03j],
       [ 1.3632931e-02-1.36094233e-02j,  4.2410789e-04+1.32689206e-03j,
        -2.2653833e-03-2.16466608e-03j,  5.0736737e-02+7.53051044e-09j]],
      dtype=complex64), array([[ 0.7348158 +5.4365490e-09j,  0.00519519+9.6373772e-03j,
        -0.00119433+2.7626354e-01j,  0.00445   +3.7570268e-02j],
       [ 0.00519521-9.6374182e-03j,  0.05434548+6.2189529e-09j,
         0.00249342+4.9275579e-03j,  0.00102966-4.9615572e-03j],
       [-0.0011944 -2.7626356e-01j,  0.00249338-4.9275775e-03j,
         0.15666467-2.1671829e-08j,  0.01034987-2.3754248e-03j],
       [ 0.00445002-3.7570275e-02j,  0.00102961+4.9615679e-03j,
         0.01034987+2.3754267e-03j,  0.0541728 -4.6095856e-08j]],
      dtype=complex64), array([[ 0.7303692 -4.6914291e-08j, -0.00671595-4.6991937e-02j,
        -0.00153839+2.7334008e-01j,  0.02921825+6.3442844e-03j],
       [-0.00671591+4.6991967e-02j,  0.05996459+8.9815231e-09j,
        -0.02123797+1.9385744e-03j,  0.00095032-1.8466730e-03j],
       [-0.0015384 -2.7334017e-01j, -0.02123796-1.9384829e-03j,
         0.15520062-2.0638026e-08j, -0.00225044-1.1226836e-02j],
       [ 0.02921824-6.3442285e-03j,  0.00095032+1.8466574e-03j,
        -0.00225049+1.1226811e-02j,  0.05446438-2.3618423e-08j]],
      dtype=complex64), array([[ 7.4048907e-01+1.8855184e-08j, -2.1953665e-02+1.1273532e-02j,
        -2.9282912e-03+3.9611671e-02j,  5.5836681e-03-2.4743517e-01j],
       [-2.1953728e-02-1.1273518e-02j,  5.4185554e-02+1.5268474e-08j,
        -7.1597297e-04-9.2425884e-04j, -6.7050784e-04+5.6728683e-03j],
       [-2.9282991e-03-3.9611753e-02j, -7.1596610e-04+9.2425878e-04j,
         6.2404253e-02+6.9703909e-09j, -1.6231678e-02+2.6380932e-03j],
       [ 5.5836407e-03+2.4743514e-01j, -6.7050033e-04-5.6728502e-03j,
        -1.6231660e-02-2.6380033e-03j,  1.4291985e-01-4.0162721e-08j]],
      dtype=complex64), array([[ 8.1165522e-01+1.7081619e-10j, -2.8481334e-03+1.6511092e-02j,
        -1.6642824e-03+1.3591245e-02j, -1.2725127e-01+6.2095892e-02j],
       [-2.8480731e-03-1.6510988e-02j,  5.3261168e-02-2.3657607e-08j,
        -1.4542077e-03+2.1699166e-03j,  5.6893716e-04-2.9918721e-03j],
       [-1.6643771e-03-1.3591264e-02j, -1.4542179e-03-2.1699492e-03j,
         6.0488246e-02-1.7318792e-08j, -2.5297895e-03+4.6629021e-03j],
       [-1.2725134e-01-6.2095899e-02j,  5.6895288e-04+2.9918139e-03j,
        -2.5297978e-03-4.6628984e-03j,  7.4594148e-02-2.5900393e-08j]],
      dtype=complex64), array([[ 0.7164814 +8.7486214e-08j, -0.00984803+8.4812324e-03j,
         0.25776216-3.2660324e-02j,  0.00358783+1.3511073e-02j],
       [-0.00984801-8.4810862e-03j,  0.05990861-2.0504910e-08j,
        -0.0066279 +1.0916360e-05j,  0.00196414-4.4527720e-03j],
       [ 0.25776216+3.2660462e-02j, -0.00662793-1.0960846e-05j,
         0.16881207+1.4531444e-08j, -0.0012401 +7.3497649e-03j],
       [ 0.00358778-1.3511001e-02j,  0.00196414+4.4528181e-03j,
        -0.00124015-7.3497705e-03j,  0.05479664-2.1849894e-08j]],
      dtype=complex64), array([[ 7.8383213e-01+2.81810184e-08j, -5.7976055e-03-1.22100346e-01j,
        -1.9611390e-03+4.19761688e-02j, -1.3354060e-01+1.40471058e-02j],
       [-5.7976409e-03+1.22100346e-01j,  8.0027901e-02-6.53358834e-09j,
        -7.4805021e-03+5.80707379e-03j,  2.7790127e-04-2.81919651e-02j],
       [-1.9611872e-03-4.19761352e-02j, -7.4804332e-03-5.80715993e-03j,
         6.1985299e-02-3.90344148e-08j, -3.4528906e-03+9.52372514e-03j],
       [-1.3354062e-01-1.40470630e-02j,  2.7795197e-04+2.81919800e-02j,
        -3.4528587e-03-9.52369533e-03j,  7.4153423e-02-3.06925365e-08j]],
      dtype=complex64), array([[ 0.650179  +2.5912561e-08j, -0.00509587+2.2399218e-01j,
        -0.00156063-2.1010837e-01j,  0.09465057+1.4242536e-02j],
       [-0.00509588-2.2399227e-01j,  0.13236877+4.4625250e-09j,
        -0.08479845-3.0616270e-03j,  0.00273259-4.2530123e-02j],
       [-0.00156069+2.1010841e-01j, -0.08479847+3.0615830e-03j,
         0.14586474-6.6301695e-08j, -0.00699474+3.7840575e-02j],
       [ 0.09465055-1.4242533e-02j,  0.00273258+4.2530157e-02j,
        -0.00699475-3.7840601e-02j,  0.07158601+5.3854563e-08j]],
      dtype=complex64), array([[ 7.7616566e-01+5.8393936e-11j, -1.5222766e-01+1.5468483e-02j,
        -4.7151523e-04+4.6500467e-02j,  6.2284535e-03+1.5164027e-01j],
       [-1.5222777e-01-1.5468478e-02j,  8.4030807e-02+1.4770590e-08j,
        -7.4236502e-04-7.1713198e-03j,  3.0418922e-04-3.5917260e-02j],
       [-4.7160947e-04-4.6500463e-02j, -7.4236875e-04+7.1712602e-03j,
         5.8321442e-02-8.9711500e-09j,  5.0501772e-03-1.6470080e-03j],
       [ 6.2285289e-03-1.5164024e-01j,  3.0416908e-04+3.5917297e-02j,
         5.0501991e-03+1.6470449e-03j,  8.1480414e-02+1.8255785e-09j]],
      dtype=complex64), array([[ 8.3586717e-01+3.1225373e-08j, -7.9309624e-03+1.3623768e-02j,
        -1.4814821e-03+1.7414011e-02j,  5.5247322e-03+1.0771623e-02j],
       [-7.9309139e-03-1.3623705e-02j,  5.5220861e-02+9.4955430e-09j,
        -1.3891585e-03+2.7161520e-03j,  7.4574450e-04-4.0653264e-03j],
       [-1.4814760e-03-1.7413978e-02j, -1.3891702e-03-2.7160654e-03j,
         5.9123032e-02-5.2740088e-08j, -2.3936017e-03+1.1090079e-03j],
       [ 5.5246847e-03-1.0771607e-02j,  7.4569497e-04+4.0653571e-03j,
        -2.3936925e-03-1.1089970e-03j,  4.9787737e-02+2.7269579e-08j]],
      dtype=complex64), array([[ 0.64936894+1.1028973e-07j, -0.00516633+3.1837565e-04j,
         0.25776228-1.6454293e-01j,  0.00293456+1.7829204e-02j],
       [-0.00516637-3.1839361e-04j,  0.05395474+2.3760181e-08j,
        -0.00356504+3.0578130e-03j,  0.00196412-6.1861826e-03j],
       [ 0.2577622 +1.6454303e-01j, -0.00356506-3.0578549e-03j,
         0.23592462-8.2796427e-09j, -0.0059076 +1.2496237e-02j],
       [ 0.00293455-1.7829128e-02j,  0.00196411+6.1861486e-03j,
        -0.00590762-1.2496176e-02j,  0.06075055-4.3813881e-08j]],
      dtype=complex64), array([[ 0.65808547+5.8511507e-09j, -0.01144172+2.3439643e-01j,
        -0.09135848+7.2046039e-03j,  0.0043944 -2.1605411e-01j],
       [-0.01144168-2.3439652e-01j,  0.14531295+1.0153628e-08j,
         0.00240085+2.9836286e-02j, -0.085287  -1.9572207e-03j],
       [-0.09135843-7.2045820e-03j,  0.0024009 -2.9836332e-02j,
         0.06785845-2.9723276e-08j, -0.00595745+3.6081851e-02j],
       [ 0.00439438+2.1605411e-01j, -0.08528706+1.9572007e-03j,
        -0.00595748-3.6081851e-02j,  0.12874176+4.6780446e-08j]],
      dtype=complex64)]
after:  [array([[ 0.834364  +1.0323221e-08j, -0.02658513+7.5414695e-02j,
        -0.00364555+6.0732979e-02j, -0.02219004-5.2193210e-02j],
       [-0.02658516-7.5414769e-02j,  0.05705505-2.1024118e-08j,
         0.00668314-6.3313493e-03j, -0.00279339+1.8779658e-03j],
       [-0.00364545-6.0733065e-02j,  0.00668317+6.3313707e-03j,
         0.05266568+2.8994888e-08j, -0.00493391+3.6680887e-03j],
       [-0.02219001+5.2193295e-02j, -0.00279342-1.8778936e-03j,
        -0.00493392-3.6681308e-03j,  0.05591451+1.8027587e-08j]],
      dtype=complex64), array([[ 7.1660799e-01-3.5965368e-08j, -8.3556734e-03-1.3385539e-02j,
         2.5589150e-01+1.3633078e-02j,  3.7273150e-03+7.3546119e-02j],
       [-8.3556883e-03+1.3385480e-02j,  5.8574304e-02+5.7533378e-09j,
        -5.5822060e-03+9.0991631e-03j,  1.3058417e-04-4.4034827e-03j],
       [ 2.5589141e-01-1.3633034e-02j, -5.5820667e-03-9.0992358e-03j,
         1.6270992e-01-1.6828688e-08j,  2.2262981e-04+2.8643413e-02j],
       [ 3.7273646e-03-7.3546134e-02j,  1.3057362e-04+4.4034994e-03j,
         2.2268484e-04-2.8643426e-02j,  6.2106416e-02-2.3732520e-08j]],
      dtype=complex64), array([[ 7.4048907e-01+1.8855184e-08j, -2.1953665e-02+1.1273532e-02j,
        -2.9282912e-03+3.9611671e-02j,  5.5836681e-03-2.4743517e-01j],
       [-2.1953728e-02-1.1273518e-02j,  5.4185554e-02+1.5268474e-08j,
        -7.1597297e-04-9.2425884e-04j, -6.7050784e-04+5.6728683e-03j],
       [-2.9282991e-03-3.9611753e-02j, -7.1596610e-04+9.2425878e-04j,
         6.2404253e-02+6.9703909e-09j, -1.6231678e-02+2.6380932e-03j],
       [ 5.5836407e-03+2.4743514e-01j, -6.7050033e-04-5.6728502e-03j,
        -1.6231660e-02-2.6380033e-03j,  1.4291985e-01-4.0162721e-08j]],
      dtype=complex64), array([[ 8.3592302e-01+5.0096631e-08j, -7.6393145e-03+1.3242954e-02j,
        -1.4859510e-03+1.6235875e-02j,  5.7167518e-03+1.0907008e-02j],
       [-7.6393150e-03-1.3242988e-02j,  5.4499924e-02-5.4536851e-09j,
        -1.2350495e-03+2.6152572e-03j,  7.4324000e-04-4.2930958e-03j],
       [-1.4859207e-03-1.6235912e-02j, -1.2350403e-03-2.6152385e-03j,
         5.9418790e-02+8.8374597e-09j, -2.2007222e-03+1.0756132e-03j],
       [ 5.7167322e-03-1.0907005e-02j,  7.4328354e-04+4.2930897e-03j,
        -2.2007665e-03-1.0755820e-03j,  5.0156984e-02-3.7880753e-08j]],
      dtype=complex64), array([[ 8.2866400e-01+7.0039299e-09j, -3.6428056e-03+1.2763038e-02j,
        -1.2833637e-03+8.3762661e-02j,  5.2158656e-03+4.5568284e-02j],
       [-3.6427514e-03-1.2763045e-02j,  5.3567640e-02-1.8636115e-09j,
        -4.0607515e-04+2.1665290e-03j,  9.3983137e-04-3.6913259e-03j],
       [-1.2835386e-03-8.3762631e-02j, -4.0618569e-04-2.1665269e-03j,
         6.4742200e-02-7.4532931e-09j,  1.8096166e-03+4.9312162e-04j],
       [ 5.2157920e-03-4.5568250e-02j,  9.3983428e-04+3.6913010e-03j,
         1.8095622e-03-4.9314549e-04j,  5.3024836e-02+3.2289922e-08j]],
      dtype=complex64), array([[ 0.7326348 +2.12773568e-08j, -0.00684327+2.67736137e-01j,
        -0.06178094+1.29675865e-02j,  0.00481563-1.05993813e-02j],
       [-0.00684327-2.67736107e-01j,  0.15350677+1.07310365e-08j,
         0.0028221 +1.89366471e-02j, -0.00641869-7.72016589e-03j],
       [-0.06178089-1.29675167e-02j,  0.00282208-1.89366825e-02j,
         0.06340896-4.75860560e-08j, -0.00272749+2.74218200e-03j],
       [ 0.00481561+1.05993431e-02j, -0.00641874+7.72020454e-03j,
        -0.00272752-2.74215243e-03j,  0.05044794+3.54846819e-08j]],
      dtype=complex64), array([[ 0.6552759 +3.7215276e-08j,  0.07901978+3.3942494e-03j,
         0.00138213-2.1167463e-01j,  0.00859066-2.1127746e-01j],
       [ 0.07901983-3.3943122e-03j,  0.06158101+1.8403304e-08j,
        -0.00186687-3.2321818e-02j,  0.00355495-3.3479635e-02j],
       [ 0.00138205+2.1167460e-01j, -0.00186682+3.2321751e-02j,
         0.14896268-2.2165104e-08j,  0.07551191+5.4452540e-03j],
       [ 0.00859062+2.1127743e-01j,  0.00355499+3.3479657e-02j,
         0.07551188-5.4452540e-03j,  0.13417916-3.6511569e-09j]],
      dtype=complex64), array([[ 0.69177073+6.7061094e-08j, -0.13663831+8.7493164e-03j,
         0.24736083+1.6792776e-02j, -0.04588495+1.0166333e-02j],
       [-0.13663831-8.7493397e-03j,  0.08818609+7.0349313e-09j,
        -0.05514681-5.1882747e-03j,  0.01236551-6.1934441e-03j],
       [ 0.24736083-1.6792670e-02j, -0.05514686+5.1882202e-03j,
         0.15973139-6.7952088e-09j, -0.02114664+7.5427103e-03j],
       [-0.04588495-1.0166289e-02j,  0.01236551+6.1933687e-03j,
        -0.02114664-7.5427196e-03j,  0.06031048-3.3773201e-08j]],
      dtype=complex64), array([[ 8.2866400e-01+7.0039299e-09j, -3.6428056e-03+1.2763038e-02j,
        -1.2833637e-03+8.3762661e-02j,  5.2158656e-03+4.5568284e-02j],
       [-3.6427514e-03-1.2763045e-02j,  5.3567640e-02-1.8636115e-09j,
        -4.0607515e-04+2.1665290e-03j,  9.3983137e-04-3.6913259e-03j],
       [-1.2835386e-03-8.3762631e-02j, -4.0618569e-04-2.1665269e-03j,
         6.4742200e-02-7.4532931e-09j,  1.8096166e-03+4.9312162e-04j],
       [ 5.2157920e-03-4.5568250e-02j,  9.3983428e-04+3.6913010e-03j,
         1.8095622e-03-4.9314549e-04j,  5.3024836e-02+3.2289922e-08j]],
      dtype=complex64), array([[ 8.0584228e-01+1.36807330e-08j, -7.6748347e-03-1.29124910e-01j,
        -1.8121132e-03-1.57404523e-02j,  1.3633000e-02+1.36094745e-02j],
       [-7.6748021e-03+1.29124925e-01j,  8.2166970e-02-1.00660369e-08j,
         3.3087966e-03+6.23110868e-03j,  4.2409802e-04-1.32682885e-03j],
       [-1.8121297e-03+1.57404132e-02j,  3.3088136e-03-6.23109471e-03j,
         6.1252434e-02-1.84793727e-08j, -2.2653728e-03+2.16471730e-03j],
       [ 1.3632931e-02-1.36094233e-02j,  4.2410789e-04+1.32689206e-03j,
        -2.2653833e-03-2.16466608e-03j,  5.0736737e-02+7.53051044e-09j]],
      dtype=complex64), array([[ 0.7348158 +5.4365490e-09j,  0.00519519+9.6373772e-03j,
        -0.00119433+2.7626354e-01j,  0.00445   +3.7570268e-02j],
       [ 0.00519521-9.6374182e-03j,  0.05434548+6.2189529e-09j,
         0.00249342+4.9275579e-03j,  0.00102966-4.9615572e-03j],
       [-0.0011944 -2.7626356e-01j,  0.00249338-4.9275775e-03j,
         0.15666467-2.1671829e-08j,  0.01034987-2.3754248e-03j],
       [ 0.00445002-3.7570275e-02j,  0.00102961+4.9615679e-03j,
         0.01034987+2.3754267e-03j,  0.0541728 -4.6095856e-08j]],
      dtype=complex64), array([[ 0.7303692 -4.6914291e-08j, -0.00671595-4.6991937e-02j,
        -0.00153839+2.7334008e-01j,  0.02921825+6.3442844e-03j],
       [-0.00671591+4.6991967e-02j,  0.05996459+8.9815231e-09j,
        -0.02123797+1.9385744e-03j,  0.00095032-1.8466730e-03j],
       [-0.0015384 -2.7334017e-01j, -0.02123796-1.9384829e-03j,
         0.15520062-2.0638026e-08j, -0.00225044-1.1226836e-02j],
       [ 0.02921824-6.3442285e-03j,  0.00095032+1.8466574e-03j,
        -0.00225049+1.1226811e-02j,  0.05446438-2.3618423e-08j]],
      dtype=complex64), array([[ 7.4048907e-01+1.8855184e-08j, -2.1953665e-02+1.1273532e-02j,
        -2.9282912e-03+3.9611671e-02j,  5.5836681e-03-2.4743517e-01j],
       [-2.1953728e-02-1.1273518e-02j,  5.4185554e-02+1.5268474e-08j,
        -7.1597297e-04-9.2425884e-04j, -6.7050784e-04+5.6728683e-03j],
       [-2.9282991e-03-3.9611753e-02j, -7.1596610e-04+9.2425878e-04j,
         6.2404253e-02+6.9703909e-09j, -1.6231678e-02+2.6380932e-03j],
       [ 5.5836407e-03+2.4743514e-01j, -6.7050033e-04-5.6728502e-03j,
        -1.6231660e-02-2.6380033e-03j,  1.4291985e-01-4.0162721e-08j]],
      dtype=complex64), array([[ 8.1165522e-01+1.7081619e-10j, -2.8481334e-03+1.6511092e-02j,
        -1.6642824e-03+1.3591245e-02j, -1.2725127e-01+6.2095892e-02j],
       [-2.8480731e-03-1.6510988e-02j,  5.3261168e-02-2.3657607e-08j,
        -1.4542077e-03+2.1699166e-03j,  5.6893716e-04-2.9918721e-03j],
       [-1.6643771e-03-1.3591264e-02j, -1.4542179e-03-2.1699492e-03j,
         6.0488246e-02-1.7318792e-08j, -2.5297895e-03+4.6629021e-03j],
       [-1.2725134e-01-6.2095899e-02j,  5.6895288e-04+2.9918139e-03j,
        -2.5297978e-03-4.6628984e-03j,  7.4594148e-02-2.5900393e-08j]],
      dtype=complex64), array([[ 0.7164814 +8.7486214e-08j, -0.00984803+8.4812324e-03j,
         0.25776216-3.2660324e-02j,  0.00358783+1.3511073e-02j],
       [-0.00984801-8.4810862e-03j,  0.05990861-2.0504910e-08j,
        -0.0066279 +1.0916360e-05j,  0.00196414-4.4527720e-03j],
       [ 0.25776216+3.2660462e-02j, -0.00662793-1.0960846e-05j,
         0.16881207+1.4531444e-08j, -0.0012401 +7.3497649e-03j],
       [ 0.00358778-1.3511001e-02j,  0.00196414+4.4528181e-03j,
        -0.00124015-7.3497705e-03j,  0.05479664-2.1849894e-08j]],
      dtype=complex64), array([[ 7.8383213e-01+2.81810184e-08j, -5.7976055e-03-1.22100346e-01j,
        -1.9611390e-03+4.19761688e-02j, -1.3354060e-01+1.40471058e-02j],
       [-5.7976409e-03+1.22100346e-01j,  8.0027901e-02-6.53358834e-09j,
        -7.4805021e-03+5.80707379e-03j,  2.7790127e-04-2.81919651e-02j],
       [-1.9611872e-03-4.19761352e-02j, -7.4804332e-03-5.80715993e-03j,
         6.1985299e-02-3.90344148e-08j, -3.4528906e-03+9.52372514e-03j],
       [-1.3354062e-01-1.40470630e-02j,  2.7795197e-04+2.81919800e-02j,
        -3.4528587e-03-9.52369533e-03j,  7.4153423e-02-3.06925365e-08j]],
      dtype=complex64), array([[ 0.650179  +2.5912561e-08j, -0.00509587+2.2399218e-01j,
        -0.00156063-2.1010837e-01j,  0.09465057+1.4242536e-02j],
       [-0.00509588-2.2399227e-01j,  0.13236877+4.4625250e-09j,
        -0.08479845-3.0616270e-03j,  0.00273259-4.2530123e-02j],
       [-0.00156069+2.1010841e-01j, -0.08479847+3.0615830e-03j,
         0.14586474-6.6301695e-08j, -0.00699474+3.7840575e-02j],
       [ 0.09465055-1.4242533e-02j,  0.00273258+4.2530157e-02j,
        -0.00699475-3.7840601e-02j,  0.07158601+5.3854563e-08j]],
      dtype=complex64), array([[ 7.7616566e-01+5.8393936e-11j, -1.5222766e-01+1.5468483e-02j,
        -4.7151523e-04+4.6500467e-02j,  6.2284535e-03+1.5164027e-01j],
       [-1.5222777e-01-1.5468478e-02j,  8.4030807e-02+1.4770590e-08j,
        -7.4236502e-04-7.1713198e-03j,  3.0418922e-04-3.5917260e-02j],
       [-4.7160947e-04-4.6500463e-02j, -7.4236875e-04+7.1712602e-03j,
         5.8321442e-02-8.9711500e-09j,  5.0501772e-03-1.6470080e-03j],
       [ 6.2285289e-03-1.5164024e-01j,  3.0416908e-04+3.5917297e-02j,
         5.0501991e-03+1.6470449e-03j,  8.1480414e-02+1.8255785e-09j]],
      dtype=complex64), array([[ 8.3586717e-01+3.1225373e-08j, -7.9309624e-03+1.3623768e-02j,
        -1.4814821e-03+1.7414011e-02j,  5.5247322e-03+1.0771623e-02j],
       [-7.9309139e-03-1.3623705e-02j,  5.5220861e-02+9.4955430e-09j,
        -1.3891585e-03+2.7161520e-03j,  7.4574450e-04-4.0653264e-03j],
       [-1.4814760e-03-1.7413978e-02j, -1.3891702e-03-2.7160654e-03j,
         5.9123032e-02-5.2740088e-08j, -2.3936017e-03+1.1090079e-03j],
       [ 5.5246847e-03-1.0771607e-02j,  7.4569497e-04+4.0653571e-03j,
        -2.3936925e-03-1.1089970e-03j,  4.9787737e-02+2.7269579e-08j]],
      dtype=complex64), array([[ 0.64936894+1.1028973e-07j, -0.00516633+3.1837565e-04j,
         0.25776228-1.6454293e-01j,  0.00293456+1.7829204e-02j],
       [-0.00516637-3.1839361e-04j,  0.05395474+2.3760181e-08j,
        -0.00356504+3.0578130e-03j,  0.00196412-6.1861826e-03j],
       [ 0.2577622 +1.6454303e-01j, -0.00356506-3.0578549e-03j,
         0.23592462-8.2796427e-09j, -0.0059076 +1.2496237e-02j],
       [ 0.00293455-1.7829128e-02j,  0.00196411+6.1861486e-03j,
        -0.00590762-1.2496176e-02j,  0.06075055-4.3813881e-08j]],
      dtype=complex64), array([[ 0.65808547+5.8511507e-09j, -0.01144172+2.3439643e-01j,
        -0.09135848+7.2046039e-03j,  0.0043944 -2.1605411e-01j],
       [-0.01144168-2.3439652e-01j,  0.14531295+1.0153628e-08j,
         0.00240085+2.9836286e-02j, -0.085287  -1.9572207e-03j],
       [-0.09135843-7.2045820e-03j,  0.0024009 -2.9836332e-02j,
         0.06785845-2.9723276e-08j, -0.00595745+3.6081851e-02j],
       [ 0.00439438+2.1605411e-01j, -0.08528706+1.9572007e-03j,
        -0.00595748-3.6081851e-02j,  0.12874176+4.6780446e-08j]],
      dtype=complex64)]
before: [array([[ 8.6253977e-01-1.3038515e-08j,  1.8626451e-09-3.0020982e-02j,
         3.3415234e-01+7.4505802e-09j, -7.4505802e-09+7.7492625e-02j],
       [-4.2840835e-08+3.0021094e-02j,  1.0449262e-03+2.7939674e-08j,
         7.4505802e-09+1.1630265e-02j, -2.6971563e-03+7.4505802e-09j],
       [ 3.3415240e-01+4.6566120e-09j, -2.5145710e-08-1.1630297e-02j,
         1.2945236e-01+1.4901161e-08j,  5.2154064e-08+3.0021038e-02j],
       [ 5.4948028e-08-7.7492610e-02j, -2.6971623e-03+3.4458932e-08j,
         2.9802322e-08-3.0021049e-02j,  6.9621690e-03-7.4505815e-09j]],
      dtype=complex64), array([[ 8.6780393e-01-1.4901161e-08j, -1.4870569e-02-0.0000000e+00j,
        -1.4901161e-08+3.8385205e-02j, -2.2351742e-08-3.3619171e-01j],
       [-1.4870569e-02-2.1071173e-08j,  2.5484091e-04-2.9802322e-08j,
        -7.9162419e-09-6.5785961e-04j,  0.0000000e+00+5.7609896e-03j],
       [ 1.5803380e-08-3.8385104e-02j,  0.0000000e+00+6.5786485e-04j,
         1.6979622e-03+0.0000000e+00j, -1.4870606e-02-2.6193447e-09j],
       [ 2.1653250e-08+3.3619171e-01j,  1.4901161e-08-5.7609798e-03j,
        -1.4870577e-02-2.9802322e-08j,  1.3024241e-01-1.4435500e-08j]],
      dtype=complex64), array([[ 9.9999923e-01+1.86264515e-09j,  2.7939675e-08+0.00000000e+00j,
        -6.5192573e-08+2.23517400e-08j, -7.4505802e-09+1.67638063e-08j],
       [ 6.1467276e-08+4.21468478e-08j,  0.0000000e+00-1.30385125e-08j,
         7.4505802e-09-9.31322663e-09j,  1.8626434e-09+2.23517400e-08j],
       [ 8.7544322e-08+3.16101350e-08j,  1.7763568e-15+1.02445483e-07j,
         1.7912410e-07+1.67638081e-08j, -6.8917871e-08-0.00000000e+00j],
       [ 2.1073422e-08+9.31322219e-09j,  5.5879377e-09-3.16101385e-08j,
         9.3132257e-09-4.21468513e-08j,  1.0536711e-08+1.67638046e-08j]],
      dtype=complex64), array([[ 9.9005508e-01-6.7753717e-08j,  3.9344933e-03+0.0000000e+00j,
        -7.4505806e-08+8.8948905e-02j, -7.0780516e-08+4.3792624e-02j],
       [ 3.9344942e-03+0.0000000e+00j,  1.5678628e-05+1.6763806e-08j,
        -2.1071173e-08+3.5347440e-04j, -8.5710781e-09+1.7400853e-04j],
       [-7.3094270e-08-8.8948868e-02j,  7.4505806e-09-3.5350997e-04j,
         7.9913838e-03-5.1222742e-09j,  3.9344528e-03+1.5832484e-08j],
       [ 3.4240657e-08-4.3792553e-02j,  3.3527613e-08-1.7401643e-04j,
         3.9344071e-03+4.7730282e-09j,  1.9370328e-03-1.6298145e-08j]],
      dtype=complex64), array([[ 8.6254013e-01-1.3969840e-08j,  4.7497451e-08+3.3415249e-01j,
        -7.7492662e-02-9.3132257e-08j,  7.0780516e-08-3.0021057e-02j],
       [ 3.6321580e-08-3.3415246e-01j,  1.2945232e-01+2.5145710e-08j,
         3.7252916e-09+3.0021008e-02j, -1.1630296e-02-1.8626448e-08j],
       [-7.7492669e-02-1.5832484e-08j,  5.2386895e-09-3.0021030e-02j,
         6.9621345e-03+1.3969837e-08j,  1.9557772e-08+2.6970999e-03j],
       [ 5.2386895e-09+3.0021045e-02j, -1.1630285e-02+1.5832484e-08j,
         8.3819023e-09-2.6971742e-03j,  1.0448545e-03-2.7939675e-09j]],
      dtype=complex64), array([[ 7.5603455e-01-1.8626451e-08j,  1.1346774e-01+0.0000000e+00j,
        -1.4901161e-08-2.9289168e-01j, -1.4901161e-08-2.9289168e-01j],
       [ 1.1346774e-01+2.0489097e-08j,  1.7029455e-02+1.8626451e-08j,
         1.4901161e-08-4.3957964e-02j,  1.6763806e-08-4.3957934e-02j],
       [ 1.6763806e-08+2.9289168e-01j,  1.4901161e-08+4.3957964e-02j,
         1.1346769e-01-1.8626451e-08j,  1.1346774e-01-1.8626451e-08j],
       [-2.0489097e-08+2.9289168e-01j, -1.4901161e-08+4.3957949e-02j,
         1.1346774e-01+1.4901161e-08j,  1.1346774e-01+1.8626451e-08j]],
      dtype=complex64), array([[ 0.83504844+3.7252903e-08j, -0.16961884-0.0000000e+00j,
         0.323502  -2.2351742e-08j, -0.06571122-4.4703484e-08j],
       [-0.16961884+2.0489097e-08j,  0.0344538 +7.4505806e-09j,
        -0.06571127-0.0000000e+00j,  0.01334757-2.2351742e-08j],
       [ 0.32350203-1.4901161e-08j, -0.06571121-2.9802322e-08j,
         0.12532628-2.2351742e-08j, -0.02545688-1.4901161e-08j],
       [-0.06571124-1.5832484e-08j,  0.01334759+0.0000000e+00j,
        -0.02545684-7.9162419e-09j,  0.00517091-6.5192580e-09j]],
      dtype=complex64), array([[ 9.9005508e-01-6.7753717e-08j,  3.9344933e-03+0.0000000e+00j,
        -7.4505806e-08+8.8948905e-02j, -7.0780516e-08+4.3792624e-02j],
       [ 3.9344942e-03+0.0000000e+00j,  1.5678628e-05+1.6763806e-08j,
        -2.1071173e-08+3.5347440e-04j, -8.5710781e-09+1.7400853e-04j],
       [-7.3094270e-08-8.8948868e-02j,  7.4505806e-09-3.5350997e-04j,
         7.9913838e-03-5.1222742e-09j,  3.9344528e-03+1.5832484e-08j],
       [ 3.4240657e-08-4.3792553e-02j,  3.3527613e-08-1.7401643e-04j,
         3.9344071e-03+4.7730282e-09j,  1.9370328e-03-1.6298145e-08j]],
      dtype=complex64), array([[ 9.5849919e-01-4.0978193e-08j, -1.8626448e-08-1.9469473e-01j,
         2.6077030e-08-4.2396747e-02j,  8.6118355e-03-3.3527609e-08j],
       [-7.4505797e-09+1.9469473e-01j,  3.9547347e-02-2.2351742e-08j,
         8.6117899e-03+1.4901161e-08j,  4.4408921e-16+1.7493137e-03j],
       [ 2.6077034e-08+4.2396795e-02j,  8.6118281e-03+1.8626453e-08j,
         1.8753344e-03+1.8626448e-08j, -4.0978190e-08+3.8089231e-04j],
       [ 8.6118281e-03-5.9604645e-08j,  3.7252903e-08-1.7492590e-03j,
        -6.6613381e-16-3.8090159e-04j,  7.7382661e-05+7.4505788e-09j]],
      dtype=complex64), array([[ 8.6780417e-01-2.2817403e-08j,  1.4870634e-02+0.0000000e+00j,
        -1.6763806e-08+3.3619183e-01j, -1.4901161e-08+3.8385198e-02j],
       [ 1.4870623e-02+0.0000000e+00j,  2.5481984e-04-9.7788870e-09j,
         0.0000000e+00+5.7609593e-03j,  6.7520887e-09+6.5769104e-04j],
       [-7.9162419e-09-3.3619177e-01j,  0.0000000e+00-5.7609444e-03j,
         1.3024236e-01+4.0978193e-08j,  1.4870654e-02+0.0000000e+00j],
       [ 3.1606760e-08-3.8385171e-02j, -1.8626451e-08-6.5769104e-04j,
         1.4870680e-02-1.0535587e-08j,  1.6978437e-03+6.5192580e-09j]],
      dtype=complex64), array([[ 8.6253971e-01-4.2840835e-08j, -2.6077029e-08-7.7492654e-02j,
         1.8626425e-09+3.3415234e-01j,  3.0021027e-02-1.8626448e-08j],
       [-9.3132257e-09+7.7492669e-02j,  6.9621503e-03+0.0000000e+00j,
        -3.0021047e-02-3.5390251e-08j,  1.7763568e-15+2.6971083e-03j],
       [ 9.3132266e-09-3.3415228e-01j, -3.0021012e-02+1.4901160e-08j,
         1.2945236e-01-9.3132275e-09j,  1.4901159e-08-1.1630300e-02j],
       [ 3.0021058e-02-3.5390258e-08j,  1.1175872e-08-2.6971828e-03j,
        -3.5390254e-08+1.1630325e-02j,  1.0448811e-03+3.3527609e-08j]],
      dtype=complex64), array([[ 8.6780393e-01-1.4901161e-08j, -1.4870569e-02-0.0000000e+00j,
        -1.4901161e-08+3.8385205e-02j, -2.2351742e-08-3.3619171e-01j],
       [-1.4870569e-02-2.1071173e-08j,  2.5484091e-04-2.9802322e-08j,
        -7.9162419e-09-6.5785961e-04j,  0.0000000e+00+5.7609896e-03j],
       [ 1.5803380e-08-3.8385104e-02j,  0.0000000e+00+6.5786485e-04j,
         1.6979622e-03+0.0000000e+00j, -1.4870606e-02-2.6193447e-09j],
       [ 2.1653250e-08+3.3619171e-01j,  1.4901161e-08-5.7609798e-03j,
        -1.4870577e-02-2.9802322e-08j,  1.3024241e-01-1.4435500e-08j]],
      dtype=complex64), array([[ 0.96037465-1.4901160e-08j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j, -0.17961617+7.6109201e-02j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j],
       [-0.17961593-7.6109096e-02j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.03962464-5.5879354e-08j]],
      dtype=complex64), array([[ 8.6358488e-01-2.2351740e-08j,  0.0000000e+00+0.0000000e+00j,
         3.3684957e-01-6.5862343e-02j,  0.0000000e+00+0.0000000e+00j],
       [ 7.4505802e-09+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
        -1.5805067e-08+2.1073424e-08j,  0.0000000e+00+0.0000000e+00j],
       [ 3.3684963e-01+6.5862320e-02j,  0.0000000e+00+0.0000000e+00j,
         1.3641447e-01-2.9802321e-08j,  0.0000000e+00+0.0000000e+00j],
       [ 2.8975958e-08+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
         0.0000000e+00-2.6341780e-08j,  0.0000000e+00+0.0000000e+00j]],
      dtype=complex64), array([[ 9.2231983e-01-3.3527609e-08j,  1.1175870e-08-1.8734580e-01j,
         1.1175869e-08+3.8054511e-02j, -1.8734588e-01-3.7252903e-09j],
       [-3.5527137e-15+1.8734586e-01j,  3.8054556e-02-3.7252899e-08j,
        -7.7298349e-03-7.4505788e-09j, -7.4505806e-09-3.8054559e-02j],
       [ 1.1175870e-08-3.8054571e-02j, -7.7298349e-03+3.3527609e-08j,
         1.5701069e-03+4.0978190e-08j, -1.1175871e-08+7.7298596e-03j],
       [-1.8734580e-01+1.4901160e-08j,  7.4505797e-09+3.8054571e-02j,
        -1.4901159e-08-7.7298377e-03j,  3.8054630e-02+1.4901159e-08j]],
      dtype=complex64), array([[ 7.56034434e-01-1.3038515e-08j,  2.04890931e-08+2.9289156e-01j,
        -2.14204174e-08-2.9289168e-01j,  1.13467783e-01-3.4458935e-08j],
       [-1.86264515e-08-2.9289162e-01j,  1.13467649e-01+7.4505806e-08j,
        -1.13467738e-01-8.3819023e-09j,  2.51457060e-08-4.3957990e-02j],
       [ 3.35276127e-08+2.9289168e-01j, -1.13467745e-01+2.2351740e-08j,
         1.13467753e-01-4.3772154e-08j, -1.02445465e-08+4.3957993e-02j],
       [ 1.13467783e-01-9.3132257e-09j, -4.28408349e-08+4.3958005e-02j,
         4.19095159e-08-4.3957993e-02j,  1.70295686e-02+1.3969839e-08j]],
      dtype=complex64), array([[ 9.2232001e-01+0.0000000e+00j, -1.8734589e-01-0.0000000e+00j,
        -1.4901161e-08+3.8054556e-02j,  3.1664968e-08+1.8734588e-01j],
       [-1.8734586e-01+2.0489097e-08j,  3.8054623e-02+0.0000000e+00j,
        -2.9802322e-08-7.7298423e-03j, -5.3551048e-09-3.8054526e-02j],
       [-6.3097104e-08-3.8054567e-02j, -1.1175871e-08+7.7298582e-03j,
         1.5701696e-03-3.4924597e-09j,  7.7297911e-03-9.8953024e-09j],
       [-9.3132257e-09-1.8734589e-01j,  2.9802322e-08+3.8054548e-02j,
         7.7297683e-03+3.3527613e-08j,  3.8054504e-02+2.6077032e-08j]],
      dtype=complex64), array([[ 9.99999166e-01-3.7252899e-08j, -1.49011612e-08-5.9604645e-08j,
        -8.94069601e-08-3.7252899e-08j, -5.21540606e-08+7.4505806e-09j],
       [ 4.84287703e-08+6.3220270e-08j,  6.32202699e-08+1.1175867e-08j,
        -6.70552254e-08-5.5879351e-08j, -1.11758744e-08-7.4505824e-09j],
       [-8.56816698e-08+1.2644054e-07j, -2.10734257e-08+3.7252903e-09j,
        -5.26835571e-08+1.8626448e-08j,  4.09781897e-08-1.0536713e-08j],
       [ 1.05367111e-08-1.4901159e-08j,  2.98023171e-08+5.2683561e-08j,
        -2.23517418e-08-2.1073422e-08j,  8.88178420e-16+7.4505797e-09j]],
      dtype=complex64), array([[0.7730641 +2.9802321e-08j, 0.        +0.0000000e+00j,
        0.33684963-2.4893372e-01j, 0.        +0.0000000e+00j],
       [0.        +0.0000000e+00j, 0.        +0.0000000e+00j,
        0.        +0.0000000e+00j, 0.        +0.0000000e+00j],
       [0.33684963+2.4893366e-01j, 0.        +0.0000000e+00j,
        0.2269355 -2.9802321e-08j, 0.        +0.0000000e+00j],
       [0.        +0.0000000e+00j, 0.        +0.0000000e+00j,
        0.        +0.0000000e+00j, 0.        +0.0000000e+00j]],
      dtype=complex64), array([[ 7.56034434e-01-1.8626450e-08j,  1.11758700e-08+2.9289156e-01j,
        -1.13467731e-01+1.4901159e-08j,  2.98023206e-08-2.9289165e-01j],
       [ 1.11758700e-08-2.9289162e-01j,  1.13467619e-01+1.8626450e-08j,
         2.98023206e-08+4.3957923e-02j, -1.13467753e-01-1.4901159e-08j],
       [-1.13467768e-01-5.1688403e-08j,  1.16415322e-08-4.3957938e-02j,
         1.70294661e-02-6.5192576e-09j,  4.65661243e-09+4.3957941e-02j],
       [ 8.84756624e-09+2.9289162e-01j, -1.13467716e-01+5.4482371e-08j,
        -9.31322575e-10-4.3957941e-02j,  1.13467701e-01+1.2107193e-08j]],
      dtype=complex64)]
after:  [array([[ 8.6253977e-01-1.3038515e-08j,  1.8626451e-09-3.0020982e-02j,
         3.3415234e-01+7.4505802e-09j, -7.4505802e-09+7.7492625e-02j],
       [-4.2840835e-08+3.0021094e-02j,  1.0449262e-03+2.7939674e-08j,
         7.4505802e-09+1.1630265e-02j, -2.6971563e-03+7.4505802e-09j],
       [ 3.3415240e-01+4.6566120e-09j, -2.5145710e-08-1.1630297e-02j,
         1.2945236e-01+1.4901161e-08j,  5.2154064e-08+3.0021038e-02j],
       [ 5.4948028e-08-7.7492610e-02j, -2.6971623e-03+3.4458932e-08j,
         2.9802322e-08-3.0021049e-02j,  6.9621690e-03-7.4505815e-09j]],
      dtype=complex64), array([[ 8.6780393e-01-1.4901161e-08j, -1.4870569e-02-0.0000000e+00j,
        -1.4901161e-08+3.8385205e-02j, -2.2351742e-08-3.3619171e-01j],
       [-1.4870569e-02-2.1071173e-08j,  2.5484091e-04-2.9802322e-08j,
        -7.9162419e-09-6.5785961e-04j,  0.0000000e+00+5.7609896e-03j],
       [ 1.5803380e-08-3.8385104e-02j,  0.0000000e+00+6.5786485e-04j,
         1.6979622e-03+0.0000000e+00j, -1.4870606e-02-2.6193447e-09j],
       [ 2.1653250e-08+3.3619171e-01j,  1.4901161e-08-5.7609798e-03j,
        -1.4870577e-02-2.9802322e-08j,  1.3024241e-01-1.4435500e-08j]],
      dtype=complex64), array([[ 9.9999923e-01+1.86264515e-09j,  2.7939675e-08+0.00000000e+00j,
        -6.5192573e-08+2.23517400e-08j, -7.4505802e-09+1.67638063e-08j],
       [ 6.1467276e-08+4.21468478e-08j,  0.0000000e+00-1.30385125e-08j,
         7.4505802e-09-9.31322663e-09j,  1.8626434e-09+2.23517400e-08j],
       [ 8.7544322e-08+3.16101350e-08j,  1.7763568e-15+1.02445483e-07j,
         1.7912410e-07+1.67638081e-08j, -6.8917871e-08-0.00000000e+00j],
       [ 2.1073422e-08+9.31322219e-09j,  5.5879377e-09-3.16101385e-08j,
         9.3132257e-09-4.21468513e-08j,  1.0536711e-08+1.67638046e-08j]],
      dtype=complex64), array([[ 9.9005508e-01-6.7753717e-08j,  3.9344933e-03+0.0000000e+00j,
        -7.4505806e-08+8.8948905e-02j, -7.0780516e-08+4.3792624e-02j],
       [ 3.9344942e-03+0.0000000e+00j,  1.5678628e-05+1.6763806e-08j,
        -2.1071173e-08+3.5347440e-04j, -8.5710781e-09+1.7400853e-04j],
       [-7.3094270e-08-8.8948868e-02j,  7.4505806e-09-3.5350997e-04j,
         7.9913838e-03-5.1222742e-09j,  3.9344528e-03+1.5832484e-08j],
       [ 3.4240657e-08-4.3792553e-02j,  3.3527613e-08-1.7401643e-04j,
         3.9344071e-03+4.7730282e-09j,  1.9370328e-03-1.6298145e-08j]],
      dtype=complex64), array([[ 8.6254013e-01-1.3969840e-08j,  4.7497451e-08+3.3415249e-01j,
        -7.7492662e-02-9.3132257e-08j,  7.0780516e-08-3.0021057e-02j],
       [ 3.6321580e-08-3.3415246e-01j,  1.2945232e-01+2.5145710e-08j,
         3.7252916e-09+3.0021008e-02j, -1.1630296e-02-1.8626448e-08j],
       [-7.7492669e-02-1.5832484e-08j,  5.2386895e-09-3.0021030e-02j,
         6.9621345e-03+1.3969837e-08j,  1.9557772e-08+2.6970999e-03j],
       [ 5.2386895e-09+3.0021045e-02j, -1.1630285e-02+1.5832484e-08j,
         8.3819023e-09-2.6971742e-03j,  1.0448545e-03-2.7939675e-09j]],
      dtype=complex64), array([[ 7.5603455e-01-1.8626451e-08j,  1.1346774e-01+0.0000000e+00j,
        -1.4901161e-08-2.9289168e-01j, -1.4901161e-08-2.9289168e-01j],
       [ 1.1346774e-01+2.0489097e-08j,  1.7029455e-02+1.8626451e-08j,
         1.4901161e-08-4.3957964e-02j,  1.6763806e-08-4.3957934e-02j],
       [ 1.6763806e-08+2.9289168e-01j,  1.4901161e-08+4.3957964e-02j,
         1.1346769e-01-1.8626451e-08j,  1.1346774e-01-1.8626451e-08j],
       [-2.0489097e-08+2.9289168e-01j, -1.4901161e-08+4.3957949e-02j,
         1.1346774e-01+1.4901161e-08j,  1.1346774e-01+1.8626451e-08j]],
      dtype=complex64), array([[ 0.83504844+3.7252903e-08j, -0.16961884-0.0000000e+00j,
         0.323502  -2.2351742e-08j, -0.06571122-4.4703484e-08j],
       [-0.16961884+2.0489097e-08j,  0.0344538 +7.4505806e-09j,
        -0.06571127-0.0000000e+00j,  0.01334757-2.2351742e-08j],
       [ 0.32350203-1.4901161e-08j, -0.06571121-2.9802322e-08j,
         0.12532628-2.2351742e-08j, -0.02545688-1.4901161e-08j],
       [-0.06571124-1.5832484e-08j,  0.01334759+0.0000000e+00j,
        -0.02545684-7.9162419e-09j,  0.00517091-6.5192580e-09j]],
      dtype=complex64), array([[ 9.9005508e-01-6.7753717e-08j,  3.9344933e-03+0.0000000e+00j,
        -7.4505806e-08+8.8948905e-02j, -7.0780516e-08+4.3792624e-02j],
       [ 3.9344942e-03+0.0000000e+00j,  1.5678628e-05+1.6763806e-08j,
        -2.1071173e-08+3.5347440e-04j, -8.5710781e-09+1.7400853e-04j],
       [-7.3094270e-08-8.8948868e-02j,  7.4505806e-09-3.5350997e-04j,
         7.9913838e-03-5.1222742e-09j,  3.9344528e-03+1.5832484e-08j],
       [ 3.4240657e-08-4.3792553e-02j,  3.3527613e-08-1.7401643e-04j,
         3.9344071e-03+4.7730282e-09j,  1.9370328e-03-1.6298145e-08j]],
      dtype=complex64), array([[ 9.5849919e-01-4.0978193e-08j, -1.8626448e-08-1.9469473e-01j,
         2.6077030e-08-4.2396747e-02j,  8.6118355e-03-3.3527609e-08j],
       [-7.4505797e-09+1.9469473e-01j,  3.9547347e-02-2.2351742e-08j,
         8.6117899e-03+1.4901161e-08j,  4.4408921e-16+1.7493137e-03j],
       [ 2.6077034e-08+4.2396795e-02j,  8.6118281e-03+1.8626453e-08j,
         1.8753344e-03+1.8626448e-08j, -4.0978190e-08+3.8089231e-04j],
       [ 8.6118281e-03-5.9604645e-08j,  3.7252903e-08-1.7492590e-03j,
        -6.6613381e-16-3.8090159e-04j,  7.7382661e-05+7.4505788e-09j]],
      dtype=complex64), array([[ 8.6780417e-01-2.2817403e-08j,  1.4870634e-02+0.0000000e+00j,
        -1.6763806e-08+3.3619183e-01j, -1.4901161e-08+3.8385198e-02j],
       [ 1.4870623e-02+0.0000000e+00j,  2.5481984e-04-9.7788870e-09j,
         0.0000000e+00+5.7609593e-03j,  6.7520887e-09+6.5769104e-04j],
       [-7.9162419e-09-3.3619177e-01j,  0.0000000e+00-5.7609444e-03j,
         1.3024236e-01+4.0978193e-08j,  1.4870654e-02+0.0000000e+00j],
       [ 3.1606760e-08-3.8385171e-02j, -1.8626451e-08-6.5769104e-04j,
         1.4870680e-02-1.0535587e-08j,  1.6978437e-03+6.5192580e-09j]],
      dtype=complex64), array([[ 8.6253971e-01-4.2840835e-08j, -2.6077029e-08-7.7492654e-02j,
         1.8626425e-09+3.3415234e-01j,  3.0021027e-02-1.8626448e-08j],
       [-9.3132257e-09+7.7492669e-02j,  6.9621503e-03+0.0000000e+00j,
        -3.0021047e-02-3.5390251e-08j,  1.7763568e-15+2.6971083e-03j],
       [ 9.3132266e-09-3.3415228e-01j, -3.0021012e-02+1.4901160e-08j,
         1.2945236e-01-9.3132275e-09j,  1.4901159e-08-1.1630300e-02j],
       [ 3.0021058e-02-3.5390258e-08j,  1.1175872e-08-2.6971828e-03j,
        -3.5390254e-08+1.1630325e-02j,  1.0448811e-03+3.3527609e-08j]],
      dtype=complex64), array([[ 8.6780393e-01-1.4901161e-08j, -1.4870569e-02-0.0000000e+00j,
        -1.4901161e-08+3.8385205e-02j, -2.2351742e-08-3.3619171e-01j],
       [-1.4870569e-02-2.1071173e-08j,  2.5484091e-04-2.9802322e-08j,
        -7.9162419e-09-6.5785961e-04j,  0.0000000e+00+5.7609896e-03j],
       [ 1.5803380e-08-3.8385104e-02j,  0.0000000e+00+6.5786485e-04j,
         1.6979622e-03+0.0000000e+00j, -1.4870606e-02-2.6193447e-09j],
       [ 2.1653250e-08+3.3619171e-01j,  1.4901161e-08-5.7609798e-03j,
        -1.4870577e-02-2.9802322e-08j,  1.3024241e-01-1.4435500e-08j]],
      dtype=complex64), array([[ 0.96037465-1.4901160e-08j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j, -0.17961617+7.6109201e-02j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j],
       [-0.17961593-7.6109096e-02j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.03962464-5.5879354e-08j]],
      dtype=complex64), array([[ 8.6358488e-01-2.2351740e-08j,  0.0000000e+00+0.0000000e+00j,
         3.3684957e-01-6.5862343e-02j,  0.0000000e+00+0.0000000e+00j],
       [ 7.4505802e-09+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
        -1.5805067e-08+2.1073424e-08j,  0.0000000e+00+0.0000000e+00j],
       [ 3.3684963e-01+6.5862320e-02j,  0.0000000e+00+0.0000000e+00j,
         1.3641447e-01-2.9802321e-08j,  0.0000000e+00+0.0000000e+00j],
       [ 2.8975958e-08+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
         0.0000000e+00-2.6341780e-08j,  0.0000000e+00+0.0000000e+00j]],
      dtype=complex64), array([[ 9.2231983e-01-3.3527609e-08j,  1.1175870e-08-1.8734580e-01j,
         1.1175869e-08+3.8054511e-02j, -1.8734588e-01-3.7252903e-09j],
       [-3.5527137e-15+1.8734586e-01j,  3.8054556e-02-3.7252899e-08j,
        -7.7298349e-03-7.4505788e-09j, -7.4505806e-09-3.8054559e-02j],
       [ 1.1175870e-08-3.8054571e-02j, -7.7298349e-03+3.3527609e-08j,
         1.5701069e-03+4.0978190e-08j, -1.1175871e-08+7.7298596e-03j],
       [-1.8734580e-01+1.4901160e-08j,  7.4505797e-09+3.8054571e-02j,
        -1.4901159e-08-7.7298377e-03j,  3.8054630e-02+1.4901159e-08j]],
      dtype=complex64), array([[ 7.56034434e-01-1.3038515e-08j,  2.04890931e-08+2.9289156e-01j,
        -2.14204174e-08-2.9289168e-01j,  1.13467783e-01-3.4458935e-08j],
       [-1.86264515e-08-2.9289162e-01j,  1.13467649e-01+7.4505806e-08j,
        -1.13467738e-01-8.3819023e-09j,  2.51457060e-08-4.3957990e-02j],
       [ 3.35276127e-08+2.9289168e-01j, -1.13467745e-01+2.2351740e-08j,
         1.13467753e-01-4.3772154e-08j, -1.02445465e-08+4.3957993e-02j],
       [ 1.13467783e-01-9.3132257e-09j, -4.28408349e-08+4.3958005e-02j,
         4.19095159e-08-4.3957993e-02j,  1.70295686e-02+1.3969839e-08j]],
      dtype=complex64), array([[ 9.2232001e-01+0.0000000e+00j, -1.8734589e-01-0.0000000e+00j,
        -1.4901161e-08+3.8054556e-02j,  3.1664968e-08+1.8734588e-01j],
       [-1.8734586e-01+2.0489097e-08j,  3.8054623e-02+0.0000000e+00j,
        -2.9802322e-08-7.7298423e-03j, -5.3551048e-09-3.8054526e-02j],
       [-6.3097104e-08-3.8054567e-02j, -1.1175871e-08+7.7298582e-03j,
         1.5701696e-03-3.4924597e-09j,  7.7297911e-03-9.8953024e-09j],
       [-9.3132257e-09-1.8734589e-01j,  2.9802322e-08+3.8054548e-02j,
         7.7297683e-03+3.3527613e-08j,  3.8054504e-02+2.6077032e-08j]],
      dtype=complex64), array([[ 9.99999166e-01-3.7252899e-08j, -1.49011612e-08-5.9604645e-08j,
        -8.94069601e-08-3.7252899e-08j, -5.21540606e-08+7.4505806e-09j],
       [ 4.84287703e-08+6.3220270e-08j,  6.32202699e-08+1.1175867e-08j,
        -6.70552254e-08-5.5879351e-08j, -1.11758744e-08-7.4505824e-09j],
       [-8.56816698e-08+1.2644054e-07j, -2.10734257e-08+3.7252903e-09j,
        -5.26835571e-08+1.8626448e-08j,  4.09781897e-08-1.0536713e-08j],
       [ 1.05367111e-08-1.4901159e-08j,  2.98023171e-08+5.2683561e-08j,
        -2.23517418e-08-2.1073422e-08j,  8.88178420e-16+7.4505797e-09j]],
      dtype=complex64), array([[0.7730641 +2.9802321e-08j, 0.        +0.0000000e+00j,
        0.33684963-2.4893372e-01j, 0.        +0.0000000e+00j],
       [0.        +0.0000000e+00j, 0.        +0.0000000e+00j,
        0.        +0.0000000e+00j, 0.        +0.0000000e+00j],
       [0.33684963+2.4893366e-01j, 0.        +0.0000000e+00j,
        0.2269355 -2.9802321e-08j, 0.        +0.0000000e+00j],
       [0.        +0.0000000e+00j, 0.        +0.0000000e+00j,
        0.        +0.0000000e+00j, 0.        +0.0000000e+00j]],
      dtype=complex64), array([[ 7.56034434e-01-1.8626450e-08j,  1.11758700e-08+2.9289156e-01j,
        -1.13467731e-01+1.4901159e-08j,  2.98023206e-08-2.9289165e-01j],
       [ 1.11758700e-08-2.9289162e-01j,  1.13467619e-01+1.8626450e-08j,
         2.98023206e-08+4.3957923e-02j, -1.13467753e-01-1.4901159e-08j],
       [-1.13467768e-01-5.1688403e-08j,  1.16415322e-08-4.3957938e-02j,
         1.70294661e-02-6.5192576e-09j,  4.65661243e-09+4.3957941e-02j],
       [ 8.84756624e-09+2.9289162e-01j, -1.13467716e-01+5.4482371e-08j,
        -9.31322575e-10-4.3957941e-02j,  1.13467701e-01+1.2107193e-08j]],
      dtype=complex64)]
1.0310969874371074

Fit function#

Another option is which fit function to use for regression (default is cdr.linear_fit_function()).

cdr.execute_with_cdr(
    circuit,
    compute_density_matrix,
    observable=obs,
    simulator=simulate,
    seed=0,
    fit_function=cdr.linear_fit_function_no_intercept,
).real
before: [array([[ 0.834364  +1.0323221e-08j, -0.02658513+7.5414695e-02j,
        -0.00364555+6.0732979e-02j, -0.02219004-5.2193210e-02j],
       [-0.02658516-7.5414769e-02j,  0.05705505-2.1024118e-08j,
         0.00668314-6.3313493e-03j, -0.00279339+1.8779658e-03j],
       [-0.00364545-6.0733065e-02j,  0.00668317+6.3313707e-03j,
         0.05266568+2.8994888e-08j, -0.00493391+3.6680887e-03j],
       [-0.02219001+5.2193295e-02j, -0.00279342-1.8778936e-03j,
        -0.00493392-3.6681308e-03j,  0.05591451+1.8027587e-08j]],
      dtype=complex64), array([[ 7.76819885e-01+2.8100930e-08j, -5.58661530e-03+1.4318428e-02j,
        -9.46061627e-04+1.3535254e-02j,  5.86175965e-03+2.2320658e-01j],
       [-5.58655662e-03-1.4318414e-02j,  5.17000929e-02-1.3525877e-08j,
        -1.15746120e-03+3.2776746e-03j,  1.88693334e-03-4.1656657e-03j],
       [-9.46051092e-04-1.3535351e-02j, -1.15737994e-03-3.2777004e-03j,
         5.64673133e-02-1.6997818e-08j,  3.88911780e-04-1.7258264e-03j],
       [ 5.86170796e-03-2.2320664e-01j,  1.88689039e-03+4.1656597e-03j,
         3.88893444e-04+1.7258924e-03j,  1.15011364e-01-3.8337145e-08j]],
      dtype=complex64), array([[ 8.2884151e-01+6.7653834e-09j, -6.6016787e-03+1.6165609e-02j,
        -7.0029169e-02+1.4509528e-02j,  6.3505936e-03+4.3827597e-02j],
       [-6.6016531e-03-1.6165607e-02j,  5.3434804e-02+2.8630694e-08j,
        -6.6371396e-04+3.9500273e-03j,  9.1461744e-04-4.5878775e-03j],
       [-7.0029229e-02-1.4509435e-02j, -6.6371489e-04-3.9500687e-03j,
         6.5377332e-02-4.4463899e-09j, -2.1428524e-03-2.9578670e-03j],
       [ 6.3506123e-03-4.3827567e-02j,  9.1454014e-04+4.5878757e-03j,
        -2.1428019e-03+2.9578651e-03j,  5.2345213e-02-1.8027587e-08j]],
      dtype=complex64), array([[ 0.7368466 +9.28514599e-09j, -0.00717952+2.68528253e-01j,
        -0.03139642+1.29676014e-02j,  0.00461674+1.41246198e-03j],
       [-0.00717949-2.68528283e-01j,  0.15387781+3.68665418e-08j,
         0.00262322+6.92480197e-03j, -0.00178938-7.72018032e-03j],
       [-0.03139638-1.29675055e-02j,  0.00262316-6.92487182e-03j,
         0.0591972 -3.91992288e-08j, -0.00239126+1.95010751e-03j],
       [ 0.00461676-1.41248165e-03j, -0.00178945+7.72024412e-03j,
        -0.00239126-1.95004523e-03j,  0.05007696+4.42702799e-08j]],
      dtype=complex64), array([[ 0.7344505 +2.7578674e-08j, -0.00475519+3.6147174e-03j,
        -0.02662884-2.3756994e-01j,  0.00849045+1.1399767e-02j],
       [-0.00475515-3.6147232e-03j,  0.04903223+2.3730214e-08j,
        -0.00196706+3.6670689e-03j,  0.00106779-7.5842985e-03j],
       [-0.02662886+2.3756994e-01j, -0.00196706-3.6671152e-03j,
         0.16123626-3.6661397e-08j, -0.00718139+5.2249338e-03j],
       [ 0.00849046-1.1399814e-02j,  0.0010678 +7.5843562e-03j,
        -0.00718141-5.2249650e-03j,  0.05527976-2.3960716e-08j]],
      dtype=complex64), array([[ 8.3291727e-01+1.16034649e-08j, -7.0233946e-03+1.33959102e-02j,
        -3.5412636e-02+4.94074784e-02j,  5.8111153e-03+1.07869962e-02j],
       [-7.0234262e-03-1.33959735e-02j,  5.3987991e-02+2.41220697e-08j,
        -4.8853963e-04+2.75066192e-03j,  6.4495590e-04-4.12295433e-03j],
       [-3.5412643e-02-4.94075716e-02j, -4.8854697e-04-2.75064888e-03j,
         6.2424410e-02-5.15172704e-09j, -2.0410705e-03+5.15588385e-04j],
       [ 5.8110934e-03-1.07870279e-02j,  6.4496347e-04+4.12294827e-03j,
        -2.0410840e-03-5.15527849e-04j,  5.0668914e-02-3.08066355e-08j]],
      dtype=complex64), array([[ 0.8240487 -2.2475502e-08j, -0.00782481-5.1324282e-02j,
        -0.00155572-5.2954964e-02j,  0.0129534 +8.6540971e-03j],
       [-0.00782478+5.1324304e-02j,  0.05985524-8.3338119e-09j,
         0.00288604+4.8846495e-03j,  0.00090631-2.7158554e-03j],
       [-0.00155573+5.2954979e-02j,  0.00288605-4.8846672e-03j,
         0.06631878-3.9542671e-09j, -0.00241776+1.3916147e-03j],
       [ 0.01295331-8.6541381e-03j,  0.00090634+2.7157837e-03j,
        -0.00241771-1.3915818e-03j,  0.04977586-3.5370582e-09j]],
      dtype=complex64), array([[ 8.0709493e-01+3.8682484e-09j, -6.0132286e-03-1.5639849e-02j,
         5.3515942e-03+1.4442093e-02j,  6.3939211e-03+1.6107586e-01j],
       [-6.0132323e-03+1.5639851e-02j,  5.3069532e-02-3.0103603e-08j,
        -1.6188417e-03+4.2199870e-03j, -5.2310061e-03-3.8588261e-03j],
       [ 5.3515891e-03-1.4442094e-02j, -1.6188041e-03-4.2200526e-03j,
         5.7426184e-02+4.3887642e-08j, -3.0263152e-04-4.8724478e-04j],
       [ 6.3939607e-03-1.6107583e-01j, -5.2309814e-03+3.8588180e-03j,
        -3.0260216e-04+4.8724297e-04j,  8.2408234e-02-3.6511569e-08j]],
      dtype=complex64), array([[ 0.80626065+1.2096187e-08j, -0.00701643-1.2976864e-01j,
        -0.00832904+1.5610894e-02j,  0.00739879+4.6804309e-02j],
       [-0.00701649+1.2976868e-01j,  0.08138669-2.7597467e-08j,
        -0.00236199+4.6784761e-03j, -0.0059638 -2.4532783e-03j],
       [-0.00832905-1.5610908e-02j, -0.002362  -4.6784743e-03j,
         0.05919627-1.9760387e-08j, -0.0016201 +1.0374445e-03j],
       [ 0.00739873-4.6804313e-02j, -0.00596385+2.4533472e-03j,
        -0.00162004-1.0374590e-03j,  0.05315534-1.6601355e-08j]],
      dtype=complex64), array([[ 8.2206905e-01+2.9663997e-08j, -8.3712935e-03+1.3300889e-02j,
        -1.4896818e-03-8.4201768e-02j,  6.2557445e-03+9.5908651e-03j],
       [-8.3712675e-03-1.3300917e-02j,  5.5446003e-02-1.0236609e-08j,
        -2.6821685e-03+3.9266194e-03j,  7.4012164e-04-4.8199911e-03j],
       [-1.4896267e-03+8.4201768e-02j, -2.6821806e-03-3.9266339e-03j,
         7.3617667e-02-3.0910363e-09j, -2.9479815e-03+1.7061614e-03j],
       [ 6.2556984e-03-9.5908446e-03j,  7.4014795e-04+4.8200288e-03j,
        -2.9480141e-03-1.7061502e-03j,  4.8865963e-02+3.6283371e-08j]],
      dtype=complex64), array([[ 0.80626065+1.2096187e-08j, -0.00701643-1.2976864e-01j,
        -0.00832904+1.5610894e-02j,  0.00739879+4.6804309e-02j],
       [-0.00701649+1.2976868e-01j,  0.08138669-2.7597467e-08j,
        -0.00236199+4.6784761e-03j, -0.0059638 -2.4532783e-03j],
       [-0.00832905-1.5610908e-02j, -0.002362  -4.6784743e-03j,
         0.05919627-1.9760387e-08j, -0.0016201 +1.0374445e-03j],
       [ 0.00739873-4.6804313e-02j, -0.00596385+2.4533472e-03j,
        -0.00162004-1.0374590e-03j,  0.05315534-1.6601355e-08j]],
      dtype=complex64)]
after:  [array([[ 0.834364  +1.0323221e-08j, -0.02658513+7.5414695e-02j,
        -0.00364555+6.0732979e-02j, -0.02219004-5.2193210e-02j],
       [-0.02658516-7.5414769e-02j,  0.05705505-2.1024118e-08j,
         0.00668314-6.3313493e-03j, -0.00279339+1.8779658e-03j],
       [-0.00364545-6.0733065e-02j,  0.00668317+6.3313707e-03j,
         0.05266568+2.8994888e-08j, -0.00493391+3.6680887e-03j],
       [-0.02219001+5.2193295e-02j, -0.00279342-1.8778936e-03j,
        -0.00493392-3.6681308e-03j,  0.05591451+1.8027587e-08j]],
      dtype=complex64), array([[ 7.76819885e-01+2.8100930e-08j, -5.58661530e-03+1.4318428e-02j,
        -9.46061627e-04+1.3535254e-02j,  5.86175965e-03+2.2320658e-01j],
       [-5.58655662e-03-1.4318414e-02j,  5.17000929e-02-1.3525877e-08j,
        -1.15746120e-03+3.2776746e-03j,  1.88693334e-03-4.1656657e-03j],
       [-9.46051092e-04-1.3535351e-02j, -1.15737994e-03-3.2777004e-03j,
         5.64673133e-02-1.6997818e-08j,  3.88911780e-04-1.7258264e-03j],
       [ 5.86170796e-03-2.2320664e-01j,  1.88689039e-03+4.1656597e-03j,
         3.88893444e-04+1.7258924e-03j,  1.15011364e-01-3.8337145e-08j]],
      dtype=complex64), array([[ 8.2884151e-01+6.7653834e-09j, -6.6016787e-03+1.6165609e-02j,
        -7.0029169e-02+1.4509528e-02j,  6.3505936e-03+4.3827597e-02j],
       [-6.6016531e-03-1.6165607e-02j,  5.3434804e-02+2.8630694e-08j,
        -6.6371396e-04+3.9500273e-03j,  9.1461744e-04-4.5878775e-03j],
       [-7.0029229e-02-1.4509435e-02j, -6.6371489e-04-3.9500687e-03j,
         6.5377332e-02-4.4463899e-09j, -2.1428524e-03-2.9578670e-03j],
       [ 6.3506123e-03-4.3827567e-02j,  9.1454014e-04+4.5878757e-03j,
        -2.1428019e-03+2.9578651e-03j,  5.2345213e-02-1.8027587e-08j]],
      dtype=complex64), array([[ 0.7368466 +9.28514599e-09j, -0.00717952+2.68528253e-01j,
        -0.03139642+1.29676014e-02j,  0.00461674+1.41246198e-03j],
       [-0.00717949-2.68528283e-01j,  0.15387781+3.68665418e-08j,
         0.00262322+6.92480197e-03j, -0.00178938-7.72018032e-03j],
       [-0.03139638-1.29675055e-02j,  0.00262316-6.92487182e-03j,
         0.0591972 -3.91992288e-08j, -0.00239126+1.95010751e-03j],
       [ 0.00461676-1.41248165e-03j, -0.00178945+7.72024412e-03j,
        -0.00239126-1.95004523e-03j,  0.05007696+4.42702799e-08j]],
      dtype=complex64), array([[ 0.7344505 +2.7578674e-08j, -0.00475519+3.6147174e-03j,
        -0.02662884-2.3756994e-01j,  0.00849045+1.1399767e-02j],
       [-0.00475515-3.6147232e-03j,  0.04903223+2.3730214e-08j,
        -0.00196706+3.6670689e-03j,  0.00106779-7.5842985e-03j],
       [-0.02662886+2.3756994e-01j, -0.00196706-3.6671152e-03j,
         0.16123626-3.6661397e-08j, -0.00718139+5.2249338e-03j],
       [ 0.00849046-1.1399814e-02j,  0.0010678 +7.5843562e-03j,
        -0.00718141-5.2249650e-03j,  0.05527976-2.3960716e-08j]],
      dtype=complex64), array([[ 8.3291727e-01+1.16034649e-08j, -7.0233946e-03+1.33959102e-02j,
        -3.5412636e-02+4.94074784e-02j,  5.8111153e-03+1.07869962e-02j],
       [-7.0234262e-03-1.33959735e-02j,  5.3987991e-02+2.41220697e-08j,
        -4.8853963e-04+2.75066192e-03j,  6.4495590e-04-4.12295433e-03j],
       [-3.5412643e-02-4.94075716e-02j, -4.8854697e-04-2.75064888e-03j,
         6.2424410e-02-5.15172704e-09j, -2.0410705e-03+5.15588385e-04j],
       [ 5.8110934e-03-1.07870279e-02j,  6.4496347e-04+4.12294827e-03j,
        -2.0410840e-03-5.15527849e-04j,  5.0668914e-02-3.08066355e-08j]],
      dtype=complex64), array([[ 0.8240487 -2.2475502e-08j, -0.00782481-5.1324282e-02j,
        -0.00155572-5.2954964e-02j,  0.0129534 +8.6540971e-03j],
       [-0.00782478+5.1324304e-02j,  0.05985524-8.3338119e-09j,
         0.00288604+4.8846495e-03j,  0.00090631-2.7158554e-03j],
       [-0.00155573+5.2954979e-02j,  0.00288605-4.8846672e-03j,
         0.06631878-3.9542671e-09j, -0.00241776+1.3916147e-03j],
       [ 0.01295331-8.6541381e-03j,  0.00090634+2.7157837e-03j,
        -0.00241771-1.3915818e-03j,  0.04977586-3.5370582e-09j]],
      dtype=complex64), array([[ 8.0709493e-01+3.8682484e-09j, -6.0132286e-03-1.5639849e-02j,
         5.3515942e-03+1.4442093e-02j,  6.3939211e-03+1.6107586e-01j],
       [-6.0132323e-03+1.5639851e-02j,  5.3069532e-02-3.0103603e-08j,
        -1.6188417e-03+4.2199870e-03j, -5.2310061e-03-3.8588261e-03j],
       [ 5.3515891e-03-1.4442094e-02j, -1.6188041e-03-4.2200526e-03j,
         5.7426184e-02+4.3887642e-08j, -3.0263152e-04-4.8724478e-04j],
       [ 6.3939607e-03-1.6107583e-01j, -5.2309814e-03+3.8588180e-03j,
        -3.0260216e-04+4.8724297e-04j,  8.2408234e-02-3.6511569e-08j]],
      dtype=complex64), array([[ 0.80626065+1.2096187e-08j, -0.00701643-1.2976864e-01j,
        -0.00832904+1.5610894e-02j,  0.00739879+4.6804309e-02j],
       [-0.00701649+1.2976868e-01j,  0.08138669-2.7597467e-08j,
        -0.00236199+4.6784761e-03j, -0.0059638 -2.4532783e-03j],
       [-0.00832905-1.5610908e-02j, -0.002362  -4.6784743e-03j,
         0.05919627-1.9760387e-08j, -0.0016201 +1.0374445e-03j],
       [ 0.00739873-4.6804313e-02j, -0.00596385+2.4533472e-03j,
        -0.00162004-1.0374590e-03j,  0.05315534-1.6601355e-08j]],
      dtype=complex64), array([[ 8.2206905e-01+2.9663997e-08j, -8.3712935e-03+1.3300889e-02j,
        -1.4896818e-03-8.4201768e-02j,  6.2557445e-03+9.5908651e-03j],
       [-8.3712675e-03-1.3300917e-02j,  5.5446003e-02-1.0236609e-08j,
        -2.6821685e-03+3.9266194e-03j,  7.4012164e-04-4.8199911e-03j],
       [-1.4896267e-03+8.4201768e-02j, -2.6821806e-03-3.9266339e-03j,
         7.3617667e-02-3.0910363e-09j, -2.9479815e-03+1.7061614e-03j],
       [ 6.2556984e-03-9.5908446e-03j,  7.4014795e-04+4.8200288e-03j,
        -2.9480141e-03-1.7061502e-03j,  4.8865963e-02+3.6283371e-08j]],
      dtype=complex64), array([[ 0.80626065+1.2096187e-08j, -0.00701643-1.2976864e-01j,
        -0.00832904+1.5610894e-02j,  0.00739879+4.6804309e-02j],
       [-0.00701649+1.2976868e-01j,  0.08138669-2.7597467e-08j,
        -0.00236199+4.6784761e-03j, -0.0059638 -2.4532783e-03j],
       [-0.00832905-1.5610908e-02j, -0.002362  -4.6784743e-03j,
         0.05919627-1.9760387e-08j, -0.0016201 +1.0374445e-03j],
       [ 0.00739873-4.6804313e-02j, -0.00596385+2.4533472e-03j,
        -0.00162004-1.0374590e-03j,  0.05315534-1.6601355e-08j]],
      dtype=complex64)]
before: [array([[ 9.1823065e-01-7.4505802e-09j, -7.4505802e-09+8.9406967e-08j,
         1.4901161e-08+4.4703484e-08j, -2.9802322e-08+2.7401173e-01j],
       [ 2.2351740e-08+0.0000000e+00j,  0.0000000e+00+2.2351740e-08j,
        -1.4901158e-08-1.5805067e-08j, -1.5805067e-08+8.9406967e-08j],
       [ 1.0536711e-08-3.7252903e-08j, -3.7252921e-09+2.1073424e-08j,
        -4.7415206e-08-1.1175870e-08j,  3.3527609e-08-2.6341780e-08j],
       [-4.8428770e-08-2.7401167e-01j,  1.4901161e-08+3.7252899e-08j,
         2.6077032e-08-2.6077032e-08j,  8.1768513e-02-2.6077032e-08j]],
      dtype=complex64), array([[ 9.9005538e-01-4.6566124e-09j,  9.3132246e-10+3.9344430e-03j,
        -8.8948965e-02-7.4505802e-09j,  7.4505802e-09+4.3792576e-02j],
       [ 0.0000000e+00-3.9344290e-03j,  1.5573343e-05-1.1175870e-08j,
         7.4505802e-09+3.5346585e-04j,  1.7402828e-04+7.4505802e-09j],
       [-8.8948950e-02-1.0535587e-08j,  1.0535587e-08-3.5348907e-04j,
         7.9914108e-03-7.9162419e-09j,  3.2596286e-09-3.9344188e-03j],
       [ 1.0535587e-08-4.3792598e-02j,  1.7403811e-04+1.0535587e-08j,
         3.2596290e-09+3.9344612e-03j,  1.9370165e-03-6.9849193e-09j]],
      dtype=complex64), array([[ 8.6780429e-01+2.32830377e-09j,  2.7474016e-08+3.36191863e-01j,
        -3.8385145e-02-4.47034800e-08j,  4.4703480e-08-1.48706045e-02j],
       [ 4.4237822e-08-3.36191893e-01j,  1.3024236e-01+2.56113708e-08j,
        -1.4901160e-08+1.48705561e-02j, -5.7609496e-03-1.49011603e-08j],
       [-3.8385153e-02+1.71203283e-08j, -1.4486432e-08-1.48705728e-02j,
         1.6978660e-03-6.51925713e-09j,  3.3527609e-08+6.57731900e-04j],
       [ 3.5557605e-08+1.48705961e-02j, -5.7609314e-03+5.92626748e-08j,
         5.5879363e-09-6.57773984e-04j,  2.5482115e-04-1.02445474e-08j]],
      dtype=complex64), array([[ 0.86805934+0.j        ,  0.        +0.j        ,
        -0.0326242 -0.3368497j ,  0.        +0.j        ],
       [ 0.        +0.j        ,  0.        +0.j        ,
         0.        +0.j        ,  0.        +0.j        ],
       [-0.0326242 +0.33684963j,  0.        +0.j        ,
         0.13194034+0.j        ,  0.        +0.j        ],
       [ 0.        +0.j        ,  0.        +0.j        ,
         0.        +0.j        ,  0.        +0.j        ]],
      dtype=complex64), array([[ 9.9610138e-01-9.3132257e-10j,  3.3527613e-08-2.9802322e-08j,
        -4.3973744e-02+4.4146188e-02j, -2.4214387e-08+1.8626451e-09j],
       [ 1.3969839e-08+2.1073424e-08j, -2.1073424e-08-1.8626451e-08j,
         7.9025346e-09-3.6878490e-08j,  3.9512660e-09+2.2390513e-08j],
       [-4.3973636e-02-4.4146042e-02j,  1.1175871e-08+3.7252903e-08j,
         3.8979095e-03-1.3038514e-08j, -2.9802321e-08-1.0826625e-08j],
       [ 4.2146848e-08+1.8439247e-08j, -7.9025337e-09-3.2927222e-08j,
         1.1175870e-08-4.2476120e-08j, -3.2104044e-08-0.0000000e+00j]],
      dtype=complex64), array([[ 9.8404944e-01+1.8626451e-09j,  9.4994903e-08-8.8409334e-02j,
         9.3132249e-09-8.8409387e-02j,  7.9429001e-03+1.8626445e-09j],
       [-2.4214389e-08+8.8409379e-02j,  7.9429112e-03+2.0489098e-08j,
         7.9429308e-03-5.5879346e-09j,  5.5879346e-09+7.1364758e-04j],
       [-1.8626451e-09+8.8409364e-02j,  7.9429001e-03+5.5879346e-09j,
         7.9428963e-03+9.3132249e-09j,  2.7939674e-08+7.1361614e-04j],
       [ 7.9429438e-03+5.5879354e-09j, -5.5879346e-09-7.1357656e-04j,
         5.5879346e-09-7.1359600e-04j,  6.4155232e-05-9.3132249e-09j]],
      dtype=complex64), array([[ 9.5849931e-01+3.3527609e-08j, -2.6077030e-08-4.2396784e-02j,
         8.6118653e-03-2.9802321e-08j,  1.4901159e-08+1.9469479e-01j],
       [ 2.9802321e-08+4.2396799e-02j,  1.8753037e-03+2.9802321e-08j,
        -4.4703484e-08+3.8089138e-04j, -8.6118234e-03-2.9802322e-08j],
       [ 8.6118551e-03-2.0489098e-08j, -6.3329935e-08-3.8091280e-04j,
         7.7309145e-05+2.6077032e-08j, -1.4901161e-08+1.7492522e-03j],
       [-4.1909516e-08-1.9469480e-01j, -8.6118132e-03-2.1420419e-08j,
         1.1175871e-08-1.7493367e-03j,  3.9547220e-02+7.4505806e-09j]],
      dtype=complex64), array([[ 9.5849919e-01-3.1432137e-08j,  2.5844201e-08-1.9469473e-01j,
        -8.6119268e-03+7.4505797e-09j,  7.4505797e-09+4.2396784e-02j],
       [ 8.6147320e-09+1.9469479e-01j,  3.9547369e-02-2.6775522e-08j,
         3.7252903e-08-1.7492264e-03j, -8.6118560e-03-3.7252903e-08j],
       [-8.6118896e-03-1.8422726e-08j,  7.9162401e-09+1.7492976e-03j,
         7.7331526e-05-5.8207625e-09j,  5.7043504e-08-3.8094161e-04j],
       [ 2.3719618e-08-4.2396769e-02j, -8.6118653e-03-7.1129762e-08j,
         1.3737009e-08+3.8093119e-04j,  1.8752844e-03+3.5157427e-08j]],
      dtype=complex64), array([[ 9.8220217e-01+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
         0.0000000e+00-1.3221407e-01j,  0.0000000e+00+0.0000000e+00j],
       [ 0.0000000e+00+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
        -5.7951915e-08+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j],
       [ 0.0000000e+00+1.3221407e-01j,  0.0000000e+00+0.0000000e+00j,
         1.7797394e-02+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j],
       [-4.7415202e-08+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
         0.0000000e+00+1.9756334e-09j,  0.0000000e+00+0.0000000e+00j]],
      dtype=complex64), array([[ 9.5849919e-01-3.1432137e-08j,  2.5844201e-08-1.9469473e-01j,
        -8.6119268e-03+7.4505797e-09j,  7.4505797e-09+4.2396784e-02j],
       [ 8.6147320e-09+1.9469479e-01j,  3.9547369e-02-2.6775522e-08j,
         3.7252903e-08-1.7492264e-03j, -8.6118560e-03-3.7252903e-08j],
       [-8.6118896e-03-1.8422726e-08j,  7.9162401e-09+1.7492976e-03j,
         7.7331526e-05-5.8207625e-09j,  5.7043504e-08-3.8094161e-04j],
       [ 2.3719618e-08-4.2396769e-02j, -8.6118653e-03-7.1129762e-08j,
         1.3737009e-08+3.8093119e-04j,  1.8752844e-03+3.5157427e-08j]],
      dtype=complex64)]
after:  [array([[ 9.1823065e-01-7.4505802e-09j, -7.4505802e-09+8.9406967e-08j,
         1.4901161e-08+4.4703484e-08j, -2.9802322e-08+2.7401173e-01j],
       [ 2.2351740e-08+0.0000000e+00j,  0.0000000e+00+2.2351740e-08j,
        -1.4901158e-08-1.5805067e-08j, -1.5805067e-08+8.9406967e-08j],
       [ 1.0536711e-08-3.7252903e-08j, -3.7252921e-09+2.1073424e-08j,
        -4.7415206e-08-1.1175870e-08j,  3.3527609e-08-2.6341780e-08j],
       [-4.8428770e-08-2.7401167e-01j,  1.4901161e-08+3.7252899e-08j,
         2.6077032e-08-2.6077032e-08j,  8.1768513e-02-2.6077032e-08j]],
      dtype=complex64), array([[ 9.9005538e-01-4.6566124e-09j,  9.3132246e-10+3.9344430e-03j,
        -8.8948965e-02-7.4505802e-09j,  7.4505802e-09+4.3792576e-02j],
       [ 0.0000000e+00-3.9344290e-03j,  1.5573343e-05-1.1175870e-08j,
         7.4505802e-09+3.5346585e-04j,  1.7402828e-04+7.4505802e-09j],
       [-8.8948950e-02-1.0535587e-08j,  1.0535587e-08-3.5348907e-04j,
         7.9914108e-03-7.9162419e-09j,  3.2596286e-09-3.9344188e-03j],
       [ 1.0535587e-08-4.3792598e-02j,  1.7403811e-04+1.0535587e-08j,
         3.2596290e-09+3.9344612e-03j,  1.9370165e-03-6.9849193e-09j]],
      dtype=complex64), array([[ 8.6780429e-01+2.32830377e-09j,  2.7474016e-08+3.36191863e-01j,
        -3.8385145e-02-4.47034800e-08j,  4.4703480e-08-1.48706045e-02j],
       [ 4.4237822e-08-3.36191893e-01j,  1.3024236e-01+2.56113708e-08j,
        -1.4901160e-08+1.48705561e-02j, -5.7609496e-03-1.49011603e-08j],
       [-3.8385153e-02+1.71203283e-08j, -1.4486432e-08-1.48705728e-02j,
         1.6978660e-03-6.51925713e-09j,  3.3527609e-08+6.57731900e-04j],
       [ 3.5557605e-08+1.48705961e-02j, -5.7609314e-03+5.92626748e-08j,
         5.5879363e-09-6.57773984e-04j,  2.5482115e-04-1.02445474e-08j]],
      dtype=complex64), array([[ 0.86805934+0.j        ,  0.        +0.j        ,
        -0.0326242 -0.3368497j ,  0.        +0.j        ],
       [ 0.        +0.j        ,  0.        +0.j        ,
         0.        +0.j        ,  0.        +0.j        ],
       [-0.0326242 +0.33684963j,  0.        +0.j        ,
         0.13194034+0.j        ,  0.        +0.j        ],
       [ 0.        +0.j        ,  0.        +0.j        ,
         0.        +0.j        ,  0.        +0.j        ]],
      dtype=complex64), array([[ 9.9610138e-01-9.3132257e-10j,  3.3527613e-08-2.9802322e-08j,
        -4.3973744e-02+4.4146188e-02j, -2.4214387e-08+1.8626451e-09j],
       [ 1.3969839e-08+2.1073424e-08j, -2.1073424e-08-1.8626451e-08j,
         7.9025346e-09-3.6878490e-08j,  3.9512660e-09+2.2390513e-08j],
       [-4.3973636e-02-4.4146042e-02j,  1.1175871e-08+3.7252903e-08j,
         3.8979095e-03-1.3038514e-08j, -2.9802321e-08-1.0826625e-08j],
       [ 4.2146848e-08+1.8439247e-08j, -7.9025337e-09-3.2927222e-08j,
         1.1175870e-08-4.2476120e-08j, -3.2104044e-08-0.0000000e+00j]],
      dtype=complex64), array([[ 9.8404944e-01+1.8626451e-09j,  9.4994903e-08-8.8409334e-02j,
         9.3132249e-09-8.8409387e-02j,  7.9429001e-03+1.8626445e-09j],
       [-2.4214389e-08+8.8409379e-02j,  7.9429112e-03+2.0489098e-08j,
         7.9429308e-03-5.5879346e-09j,  5.5879346e-09+7.1364758e-04j],
       [-1.8626451e-09+8.8409364e-02j,  7.9429001e-03+5.5879346e-09j,
         7.9428963e-03+9.3132249e-09j,  2.7939674e-08+7.1361614e-04j],
       [ 7.9429438e-03+5.5879354e-09j, -5.5879346e-09-7.1357656e-04j,
         5.5879346e-09-7.1359600e-04j,  6.4155232e-05-9.3132249e-09j]],
      dtype=complex64), array([[ 9.5849931e-01+3.3527609e-08j, -2.6077030e-08-4.2396784e-02j,
         8.6118653e-03-2.9802321e-08j,  1.4901159e-08+1.9469479e-01j],
       [ 2.9802321e-08+4.2396799e-02j,  1.8753037e-03+2.9802321e-08j,
        -4.4703484e-08+3.8089138e-04j, -8.6118234e-03-2.9802322e-08j],
       [ 8.6118551e-03-2.0489098e-08j, -6.3329935e-08-3.8091280e-04j,
         7.7309145e-05+2.6077032e-08j, -1.4901161e-08+1.7492522e-03j],
       [-4.1909516e-08-1.9469480e-01j, -8.6118132e-03-2.1420419e-08j,
         1.1175871e-08-1.7493367e-03j,  3.9547220e-02+7.4505806e-09j]],
      dtype=complex64), array([[ 9.5849919e-01-3.1432137e-08j,  2.5844201e-08-1.9469473e-01j,
        -8.6119268e-03+7.4505797e-09j,  7.4505797e-09+4.2396784e-02j],
       [ 8.6147320e-09+1.9469479e-01j,  3.9547369e-02-2.6775522e-08j,
         3.7252903e-08-1.7492264e-03j, -8.6118560e-03-3.7252903e-08j],
       [-8.6118896e-03-1.8422726e-08j,  7.9162401e-09+1.7492976e-03j,
         7.7331526e-05-5.8207625e-09j,  5.7043504e-08-3.8094161e-04j],
       [ 2.3719618e-08-4.2396769e-02j, -8.6118653e-03-7.1129762e-08j,
         1.3737009e-08+3.8093119e-04j,  1.8752844e-03+3.5157427e-08j]],
      dtype=complex64), array([[ 9.8220217e-01+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
         0.0000000e+00-1.3221407e-01j,  0.0000000e+00+0.0000000e+00j],
       [ 0.0000000e+00+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
        -5.7951915e-08+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j],
       [ 0.0000000e+00+1.3221407e-01j,  0.0000000e+00+0.0000000e+00j,
         1.7797394e-02+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j],
       [-4.7415202e-08+0.0000000e+00j,  0.0000000e+00+0.0000000e+00j,
         0.0000000e+00+1.9756334e-09j,  0.0000000e+00+0.0000000e+00j]],
      dtype=complex64), array([[ 9.5849919e-01-3.1432137e-08j,  2.5844201e-08-1.9469473e-01j,
        -8.6119268e-03+7.4505797e-09j,  7.4505797e-09+4.2396784e-02j],
       [ 8.6147320e-09+1.9469479e-01j,  3.9547369e-02-2.6775522e-08j,
         3.7252903e-08-1.7492264e-03j, -8.6118560e-03-3.7252903e-08j],
       [-8.6118896e-03-1.8422726e-08j,  7.9162401e-09+1.7492976e-03j,
         7.7331526e-05-5.8207625e-09j,  5.7043504e-08-3.8094161e-04j],
       [ 2.3719618e-08-4.2396769e-02j, -8.6118653e-03-7.1129762e-08j,
         1.3737009e-08+3.8093119e-04j,  1.8752844e-03+3.5157427e-08j]],
      dtype=complex64)]
1.0316119266170594

Beyond the built-in cdr.linear_fit_function() and cdr.linear_fit_function_no_intercept(), the user could also define other custom functions.

Variable noise CDR#

The circuit and the associated training circuits can also be run at different noise scale factors to implement variable noise Clifford data regression [2].

from mitiq.zne import scaling

cdr.execute_with_cdr(
    circuit,
    compute_density_matrix,
    observable=obs,
    simulator=simulate,
    seed=0,
    scale_factors=(1.0, 3.0),
).real
before: [array([[ 0.834364  +1.0323221e-08j, -0.02658513+7.5414695e-02j,
        -0.00364555+6.0732979e-02j, -0.02219004-5.2193210e-02j],
       [-0.02658516-7.5414769e-02j,  0.05705505-2.1024118e-08j,
         0.00668314-6.3313493e-03j, -0.00279339+1.8779658e-03j],
       [-0.00364545-6.0733065e-02j,  0.00668317+6.3313707e-03j,
         0.05266568+2.8994888e-08j, -0.00493391+3.6680887e-03j],
       [-0.02219001+5.2193295e-02j, -0.00279342-1.8778936e-03j,
        -0.00493392-3.6681308e-03j,  0.05591451+1.8027587e-08j]],
      dtype=complex64), array([[ 0.63464904-4.39906032e-08j, -0.04127588+6.65932968e-02j,
        -0.00993937+7.22437650e-02j,  0.00508331-2.21503843e-02j],
       [-0.0412758 -6.65932819e-02j,  0.11976352+3.27728173e-08j,
         0.01324185-9.72997770e-03j,  0.00361913+7.56994681e-03j],
       [-0.00993929-7.22438097e-02j,  0.01324196+9.73000843e-03j,
         0.13068399+3.73828648e-08j, -0.00891372+1.05015645e-02j],
       [ 0.00508333+2.21503563e-02j,  0.00361911-7.56998966e-03j,
        -0.00891367-1.05016371e-02j,  0.11490202-4.15319086e-08j]],
      dtype=complex64), array([[ 8.0085951e-01-1.0988151e-08j, -7.0634577e-03-1.2830047e-01j,
        -1.7937033e-03+8.2613796e-02j, -6.5871780e-03+1.4687504e-02j],
       [-7.0633907e-03+1.2830046e-01j,  8.2150400e-02-9.5946593e-09j,
        -1.4994835e-02+5.1340689e-03j,  4.3966356e-04-4.3560215e-03j],
       [-1.7937402e-03-8.2613751e-02j, -1.4994859e-02-5.1340400e-03j,
         6.5483026e-02-4.0654847e-08j, -1.5432771e-03+2.6791794e-03j],
       [-6.5871920e-03-1.4687432e-02j,  4.3968696e-04+4.3560783e-03j,
        -1.5433441e-03-2.6791906e-03j,  5.1505800e-02+3.1377130e-08j]],
      dtype=complex64), array([[ 0.60099083-8.2409475e-09j, -0.01953385-4.5784198e-02j,
        -0.0113767 +7.8696899e-02j,  0.00276175+3.3343770e-02j],
       [-0.01953383+4.5784354e-02j,  0.13559328-2.5807040e-08j,
        -0.0057434 +1.2443053e-02j,  0.00404668+2.0364241e-03j],
       [-0.01137666-7.8696840e-02j, -0.00574347-1.2443054e-02j,
         0.1429298 +3.9770871e-08j, -0.00251155+7.9111112e-03j],
       [ 0.00276172-3.3343788e-02j,  0.0040467 -2.0363838e-03j,
        -0.0025116 -7.9110963e-03j,  0.1204818 +9.1278923e-10j]],
      dtype=complex64), array([[ 0.82910657+2.9007939e-08j, -0.00718374-5.1952995e-02j,
        -0.00148769+4.7538240e-02j,  0.00958697+9.8697348e-03j],
       [-0.00718379+5.1952943e-02j,  0.05920316+6.8148016e-09j,
        -0.00454839+3.6678796e-03j,  0.00084997-2.2536987e-03j],
       [-0.00148774-4.7538158e-02j, -0.00454842-3.6679204e-03j,
         0.06079705-6.2739282e-08j, -0.00188072+1.3081398e-04j],
       [ 0.009587  -9.8697180e-03j,  0.00084995+2.2535902e-03j,
        -0.00188074-1.3081031e-04j,  0.05089176-3.2746314e-08j]],
      dtype=complex64), array([[ 6.1694735e-01-9.2208037e-09j, -2.0076374e-02-5.0475546e-03j,
        -1.0826622e-02+5.3359937e-02j,  1.2675283e-02+2.3850037e-02j],
       [-2.0076338e-02+5.0474992e-03j,  1.2340922e-01+2.7359473e-08j,
         1.9808080e-04+9.7132018e-03j,  4.6883486e-03+2.5198767e-03j],
       [-1.0826695e-02-5.3359997e-02j,  1.9812137e-04-9.7132111e-03j,
         1.4014505e-01-1.8510489e-08j, -3.4676769e-03+5.5686901e-03j],
       [ 1.2675338e-02-2.3850108e-02j,  4.6883924e-03-2.5198269e-03j,
        -3.4676532e-03-5.5686827e-03j,  1.1949403e-01-2.9779747e-08j]],
      dtype=complex64), array([[ 8.3454120e-01+5.0668593e-08j, -5.1423721e-03+1.5568423e-02j,
        -1.4859180e-03+4.9407504e-02j,  7.1771177e-03+5.0549367e-03j],
       [-5.1423898e-03-1.5568423e-02j,  5.3926896e-02+1.2330722e-08j,
        -1.1738810e-03+1.1835595e-03j,  7.4326905e-04-4.1230414e-03j],
       [-1.4859687e-03-4.9407549e-02j, -1.1738341e-03-1.1835458e-03j,
         6.0800534e-02+1.6123636e-09j, -1.8657612e-03+1.7006423e-03j],
       [ 7.1771024e-03-5.0549512e-03j,  7.4326131e-04+4.1230554e-03j,
        -1.8658016e-03-1.7006148e-03j,  5.0730027e-02-3.4343696e-08j]],
      dtype=complex64), array([[ 0.6190906 -3.05702450e-08j, -0.01557683+3.70484665e-02j,
        -0.0108283 +5.66710308e-02j,  0.01327206+1.32908514e-02j],
       [-0.01557682-3.70484293e-02j,  0.12144597+4.25691695e-08j,
         0.00267828+4.59684245e-03j,  0.00458403-7.91115686e-04j],
       [-0.01082831-5.66710234e-02j,  0.00267831-4.59681125e-03j,
         0.13998182-2.62357762e-08j, -0.00357906+8.09368584e-03j],
       [ 0.01327209-1.32908495e-02j,  0.00458404+7.91082683e-04j,
        -0.00357904-8.09368212e-03j,  0.11947742+1.55174149e-08j]],
      dtype=complex64), array([[ 8.0135584e-01+1.3704854e-08j, -7.9900203e-03-1.2810995e-01j,
        -1.8120746e-03-4.8221804e-02j,  2.0086214e-02+1.3128570e-02j],
       [-7.9900268e-03+1.2811004e-01j,  8.2432851e-02-1.9779405e-08j,
         9.1820331e-03+6.6995909e-03j,  4.2412829e-04-2.3018358e-04j],
       [-1.8121840e-03+4.8221756e-02j,  9.1820322e-03-6.6995937e-03j,
         6.5738909e-02-6.4102696e-09j, -2.5743088e-03+3.2422941e-03j],
       [ 2.0086121e-02-1.3128538e-02j,  4.2411292e-04+2.3027073e-04j,
        -2.5742815e-03-3.2423362e-03j,  5.0470892e-02+4.3357491e-09j]],
      dtype=complex64), array([[ 0.60157996-5.1875134e-08j, -0.02150373-4.5088373e-02j,
        -0.01147614+1.4279591e-03j,  0.01855122+2.9848585e-02j],
       [-0.02150366+4.5088354e-02j,  0.13675292-7.1916726e-09j,
         0.0057118 +1.5950905e-02j,  0.00396462+2.7939666e-03j],
       [-0.01147613-1.4280207e-03j,  0.00571185-1.5950980e-02j,
         0.14372492+3.4990258e-08j, -0.00462411+9.0813311e-03j],
       [ 0.01855125-2.9848617e-02j,  0.00396461-2.7939372e-03j,
        -0.00462414-9.0812678e-03j,  0.11793815+1.8255784e-08j]],
      dtype=complex64), array([[ 0.80626065+1.2096187e-08j, -0.00701643-1.2976864e-01j,
        -0.00832904+1.5610894e-02j,  0.00739879+4.6804309e-02j],
       [-0.00701649+1.2976868e-01j,  0.08138669-2.7597467e-08j,
        -0.00236199+4.6784761e-03j, -0.0059638 -2.4532783e-03j],
       [-0.00832905-1.5610908e-02j, -0.002362  -4.6784743e-03j,
         0.05919627-1.9760387e-08j, -0.0016201 +1.0374445e-03j],
       [ 0.00739873-4.6804313e-02j, -0.00596385+2.4533472e-03j,
        -0.00162004-1.0374590e-03j,  0.05315534-1.6601355e-08j]],
      dtype=complex64), array([[ 6.05362892e-01-2.45544829e-08j, -1.94237791e-02-4.73726727e-02j,
        -1.51707884e-02+3.73508111e-02j,  1.18529825e-02+5.21617085e-02j],
       [-1.94237493e-02+4.73727137e-02j,  1.34018421e-01-1.36157725e-08j,
         7.90198450e-04+1.33802034e-02j,  4.13819391e-04+2.24445853e-03j],
       [-1.51707595e-02-3.73509564e-02j,  7.90298451e-04-1.33802714e-02j,
         1.38680845e-01-2.07613446e-08j, -2.62526097e-03+6.69585867e-03j],
       [ 1.18530160e-02-5.21617644e-02j,  4.13888658e-04-2.24448205e-03j,
        -2.62524327e-03-6.69583632e-03j,  1.21933930e-01-7.00565721e-08j]],
      dtype=complex64), array([[ 0.7188061 +1.4157011e-08j, -0.01003576-1.1302939e-01j,
         0.04661921+1.0862911e-02j,  0.00726878-2.3510724e-01j],
       [-0.01003576+1.1302949e-01j,  0.0757439 -1.8350292e-08j,
        -0.00246349+1.0536441e-02j,  0.04789639+2.9211822e-03j],
       [ 0.04661917-1.0862906e-02j, -0.00246343-1.0536498e-02j,
         0.06755696-9.1301970e-09j, -0.0045795 -1.4886189e-02j],
       [ 0.00726871+2.3510727e-01j,  0.04789639-2.9211531e-03j,
        -0.00457953+1.4886230e-02j,  0.13789165+8.8996943e-09j]],
      dtype=complex64), array([[ 0.56776106-4.3888949e-08j, -0.02497115-4.1653536e-02j,
         0.01435563+2.7561428e-02j,  0.01163168-1.2286130e-01j],
       [-0.02497107+4.1653574e-02j,  0.12596045-4.2910315e-08j,
         0.00071805+6.6347420e-03j,  0.02879069+1.3156616e-02j],
       [ 0.01435559-2.7561426e-02j,  0.00071802-6.6347662e-03j,
         0.14997266+3.1772437e-08j, -0.00795652+2.4281344e-03j],
       [ 0.01163167+1.2286131e-01j,  0.02879068-1.3156507e-02j,
        -0.00795658-2.4280171e-03j,  0.15630166+4.1988304e-08j]],
      dtype=complex64), array([[ 7.0632929e-01+1.5086496e-08j, -1.3860244e-01+9.9388883e-03j,
         5.2939406e-05+2.6754764e-01j,  4.8313732e-03-4.7400642e-02j],
       [-1.3860238e-01-9.9388883e-03j,  8.4142782e-02+1.4659949e-08j,
         2.8882672e-03-5.4706708e-02j, -7.8091526e-04+3.9456761e-03j],
       [ 5.2913831e-05-2.6754764e-01j,  2.8883379e-03+5.4706767e-02j,
         1.5238236e-01+3.5958365e-09j, -2.1769965e-02-2.1787151e-03j],
       [ 4.8313662e-03+4.7400694e-02j, -7.8087859e-04-3.9457283e-03j,
        -2.1770021e-02+2.1787372e-03j,  5.7144430e-02-9.1278922e-09j]],
      dtype=complex64), array([[ 0.5351443 +7.3124653e-09j, -0.10211093+2.4247425e-02j,
        -0.00684953+1.9190238e-01j,  0.01012419-1.9141780e-02j],
       [-0.10211085-2.4247414e-02j,  0.14779449+3.7037115e-08j,
         0.01177291-3.5128452e-02j,  0.00069468+5.7504384e-04j],
       [-0.00684957-1.9190235e-01j,  0.01177298+3.5128515e-02j,
         0.19052157-5.0553769e-08j, -0.01617902+1.5628689e-03j],
       [ 0.01012421+1.9141873e-02j,  0.00069464-5.7504384e-04j,
        -0.01617904-1.5628177e-03j,  0.1265355 +1.5517415e-08j]],
      dtype=complex64), array([[ 7.3659617e-01-7.91819765e-09j, -3.3890478e-02+1.13772154e-02j,
        -3.0404418e-03+7.02382624e-02j,  5.2780574e-03-2.45802000e-01j],
       [-3.3890456e-02-1.13770990e-02j,  5.5112340e-02-1.21797425e-08j,
        -3.1970764e-04-2.80978717e-03j, -7.8237319e-04+1.03840930e-02j],
       [-3.0404488e-03-7.02383369e-02j, -3.1970118e-04+2.80985469e-03j,
         6.6020034e-02-3.33859553e-08j, -2.7839057e-02+2.55175424e-03j],
       [ 5.2780565e-03+2.45801970e-01j, -7.8240689e-04-1.03840642e-02j,
        -2.7839189e-02-2.55175424e-03j,  1.4227007e-01+7.21103461e-08j]],
      dtype=complex64), array([[ 0.57322526-2.0342600e-08j, -0.04004486+2.5757829e-02j,
        -0.01368627+6.1563484e-02j,  0.00854981-1.3247952e-01j],
       [-0.04004479-2.5757773e-02j,  0.12042567+3.8475449e-08j,
         0.00420281-3.0287723e-03j,  0.00182701+1.6248589e-02j],
       [-0.01368625-6.1563417e-02j,  0.00420276+3.0286736e-03j,
         0.14524409-2.4221185e-08j, -0.02222407+1.0874897e-02j],
       [ 0.00854985+1.3247950e-01j,  0.00182697-1.6248688e-02j,
        -0.02222423-1.0874867e-02j,  0.16110052-2.4645310e-08j]],
      dtype=complex64), array([[ 0.65808547+5.8511507e-09j, -0.01144172+2.3439643e-01j,
        -0.09135848+7.2046039e-03j,  0.0043944 -2.1605411e-01j],
       [-0.01144168-2.3439652e-01j,  0.14531295+1.0153628e-08j,
         0.00240085+2.9836286e-02j, -0.085287  -1.9572207e-03j],
       [-0.09135843-7.2045820e-03j,  0.0024009 -2.9836332e-02j,
         0.06785845-2.9723276e-08j, -0.00595745+3.6081851e-02j],
       [ 0.00439438+2.1605411e-01j, -0.08528706+1.9572007e-03j,
        -0.00595748-3.6081851e-02j,  0.12874176+4.6780446e-08j]],
      dtype=complex64), array([[ 0.5305117 -6.0030914e-08j, -0.02792542+1.5514477e-01j,
        -0.06710235+1.9416086e-02j,  0.00727395-1.1662543e-01j],
       [-0.02792539-1.5514484e-01j,  0.1790986 +2.9255357e-08j,
         0.00854182+1.2596550e-02j, -0.04557572+4.8207040e-03j],
       [-0.06710239-1.9416019e-02j,  0.00854183-1.2596453e-02j,
         0.1386213 +2.0496268e-08j, -0.01079266+3.0160353e-02j],
       [ 0.00727401+1.1662545e-01j, -0.04557572-4.8207450e-03j,
        -0.01079264-3.0160319e-02j,  0.15176392-2.4645310e-08j]],
      dtype=complex64), array([[ 7.3455101e-01+3.9934762e-09j, -6.8459986e-03+1.0236387e-02j,
        -2.6750665e-02+2.7702895e-01j,  4.9114479e-03+7.2460179e-03j],
       [-6.8459320e-03-1.0236333e-02j,  5.4742191e-02+8.9169827e-09j,
         2.9683853e-03+1.0368704e-03j,  6.9354021e-04-5.5355774e-03j],
       [-2.6750706e-02-2.7702892e-01j,  2.9684275e-03-1.0368079e-03j,
         1.5838504e-01-5.4894129e-09j, -2.1203426e-03-2.4761469e-03j],
       [ 4.9114265e-03-7.2459574e-03j,  6.9357973e-04+5.5355504e-03j,
        -2.1204064e-03+2.4761176e-03j,  5.2320600e-02-7.1882154e-09j]],
      dtype=complex64), array([[ 0.5581466 +3.0470407e-08j, -0.01957885+2.4902806e-02j,
        -0.02636353+1.9495346e-01j,  0.00848996+1.8936247e-02j],
       [-0.01957877-2.4902854e-02j,  0.12357864+2.7876952e-08j,
         0.01013865+4.9893893e-03j,  0.00480246-2.4759965e-03j],
       [-0.02636356-1.9495340e-01j,  0.01013872-4.9893325e-03j,
         0.19611135-5.3720871e-08j, -0.00431404+9.0745057e-04j],
       [ 0.00848994-1.8936113e-02j,  0.00480243+2.4760794e-03j,
        -0.00431407-9.0746523e-04j,  0.12215937+2.1450546e-08j]],
      dtype=complex64)]
after:  [array([[ 0.834364  +1.0323221e-08j, -0.02658513+7.5414695e-02j,
        -0.00364555+6.0732979e-02j, -0.02219004-5.2193210e-02j],
       [-0.02658516-7.5414769e-02j,  0.05705505-2.1024118e-08j,
         0.00668314-6.3313493e-03j, -0.00279339+1.8779658e-03j],
       [-0.00364545-6.0733065e-02j,  0.00668317+6.3313707e-03j,
         0.05266568+2.8994888e-08j, -0.00493391+3.6680887e-03j],
       [-0.02219001+5.2193295e-02j, -0.00279342-1.8778936e-03j,
        -0.00493392-3.6681308e-03j,  0.05591451+1.8027587e-08j]],
      dtype=complex64), array([[ 0.63464904-4.39906032e-08j, -0.04127588+6.65932968e-02j,
        -0.00993937+7.22437650e-02j,  0.00508331-2.21503843e-02j],
       [-0.0412758 -6.65932819e-02j,  0.11976352+3.27728173e-08j,
         0.01324185-9.72997770e-03j,  0.00361913+7.56994681e-03j],
       [-0.00993929-7.22438097e-02j,  0.01324196+9.73000843e-03j,
         0.13068399+3.73828648e-08j, -0.00891372+1.05015645e-02j],
       [ 0.00508333+2.21503563e-02j,  0.00361911-7.56998966e-03j,
        -0.00891367-1.05016371e-02j,  0.11490202-4.15319086e-08j]],
      dtype=complex64), array([[ 8.0085951e-01-1.0988151e-08j, -7.0634577e-03-1.2830047e-01j,
        -1.7937033e-03+8.2613796e-02j, -6.5871780e-03+1.4687504e-02j],
       [-7.0633907e-03+1.2830046e-01j,  8.2150400e-02-9.5946593e-09j,
        -1.4994835e-02+5.1340689e-03j,  4.3966356e-04-4.3560215e-03j],
       [-1.7937402e-03-8.2613751e-02j, -1.4994859e-02-5.1340400e-03j,
         6.5483026e-02-4.0654847e-08j, -1.5432771e-03+2.6791794e-03j],
       [-6.5871920e-03-1.4687432e-02j,  4.3968696e-04+4.3560783e-03j,
        -1.5433441e-03-2.6791906e-03j,  5.1505800e-02+3.1377130e-08j]],
      dtype=complex64), array([[ 0.60099083-8.2409475e-09j, -0.01953385-4.5784198e-02j,
        -0.0113767 +7.8696899e-02j,  0.00276175+3.3343770e-02j],
       [-0.01953383+4.5784354e-02j,  0.13559328-2.5807040e-08j,
        -0.0057434 +1.2443053e-02j,  0.00404668+2.0364241e-03j],
       [-0.01137666-7.8696840e-02j, -0.00574347-1.2443054e-02j,
         0.1429298 +3.9770871e-08j, -0.00251155+7.9111112e-03j],
       [ 0.00276172-3.3343788e-02j,  0.0040467 -2.0363838e-03j,
        -0.0025116 -7.9110963e-03j,  0.1204818 +9.1278923e-10j]],
      dtype=complex64), array([[ 0.82910657+2.9007939e-08j, -0.00718374-5.1952995e-02j,
        -0.00148769+4.7538240e-02j,  0.00958697+9.8697348e-03j],
       [-0.00718379+5.1952943e-02j,  0.05920316+6.8148016e-09j,
        -0.00454839+3.6678796e-03j,  0.00084997-2.2536987e-03j],
       [-0.00148774-4.7538158e-02j, -0.00454842-3.6679204e-03j,
         0.06079705-6.2739282e-08j, -0.00188072+1.3081398e-04j],
       [ 0.009587  -9.8697180e-03j,  0.00084995+2.2535902e-03j,
        -0.00188074-1.3081031e-04j,  0.05089176-3.2746314e-08j]],
      dtype=complex64), array([[ 6.1694735e-01-9.2208037e-09j, -2.0076374e-02-5.0475546e-03j,
        -1.0826622e-02+5.3359937e-02j,  1.2675283e-02+2.3850037e-02j],
       [-2.0076338e-02+5.0474992e-03j,  1.2340922e-01+2.7359473e-08j,
         1.9808080e-04+9.7132018e-03j,  4.6883486e-03+2.5198767e-03j],
       [-1.0826695e-02-5.3359997e-02j,  1.9812137e-04-9.7132111e-03j,
         1.4014505e-01-1.8510489e-08j, -3.4676769e-03+5.5686901e-03j],
       [ 1.2675338e-02-2.3850108e-02j,  4.6883924e-03-2.5198269e-03j,
        -3.4676532e-03-5.5686827e-03j,  1.1949403e-01-2.9779747e-08j]],
      dtype=complex64), array([[ 8.3454120e-01+5.0668593e-08j, -5.1423721e-03+1.5568423e-02j,
        -1.4859180e-03+4.9407504e-02j,  7.1771177e-03+5.0549367e-03j],
       [-5.1423898e-03-1.5568423e-02j,  5.3926896e-02+1.2330722e-08j,
        -1.1738810e-03+1.1835595e-03j,  7.4326905e-04-4.1230414e-03j],
       [-1.4859687e-03-4.9407549e-02j, -1.1738341e-03-1.1835458e-03j,
         6.0800534e-02+1.6123636e-09j, -1.8657612e-03+1.7006423e-03j],
       [ 7.1771024e-03-5.0549512e-03j,  7.4326131e-04+4.1230554e-03j,
        -1.8658016e-03-1.7006148e-03j,  5.0730027e-02-3.4343696e-08j]],
      dtype=complex64), array([[ 0.6190906 -3.05702450e-08j, -0.01557683+3.70484665e-02j,
        -0.0108283 +5.66710308e-02j,  0.01327206+1.32908514e-02j],
       [-0.01557682-3.70484293e-02j,  0.12144597+4.25691695e-08j,
         0.00267828+4.59684245e-03j,  0.00458403-7.91115686e-04j],
       [-0.01082831-5.66710234e-02j,  0.00267831-4.59681125e-03j,
         0.13998182-2.62357762e-08j, -0.00357906+8.09368584e-03j],
       [ 0.01327209-1.32908495e-02j,  0.00458404+7.91082683e-04j,
        -0.00357904-8.09368212e-03j,  0.11947742+1.55174149e-08j]],
      dtype=complex64), array([[ 8.0135584e-01+1.3704854e-08j, -7.9900203e-03-1.2810995e-01j,
        -1.8120746e-03-4.8221804e-02j,  2.0086214e-02+1.3128570e-02j],
       [-7.9900268e-03+1.2811004e-01j,  8.2432851e-02-1.9779405e-08j,
         9.1820331e-03+6.6995909e-03j,  4.2412829e-04-2.3018358e-04j],
       [-1.8121840e-03+4.8221756e-02j,  9.1820322e-03-6.6995937e-03j,
         6.5738909e-02-6.4102696e-09j, -2.5743088e-03+3.2422941e-03j],
       [ 2.0086121e-02-1.3128538e-02j,  4.2411292e-04+2.3027073e-04j,
        -2.5742815e-03-3.2423362e-03j,  5.0470892e-02+4.3357491e-09j]],
      dtype=complex64), array([[ 0.60157996-5.1875134e-08j, -0.02150373-4.5088373e-02j,
        -0.01147614+1.4279591e-03j,  0.01855122+2.9848585e-02j],
       [-0.02150366+4.5088354e-02j,  0.13675292-7.1916726e-09j,
         0.0057118 +1.5950905e-02j,  0.00396462+2.7939666e-03j],
       [-0.01147613-1.4280207e-03j,  0.00571185-1.5950980e-02j,
         0.14372492+3.4990258e-08j, -0.00462411+9.0813311e-03j],
       [ 0.01855125-2.9848617e-02j,  0.00396461-2.7939372e-03j,
        -0.00462414-9.0812678e-03j,  0.11793815+1.8255784e-08j]],
      dtype=complex64), array([[ 0.80626065+1.2096187e-08j, -0.00701643-1.2976864e-01j,
        -0.00832904+1.5610894e-02j,  0.00739879+4.6804309e-02j],
       [-0.00701649+1.2976868e-01j,  0.08138669-2.7597467e-08j,
        -0.00236199+4.6784761e-03j, -0.0059638 -2.4532783e-03j],
       [-0.00832905-1.5610908e-02j, -0.002362  -4.6784743e-03j,
         0.05919627-1.9760387e-08j, -0.0016201 +1.0374445e-03j],
       [ 0.00739873-4.6804313e-02j, -0.00596385+2.4533472e-03j,
        -0.00162004-1.0374590e-03j,  0.05315534-1.6601355e-08j]],
      dtype=complex64), array([[ 6.05362892e-01-2.45544829e-08j, -1.94237791e-02-4.73726727e-02j,
        -1.51707884e-02+3.73508111e-02j,  1.18529825e-02+5.21617085e-02j],
       [-1.94237493e-02+4.73727137e-02j,  1.34018421e-01-1.36157725e-08j,
         7.90198450e-04+1.33802034e-02j,  4.13819391e-04+2.24445853e-03j],
       [-1.51707595e-02-3.73509564e-02j,  7.90298451e-04-1.33802714e-02j,
         1.38680845e-01-2.07613446e-08j, -2.62526097e-03+6.69585867e-03j],
       [ 1.18530160e-02-5.21617644e-02j,  4.13888658e-04-2.24448205e-03j,
        -2.62524327e-03-6.69583632e-03j,  1.21933930e-01-7.00565721e-08j]],
      dtype=complex64), array([[ 0.7188061 +1.4157011e-08j, -0.01003576-1.1302939e-01j,
         0.04661921+1.0862911e-02j,  0.00726878-2.3510724e-01j],
       [-0.01003576+1.1302949e-01j,  0.0757439 -1.8350292e-08j,
        -0.00246349+1.0536441e-02j,  0.04789639+2.9211822e-03j],
       [ 0.04661917-1.0862906e-02j, -0.00246343-1.0536498e-02j,
         0.06755696-9.1301970e-09j, -0.0045795 -1.4886189e-02j],
       [ 0.00726871+2.3510727e-01j,  0.04789639-2.9211531e-03j,
        -0.00457953+1.4886230e-02j,  0.13789165+8.8996943e-09j]],
      dtype=complex64), array([[ 0.56776106-4.3888949e-08j, -0.02497115-4.1653536e-02j,
         0.01435563+2.7561428e-02j,  0.01163168-1.2286130e-01j],
       [-0.02497107+4.1653574e-02j,  0.12596045-4.2910315e-08j,
         0.00071805+6.6347420e-03j,  0.02879069+1.3156616e-02j],
       [ 0.01435559-2.7561426e-02j,  0.00071802-6.6347662e-03j,
         0.14997266+3.1772437e-08j, -0.00795652+2.4281344e-03j],
       [ 0.01163167+1.2286131e-01j,  0.02879068-1.3156507e-02j,
        -0.00795658-2.4280171e-03j,  0.15630166+4.1988304e-08j]],
      dtype=complex64), array([[ 7.0632929e-01+1.5086496e-08j, -1.3860244e-01+9.9388883e-03j,
         5.2939406e-05+2.6754764e-01j,  4.8313732e-03-4.7400642e-02j],
       [-1.3860238e-01-9.9388883e-03j,  8.4142782e-02+1.4659949e-08j,
         2.8882672e-03-5.4706708e-02j, -7.8091526e-04+3.9456761e-03j],
       [ 5.2913831e-05-2.6754764e-01j,  2.8883379e-03+5.4706767e-02j,
         1.5238236e-01+3.5958365e-09j, -2.1769965e-02-2.1787151e-03j],
       [ 4.8313662e-03+4.7400694e-02j, -7.8087859e-04-3.9457283e-03j,
        -2.1770021e-02+2.1787372e-03j,  5.7144430e-02-9.1278922e-09j]],
      dtype=complex64), array([[ 0.5351443 +7.3124653e-09j, -0.10211093+2.4247425e-02j,
        -0.00684953+1.9190238e-01j,  0.01012419-1.9141780e-02j],
       [-0.10211085-2.4247414e-02j,  0.14779449+3.7037115e-08j,
         0.01177291-3.5128452e-02j,  0.00069468+5.7504384e-04j],
       [-0.00684957-1.9190235e-01j,  0.01177298+3.5128515e-02j,
         0.19052157-5.0553769e-08j, -0.01617902+1.5628689e-03j],
       [ 0.01012421+1.9141873e-02j,  0.00069464-5.7504384e-04j,
        -0.01617904-1.5628177e-03j,  0.1265355 +1.5517415e-08j]],
      dtype=complex64), array([[ 7.3659617e-01-7.91819765e-09j, -3.3890478e-02+1.13772154e-02j,
        -3.0404418e-03+7.02382624e-02j,  5.2780574e-03-2.45802000e-01j],
       [-3.3890456e-02-1.13770990e-02j,  5.5112340e-02-1.21797425e-08j,
        -3.1970764e-04-2.80978717e-03j, -7.8237319e-04+1.03840930e-02j],
       [-3.0404488e-03-7.02383369e-02j, -3.1970118e-04+2.80985469e-03j,
         6.6020034e-02-3.33859553e-08j, -2.7839057e-02+2.55175424e-03j],
       [ 5.2780565e-03+2.45801970e-01j, -7.8240689e-04-1.03840642e-02j,
        -2.7839189e-02-2.55175424e-03j,  1.4227007e-01+7.21103461e-08j]],
      dtype=complex64), array([[ 0.57322526-2.0342600e-08j, -0.04004486+2.5757829e-02j,
        -0.01368627+6.1563484e-02j,  0.00854981-1.3247952e-01j],
       [-0.04004479-2.5757773e-02j,  0.12042567+3.8475449e-08j,
         0.00420281-3.0287723e-03j,  0.00182701+1.6248589e-02j],
       [-0.01368625-6.1563417e-02j,  0.00420276+3.0286736e-03j,
         0.14524409-2.4221185e-08j, -0.02222407+1.0874897e-02j],
       [ 0.00854985+1.3247950e-01j,  0.00182697-1.6248688e-02j,
        -0.02222423-1.0874867e-02j,  0.16110052-2.4645310e-08j]],
      dtype=complex64), array([[ 0.65808547+5.8511507e-09j, -0.01144172+2.3439643e-01j,
        -0.09135848+7.2046039e-03j,  0.0043944 -2.1605411e-01j],
       [-0.01144168-2.3439652e-01j,  0.14531295+1.0153628e-08j,
         0.00240085+2.9836286e-02j, -0.085287  -1.9572207e-03j],
       [-0.09135843-7.2045820e-03j,  0.0024009 -2.9836332e-02j,
         0.06785845-2.9723276e-08j, -0.00595745+3.6081851e-02j],
       [ 0.00439438+2.1605411e-01j, -0.08528706+1.9572007e-03j,
        -0.00595748-3.6081851e-02j,  0.12874176+4.6780446e-08j]],
      dtype=complex64), array([[ 0.5305117 -6.0030914e-08j, -0.02792542+1.5514477e-01j,
        -0.06710235+1.9416086e-02j,  0.00727395-1.1662543e-01j],
       [-0.02792539-1.5514484e-01j,  0.1790986 +2.9255357e-08j,
         0.00854182+1.2596550e-02j, -0.04557572+4.8207040e-03j],
       [-0.06710239-1.9416019e-02j,  0.00854183-1.2596453e-02j,
         0.1386213 +2.0496268e-08j, -0.01079266+3.0160353e-02j],
       [ 0.00727401+1.1662545e-01j, -0.04557572-4.8207450e-03j,
        -0.01079264-3.0160319e-02j,  0.15176392-2.4645310e-08j]],
      dtype=complex64), array([[ 7.3455101e-01+3.9934762e-09j, -6.8459986e-03+1.0236387e-02j,
        -2.6750665e-02+2.7702895e-01j,  4.9114479e-03+7.2460179e-03j],
       [-6.8459320e-03-1.0236333e-02j,  5.4742191e-02+8.9169827e-09j,
         2.9683853e-03+1.0368704e-03j,  6.9354021e-04-5.5355774e-03j],
       [-2.6750706e-02-2.7702892e-01j,  2.9684275e-03-1.0368079e-03j,
         1.5838504e-01-5.4894129e-09j, -2.1203426e-03-2.4761469e-03j],
       [ 4.9114265e-03-7.2459574e-03j,  6.9357973e-04+5.5355504e-03j,
        -2.1204064e-03+2.4761176e-03j,  5.2320600e-02-7.1882154e-09j]],
      dtype=complex64), array([[ 0.5581466 +3.0470407e-08j, -0.01957885+2.4902806e-02j,
        -0.02636353+1.9495346e-01j,  0.00848996+1.8936247e-02j],
       [-0.01957877-2.4902854e-02j,  0.12357864+2.7876952e-08j,
         0.01013865+4.9893893e-03j,  0.00480246-2.4759965e-03j],
       [-0.02636356-1.9495340e-01j,  0.01013872-4.9893325e-03j,
         0.19611135-5.3720871e-08j, -0.00431404+9.0745057e-04j],
       [ 0.00848994-1.8936113e-02j,  0.00480243+2.4760794e-03j,
        -0.00431407-9.0746523e-04j,  0.12215937+2.1450546e-08j]],
      dtype=complex64)]
before: [array([[ 9.5268482e-01+3.72528941e-09j,  2.6077029e-08-1.93513691e-01j,
         3.7252894e-09+8.55914056e-02j, -1.7385796e-02-2.60770285e-08j],
       [-1.4901159e-08+1.93513721e-01j,  3.9307393e-02+1.49011594e-08j,
        -1.7385736e-02+1.49011594e-08j,  1.4901159e-08-3.53148533e-03j],
       [-9.6857541e-08-8.55914503e-02j, -1.7385788e-02+7.45058060e-09j,
         7.6897405e-03+7.45058060e-09j,  7.4505806e-09+1.56197720e-03j],
       [-1.7385691e-02+1.15483985e-07j,  4.8428763e-08+3.53150861e-03j,
         2.6077029e-08-1.56196777e-03j,  3.1725515e-04-4.84287703e-08j]],
      dtype=complex64), array([[ 9.9005497e-01+3.53902543e-08j,  3.1664964e-08-8.89489651e-02j,
        -9.3132257e-09+4.37925905e-02j,  3.9344728e-03-1.67638046e-08j],
       [-5.4016706e-08+8.89489204e-02j,  7.9913586e-03+1.30385125e-08j,
        -3.9344132e-03-2.04890949e-08j, -3.1664968e-08+3.53471143e-04j],
       [ 4.6566122e-08-4.37926054e-02j, -3.9344188e-03+2.42143869e-08j,
         1.9370799e-03-1.86264337e-09j,  3.9115541e-08-1.74035260e-04j],
       [ 3.9344397e-03+8.75443078e-08j,  2.4214383e-08-3.53454030e-04j,
         1.3038514e-08+1.73950568e-04j,  1.5583799e-05+2.04890949e-08j]],
      dtype=complex64), array([[ 9.9804628e-01-1.4901160e-08j,  2.2351738e-08+0.0000000e+00j,
        -5.5879347e-08+4.4146121e-02j,  0.0000000e+00+1.1175869e-08j],
       [ 3.3527609e-08+8.4293696e-08j,  0.0000000e+00-1.8626451e-08j,
         3.0293048e-08-1.4901159e-08j,  7.4505806e-09+0.0000000e+00j],
       [ 3.7252899e-08-4.4146072e-02j,  0.0000000e+00+4.4703480e-08j,
         1.9528106e-03-1.8626450e-08j, -1.8626450e-08+1.0826625e-08j],
       [ 2.1731967e-08+2.6077029e-08j, -3.7252903e-09-3.2268680e-08j,
         7.4505806e-09-1.0742507e-08j, -4.2352642e-08-2.2204460e-16j]],
      dtype=complex64), array([[ 9.5268470e-01-1.6763805e-08j,  9.3132257e-09-1.9351369e-01j,
        -5.5879328e-09-8.5591510e-02j,  1.7385740e-02+3.1664964e-08j],
       [-2.7939674e-08+1.9351365e-01j,  3.9307430e-02-5.5879346e-09j,
         1.7385717e-02+9.3132249e-09j,  1.3038515e-08+3.5315147e-03j],
       [ 3.1664964e-08+8.5591473e-02j,  1.7385751e-02+3.9115545e-08j,
         7.6897522e-03+2.4214382e-08j,  1.3038514e-08+1.5619812e-03j],
       [ 1.7385729e-02+3.1664968e-08j, -9.3132266e-09-3.5314420e-03j,
         3.5390254e-08-1.5619704e-03j,  3.1726895e-04+1.3038515e-08j]],
      dtype=complex64), array([[ 9.5849919e-01-3.1432137e-08j,  2.5844201e-08-1.9469473e-01j,
        -8.6119268e-03+7.4505797e-09j,  7.4505797e-09+4.2396784e-02j],
       [ 8.6147320e-09+1.9469479e-01j,  3.9547369e-02-2.6775522e-08j,
         3.7252903e-08-1.7492264e-03j, -8.6118560e-03-3.7252903e-08j],
       [-8.6118896e-03-1.8422726e-08j,  7.9162401e-09+1.7492976e-03j,
         7.7331526e-05-5.8207625e-09j,  5.7043504e-08-3.8094161e-04j],
       [ 2.3719618e-08-4.2396769e-02j, -8.6118653e-03-7.1129762e-08j,
         1.3737009e-08+3.8093119e-04j,  1.8752844e-03+3.5157427e-08j]],
      dtype=complex64), array([[ 8.3504814e-01-1.4901160e-08j, -7.4505797e-09-1.6961879e-01j,
         6.5711170e-02+1.4901161e-08j,  4.4408921e-16-3.2350194e-01j],
       [ 0.0000000e+00+1.6961879e-01j,  3.4453772e-02-2.2351740e-08j,
        -4.4703480e-08+1.3347561e-02j,  6.5711163e-02+5.9604641e-08j],
       [ 6.5711170e-02+1.4901161e-08j, -1.8626451e-09-1.3347527e-02j,
         5.1709097e-03+1.1175870e-08j, -1.1175870e-08-2.5456889e-02j],
       [ 1.6763806e-08+3.2350191e-01j,  6.5711170e-02+4.0978193e-08j,
         3.7252901e-09+2.5456876e-02j,  1.2532634e-01+3.7252901e-09j]],
      dtype=complex64), array([[ 8.3504844e-01+0.0000000e+00j, -1.6961889e-01-2.9802322e-08j,
         3.7252903e-09+3.2350194e-01j,  1.4901161e-08-6.5711200e-02j],
       [-1.6961889e-01-0.0000000e+00j,  3.4453783e-02+0.0000000e+00j,
        -2.0954758e-08-6.5711193e-02j,  7.4505806e-09+1.3347570e-02j],
       [ 0.0000000e+00-3.2350203e-01j,  2.9802322e-08+6.5711223e-02j,
         1.2532625e-01+0.0000000e+00j, -2.5456840e-02+7.4505806e-09j],
       [-1.0244548e-08+6.5711230e-02j,  7.4505806e-09-1.3347548e-02j,
        -2.5456849e-02-5.3551048e-09j,  5.1708911e-03+2.7939677e-09j]],
      dtype=complex64), array([[ 8.6253977e-01-1.3969839e-08j, -3.0021060e-02+2.9802322e-08j,
        -2.9802322e-08+7.7492602e-02j, -2.2351742e-08-3.3415237e-01j],
       [-3.0020943e-02+8.4284693e-08j,  1.0449047e-03-1.4901161e-08j,
        -6.8452209e-08-2.6971824e-03j, -1.5716068e-08+1.1630243e-02j],
       [-7.3807314e-08-7.7492565e-02j, -2.9802322e-08+2.6971453e-03j,
         6.9620456e-03+4.0978193e-08j, -3.0021001e-02-1.3038516e-08j],
       [-2.2351742e-08+3.3415231e-01j,  8.9406967e-08-1.1630308e-02j,
        -3.0021068e-02-7.4505806e-08j,  1.2945236e-01+2.5145710e-08j]],
      dtype=complex64), array([[ 7.56034434e-01-1.8626450e-08j,  1.11758700e-08+2.9289156e-01j,
        -1.13467731e-01+1.4901159e-08j,  2.98023206e-08-2.9289165e-01j],
       [ 1.11758700e-08-2.9289162e-01j,  1.13467619e-01+1.8626450e-08j,
         2.98023206e-08+4.3957923e-02j, -1.13467753e-01-1.4901159e-08j],
       [-1.13467768e-01-5.1688403e-08j,  1.16415322e-08-4.3957938e-02j,
         1.70294661e-02-6.5192576e-09j,  4.65661243e-09+4.3957941e-02j],
       [ 8.84756624e-09+2.9289162e-01j, -1.13467716e-01+5.4482371e-08j,
        -9.31322575e-10-4.3957941e-02j,  1.13467701e-01+1.2107193e-08j]],
      dtype=complex64), array([[ 0.8680593 -3.7252901e-09j,  0.        +0.0000000e+00j,
        -0.0326242 +3.3684942e-01j,  0.        +0.0000000e+00j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j],
       [-0.0326242 -3.3684960e-01j,  0.        +0.0000000e+00j,
         0.13194019+3.7252901e-09j,  0.        +0.0000000e+00j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j]],
      dtype=complex64)]
after:  [array([[ 9.5268482e-01+3.72528941e-09j,  2.6077029e-08-1.93513691e-01j,
         3.7252894e-09+8.55914056e-02j, -1.7385796e-02-2.60770285e-08j],
       [-1.4901159e-08+1.93513721e-01j,  3.9307393e-02+1.49011594e-08j,
        -1.7385736e-02+1.49011594e-08j,  1.4901159e-08-3.53148533e-03j],
       [-9.6857541e-08-8.55914503e-02j, -1.7385788e-02+7.45058060e-09j,
         7.6897405e-03+7.45058060e-09j,  7.4505806e-09+1.56197720e-03j],
       [-1.7385691e-02+1.15483985e-07j,  4.8428763e-08+3.53150861e-03j,
         2.6077029e-08-1.56196777e-03j,  3.1725515e-04-4.84287703e-08j]],
      dtype=complex64), array([[ 9.9005497e-01+3.53902543e-08j,  3.1664964e-08-8.89489651e-02j,
        -9.3132257e-09+4.37925905e-02j,  3.9344728e-03-1.67638046e-08j],
       [-5.4016706e-08+8.89489204e-02j,  7.9913586e-03+1.30385125e-08j,
        -3.9344132e-03-2.04890949e-08j, -3.1664968e-08+3.53471143e-04j],
       [ 4.6566122e-08-4.37926054e-02j, -3.9344188e-03+2.42143869e-08j,
         1.9370799e-03-1.86264337e-09j,  3.9115541e-08-1.74035260e-04j],
       [ 3.9344397e-03+8.75443078e-08j,  2.4214383e-08-3.53454030e-04j,
         1.3038514e-08+1.73950568e-04j,  1.5583799e-05+2.04890949e-08j]],
      dtype=complex64), array([[ 9.9804628e-01-1.4901160e-08j,  2.2351738e-08+0.0000000e+00j,
        -5.5879347e-08+4.4146121e-02j,  0.0000000e+00+1.1175869e-08j],
       [ 3.3527609e-08+8.4293696e-08j,  0.0000000e+00-1.8626451e-08j,
         3.0293048e-08-1.4901159e-08j,  7.4505806e-09+0.0000000e+00j],
       [ 3.7252899e-08-4.4146072e-02j,  0.0000000e+00+4.4703480e-08j,
         1.9528106e-03-1.8626450e-08j, -1.8626450e-08+1.0826625e-08j],
       [ 2.1731967e-08+2.6077029e-08j, -3.7252903e-09-3.2268680e-08j,
         7.4505806e-09-1.0742507e-08j, -4.2352642e-08-2.2204460e-16j]],
      dtype=complex64), array([[ 9.5268470e-01-1.6763805e-08j,  9.3132257e-09-1.9351369e-01j,
        -5.5879328e-09-8.5591510e-02j,  1.7385740e-02+3.1664964e-08j],
       [-2.7939674e-08+1.9351365e-01j,  3.9307430e-02-5.5879346e-09j,
         1.7385717e-02+9.3132249e-09j,  1.3038515e-08+3.5315147e-03j],
       [ 3.1664964e-08+8.5591473e-02j,  1.7385751e-02+3.9115545e-08j,
         7.6897522e-03+2.4214382e-08j,  1.3038514e-08+1.5619812e-03j],
       [ 1.7385729e-02+3.1664968e-08j, -9.3132266e-09-3.5314420e-03j,
         3.5390254e-08-1.5619704e-03j,  3.1726895e-04+1.3038515e-08j]],
      dtype=complex64), array([[ 9.5849919e-01-3.1432137e-08j,  2.5844201e-08-1.9469473e-01j,
        -8.6119268e-03+7.4505797e-09j,  7.4505797e-09+4.2396784e-02j],
       [ 8.6147320e-09+1.9469479e-01j,  3.9547369e-02-2.6775522e-08j,
         3.7252903e-08-1.7492264e-03j, -8.6118560e-03-3.7252903e-08j],
       [-8.6118896e-03-1.8422726e-08j,  7.9162401e-09+1.7492976e-03j,
         7.7331526e-05-5.8207625e-09j,  5.7043504e-08-3.8094161e-04j],
       [ 2.3719618e-08-4.2396769e-02j, -8.6118653e-03-7.1129762e-08j,
         1.3737009e-08+3.8093119e-04j,  1.8752844e-03+3.5157427e-08j]],
      dtype=complex64), array([[ 8.3504814e-01-1.4901160e-08j, -7.4505797e-09-1.6961879e-01j,
         6.5711170e-02+1.4901161e-08j,  4.4408921e-16-3.2350194e-01j],
       [ 0.0000000e+00+1.6961879e-01j,  3.4453772e-02-2.2351740e-08j,
        -4.4703480e-08+1.3347561e-02j,  6.5711163e-02+5.9604641e-08j],
       [ 6.5711170e-02+1.4901161e-08j, -1.8626451e-09-1.3347527e-02j,
         5.1709097e-03+1.1175870e-08j, -1.1175870e-08-2.5456889e-02j],
       [ 1.6763806e-08+3.2350191e-01j,  6.5711170e-02+4.0978193e-08j,
         3.7252901e-09+2.5456876e-02j,  1.2532634e-01+3.7252901e-09j]],
      dtype=complex64), array([[ 8.3504844e-01+0.0000000e+00j, -1.6961889e-01-2.9802322e-08j,
         3.7252903e-09+3.2350194e-01j,  1.4901161e-08-6.5711200e-02j],
       [-1.6961889e-01-0.0000000e+00j,  3.4453783e-02+0.0000000e+00j,
        -2.0954758e-08-6.5711193e-02j,  7.4505806e-09+1.3347570e-02j],
       [ 0.0000000e+00-3.2350203e-01j,  2.9802322e-08+6.5711223e-02j,
         1.2532625e-01+0.0000000e+00j, -2.5456840e-02+7.4505806e-09j],
       [-1.0244548e-08+6.5711230e-02j,  7.4505806e-09-1.3347548e-02j,
        -2.5456849e-02-5.3551048e-09j,  5.1708911e-03+2.7939677e-09j]],
      dtype=complex64), array([[ 8.6253977e-01-1.3969839e-08j, -3.0021060e-02+2.9802322e-08j,
        -2.9802322e-08+7.7492602e-02j, -2.2351742e-08-3.3415237e-01j],
       [-3.0020943e-02+8.4284693e-08j,  1.0449047e-03-1.4901161e-08j,
        -6.8452209e-08-2.6971824e-03j, -1.5716068e-08+1.1630243e-02j],
       [-7.3807314e-08-7.7492565e-02j, -2.9802322e-08+2.6971453e-03j,
         6.9620456e-03+4.0978193e-08j, -3.0021001e-02-1.3038516e-08j],
       [-2.2351742e-08+3.3415231e-01j,  8.9406967e-08-1.1630308e-02j,
        -3.0021068e-02-7.4505806e-08j,  1.2945236e-01+2.5145710e-08j]],
      dtype=complex64), array([[ 7.56034434e-01-1.8626450e-08j,  1.11758700e-08+2.9289156e-01j,
        -1.13467731e-01+1.4901159e-08j,  2.98023206e-08-2.9289165e-01j],
       [ 1.11758700e-08-2.9289162e-01j,  1.13467619e-01+1.8626450e-08j,
         2.98023206e-08+4.3957923e-02j, -1.13467753e-01-1.4901159e-08j],
       [-1.13467768e-01-5.1688403e-08j,  1.16415322e-08-4.3957938e-02j,
         1.70294661e-02-6.5192576e-09j,  4.65661243e-09+4.3957941e-02j],
       [ 8.84756624e-09+2.9289162e-01j, -1.13467716e-01+5.4482371e-08j,
        -9.31322575e-10-4.3957941e-02j,  1.13467701e-01+1.2107193e-08j]],
      dtype=complex64), array([[ 0.8680593 -3.7252901e-09j,  0.        +0.0000000e+00j,
        -0.0326242 +3.3684942e-01j,  0.        +0.0000000e+00j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j],
       [-0.0326242 -3.3684960e-01j,  0.        +0.0000000e+00j,
         0.13194019+3.7252901e-09j,  0.        +0.0000000e+00j],
       [ 0.        +0.0000000e+00j,  0.        +0.0000000e+00j,
         0.        +0.0000000e+00j,  0.        +0.0000000e+00j]],
      dtype=complex64)]
1.030274271558872