diff --git a/dev/generated/examples/multilevel_transmon/index.html b/dev/generated/examples/multilevel_transmon/index.html index ca5ec275..e5a1611c 100644 --- a/dev/generated/examples/multilevel_transmon/index.html +++ b/dev/generated/examples/multilevel_transmon/index.html @@ -93,141 +93,141 @@ inequality constraints with only upper bounds: 0 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 0 1.9771356e+01 3.54e+00 3.63e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0 - 1 5.2563654e+01 1.21e+00 6.94e+03 -1.0 1.98e+00 2.0 1.50e-02 5.45e-01h 1 - 2 5.2772341e+01 1.20e+00 7.03e+03 -1.0 1.32e+00 2.4 4.86e-01 5.22e-03h 1 - 3 8.2183901e+01 8.26e-01 1.35e+04 -1.0 1.87e+00 2.9 3.85e-01 4.06e-01h 1 - 4 8.1299618e+01 8.03e-01 1.55e+04 -1.0 1.41e+00 3.3 3.83e-01 2.87e-02h 1 - 5 8.7631990e+01 8.02e-01 1.41e+04 -1.0 1.58e+01 2.8 3.15e-03 2.75e-02h 1 - 6 8.7603921e+01 7.98e-01 1.45e+04 -1.0 1.16e+00 3.2 7.66e-01 5.67e-03h 1 - 7 8.7539103e+01 7.89e-01 3.10e+04 -1.0 1.31e+00 3.7 8.79e-01 1.06e-02h 1 - 8 8.5393624e+01 5.23e-01 9.67e+03 -1.0 1.13e+00 3.2 1.00e+00 3.33e-01h 1 - 9 8.5756939e+01 5.15e-01 1.34e+04 -1.0 9.95e-01 3.6 9.29e-01 1.38e-02h 1 + 0 5.5723239e+01 3.38e+00 3.62e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0 + 1 8.1026844e+01 1.49e+00 7.68e+03 -1.0 1.94e+00 2.0 1.21e-02 5.33e-01h 1 + 2 8.0785812e+01 1.48e+00 7.71e+03 -1.0 1.56e+00 2.4 3.35e-01 6.09e-03h 1 + 3 8.0276483e+01 1.46e+00 1.13e+04 -1.0 2.28e+00 2.9 2.74e-01 1.86e-02h 1 + 4 7.5205549e+01 1.33e+00 9.76e+03 -1.0 2.67e+00 2.4 3.79e-01 8.80e-02f 1 + 5 7.4443813e+01 1.30e+00 1.12e+04 -1.0 1.68e+00 2.8 3.60e-01 2.66e-02h 1 + 6 6.4145735e+01 9.75e-01 2.19e+04 -1.0 1.78e+00 3.2 6.58e-01 2.79e-01f 1 + 7 6.4269614e+01 9.66e-01 2.37e+04 -1.0 2.31e+00 3.7 2.99e-01 9.58e-03h 1 + 8 6.4747156e+01 9.14e-01 6.99e+04 -1.0 2.40e+00 4.1 8.67e-01 5.38e-02h 1 + 9 6.5623209e+01 8.57e-01 4.65e+04 -1.0 1.79e+00 3.6 4.41e-01 6.24e-02h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 10 9.1485247e+01 3.80e-01 9.06e+03 -1.0 9.49e-01 3.1 3.50e-01 2.81e-01h 1 - 11 9.1565466e+01 3.77e-01 8.59e+03 -1.0 7.32e-01 3.6 1.67e-01 7.52e-03h 1 - 12 9.1942983e+01 3.62e-01 8.09e+03 -1.0 6.93e-01 4.0 4.10e-03 3.92e-02h 1 - 13 8.8479460e+01 2.79e-01 8.33e+03 -1.0 6.74e-01 3.5 1.00e+00 2.40e-01f 1 - 14 8.8336218e+01 2.77e-01 1.84e+04 -1.0 6.83e-01 3.9 1.00e+00 8.69e-03h 1 - 15 8.5793403e+01 2.30e-01 1.77e+04 -1.0 1.41e+00 3.4 7.44e-02 1.75e-01h 1 - 16 8.4927123e+01 2.22e-01 1.23e+04 -1.0 5.75e-01 3.9 9.07e-01 3.37e-02h 1 - 17 6.1171074e+01 4.45e-01 3.35e+04 -1.0 2.02e+00 3.4 8.63e-03 4.27e-01f 1 - 18 6.0989602e+01 4.33e-01 3.31e+04 -1.0 6.17e-01 3.8 5.34e-01 2.76e-02h 1 - 19 4.3661867e+01 2.48e-01 2.88e+04 -1.0 1.20e+00 3.3 9.66e-02 4.87e-01f 1 + 10 6.5826217e+01 8.39e-01 5.77e+04 -1.0 2.51e+00 4.0 9.75e-01 2.09e-02h 1 + 11 6.3556931e+01 5.99e-01 4.03e+04 -1.0 1.69e+00 3.6 4.71e-01 2.67e-01h 1 + 12 6.3729522e+01 5.94e-01 3.30e+04 -1.0 9.95e-01 4.0 2.81e-01 7.69e-03h 1 + 13 6.4331751e+01 5.77e-01 4.54e+04 -1.0 1.28e+00 4.4 4.40e-01 2.81e-02h 1 + 14 7.5228193e+01 3.15e-01 6.82e+04 -1.0 1.19e+00 3.9 4.93e-01 4.79e-01h 1 + 15 7.6075723e+01 3.05e-01 6.48e+04 -1.0 7.38e-01 4.4 2.53e-01 3.15e-02h 1 + 16 7.6387246e+01 2.96e-01 4.87e+04 -1.0 1.79e+00 3.9 3.48e-01 3.04e-02h 1 + 17 8.0259755e+01 2.33e-01 7.56e+04 -1.0 6.90e-01 4.3 7.88e-01 2.23e-01h 1 + 18 8.0282216e+01 2.32e-01 1.28e+05 -1.0 5.46e-01 4.7 1.00e+00 3.34e-03h 1 + 19 7.8735183e+01 1.60e-01 8.32e+04 -1.0 6.26e-01 4.2 1.00e+00 3.14e-01h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 20 4.3938259e+01 1.42e-01 5.17e+04 -1.0 7.64e-01 3.8 8.34e-03 6.20e-01h 1 - 21 4.4235631e+01 1.39e-01 4.66e+04 -1.0 5.65e-01 4.2 4.41e-01 2.62e-02h 1 - 22 5.3364889e+01 1.30e-01 7.98e+04 -1.0 8.84e-01 3.7 4.52e-01 8.54e-01h 1 - 23 5.6788650e+01 1.43e-02 3.08e+04 -1.0 2.84e-01 4.1 2.99e-01 1.00e+00h 1 - 24 5.7852254e+01 2.70e-03 1.96e+04 -1.0 7.08e-02 3.7 9.09e-01 1.00e+00f 1 - 25 5.7461678e+01 4.29e-05 1.23e+02 -1.0 1.72e-02 3.2 1.00e+00 1.00e+00f 1 - 26 5.6371418e+01 9.88e-05 1.99e+01 -1.0 3.84e-02 2.7 1.00e+00 1.00e+00f 1 - 27 5.2858039e+01 7.43e-04 1.10e+01 -1.0 6.36e-02 2.2 1.00e+00 1.00e+00f 1 - 28 4.2429948e+01 5.95e-03 1.05e+01 -1.0 1.81e-01 1.8 1.00e+00 1.00e+00f 1 - 29 1.6900244e+01 3.27e-02 1.44e+01 -1.0 3.81e-01 1.3 1.00e+00 1.00e+00f 1 + 20 7.8661221e+01 1.56e-01 1.12e+05 -1.0 4.77e-01 4.7 1.00e+00 2.86e-02h 1 + 21 6.6465063e+01 9.46e-02 1.34e+05 -1.0 4.81e-01 4.2 1.00e+00 1.00e+00f 1 + 22 6.9098663e+01 8.65e-03 8.93e+04 -1.0 1.78e-01 4.6 2.14e-01 1.00e+00f 1 + 23 6.9857611e+01 2.29e-04 6.58e+03 -1.0 2.98e-02 4.1 9.48e-01 1.00e+00f 1 + 24 6.9618402e+01 2.21e-06 5.52e+01 -1.0 4.90e-03 3.7 1.00e+00 1.00e+00f 1 + 25 6.8838026e+01 2.14e-05 2.22e+01 -1.0 1.43e-02 3.2 1.00e+00 1.00e+00f 1 + 26 6.6608868e+01 1.63e-04 1.33e+01 -1.0 2.57e-02 2.7 1.00e+00 1.00e+00f 1 + 27 5.9815428e+01 1.46e-03 1.30e+01 -1.0 7.84e-02 2.2 1.00e+00 1.00e+00f 1 + 28 4.0916288e+01 1.09e-02 1.03e+01 -1.0 2.05e-01 1.8 1.00e+00 1.00e+00f 1 + 29 7.3768141e+00 3.66e-02 1.83e+01 -1.0 3.39e-01 1.3 1.00e+00 1.00e+00f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 30 6.6377911e-01 2.88e-02 9.10e+01 -1.0 3.86e-01 0.8 1.00e+00 1.00e+00f 1 - 31 1.4328959e+01 1.33e-02 1.78e+02 -1.0 3.82e-01 0.3 6.73e-01 1.00e+00H 1 - 32 1.2693054e+01 5.58e-04 2.16e+01 -1.0 7.74e-02 1.7 1.00e+00 1.00e+00f 1 - 33 9.2226954e+00 1.17e-03 1.61e+00 -1.0 1.06e-01 1.2 1.00e+00 1.00e+00f 1 - 34 4.0478634e+00 6.59e-03 1.95e+00 -1.0 1.48e-01 0.7 1.00e+00 1.00e+00f 1 - 35 4.0733671e-01 2.51e-02 9.51e+01 -1.0 2.29e-01 0.2 1.00e+00 1.00e+00f 1 - 36 1.1643020e+00 1.88e-02 3.32e+01 -1.0 7.32e-01 -0.2 6.77e-01 2.50e-01h 3 - 37 1.1592940e+00 4.49e-04 3.50e+00 -1.0 5.05e-02 1.1 1.00e+00 1.00e+00h 1 - 38 5.7018058e-01 1.40e-03 8.47e-01 -1.0 6.01e-02 0.6 1.00e+00 1.00e+00f 1 - 39 7.2749626e-02 1.52e-03 9.60e+01 -1.7 8.02e-02 0.1 1.00e+00 1.00e+00f 1 + 30 2.7815621e-01 2.09e-02 8.11e+01 -1.0 2.85e-01 0.8 1.00e+00 1.00e+00f 1 + 31 1.3626490e+01 8.90e-03 8.86e+01 -1.0 3.94e-01 0.3 1.00e+00 1.00e+00H 1 + 32 1.1337699e+01 5.87e-04 2.20e+01 -1.0 5.10e-02 1.7 1.00e+00 1.00e+00f 1 + 33 8.4813411e+00 1.70e-03 1.40e+00 -1.0 9.22e-02 1.2 1.00e+00 1.00e+00f 1 + 34 3.0724703e+00 9.09e-03 1.31e+00 -1.0 1.89e-01 0.7 1.00e+00 1.00e+00f 1 + 35 2.1968123e+00 2.63e-02 7.53e+01 -1.0 2.66e-01 0.2 1.00e+00 1.00e+00f 1 + 36 6.9103718e-01 7.22e-01 5.19e+02 -1.0 9.53e-01 -0.2 1.87e-01 5.46e-01F 1 + 37 5.9787453e+00 5.40e-01 3.98e+02 -1.0 1.04e+00 1.1 8.37e-01 2.66e-01h 2 + 38 3.2434670e+00 1.04e-01 3.37e+02 -1.0 7.78e-01 1.5 4.09e-01 1.00e+00h 1 + 39 2.2241465e-01 1.75e-02 9.63e+01 -1.0 2.86e-01 1.9 1.00e+00 1.00e+00f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 40 1.6452813e-01 8.99e-04 4.80e+01 -1.7 8.32e-02 -0.4 1.00e+00 5.00e-01h 2 - 41 1.8829481e-01 7.48e-05 1.62e+00 -1.7 1.70e-02 1.0 1.00e+00 1.00e+00h 1 - 42 8.2973075e-02 2.06e-04 8.17e-02 -1.7 2.58e-02 0.5 1.00e+00 1.00e+00f 1 - 43 2.6522958e-02 2.50e-04 9.63e+01 -2.5 3.34e-02 0.0 1.00e+00 1.00e+00h 1 - 44 5.5926169e-02 1.50e-04 9.63e+01 -2.5 2.14e-02 -0.5 1.00e+00 1.00e+00h 1 - 45 6.3760313e-02 1.67e-07 2.04e-01 -2.5 1.17e-03 1.8 1.00e+00 1.00e+00h 1 - 46 5.7167958e-02 1.79e-06 5.83e-02 -2.5 2.92e-03 1.3 1.00e+00 1.00e+00f 1 - 47 4.2181147e-02 1.14e-05 4.76e-02 -2.5 7.15e-03 0.8 1.00e+00 1.00e+00f 1 - 48 2.0532016e-02 4.18e-05 2.87e-02 -2.5 1.29e-02 0.3 1.00e+00 1.00e+00h 1 - 49 1.6605396e-02 6.19e-05 9.64e+01 -2.5 1.33e-02 -0.1 1.00e+00 1.00e+00h 1 + 40 1.1502289e+00 4.39e-04 1.69e+01 -1.0 3.26e-02 1.5 1.00e+00 1.00e+00h 1 + 41 6.1451414e-01 2.36e-04 6.51e-01 -1.0 4.40e-02 1.0 1.00e+00 1.00e+00f 1 + 42 8.5819949e-02 6.92e-04 1.54e-01 -1.7 4.88e-02 0.5 1.00e+00 1.00e+00f 1 + 43 8.6767541e-02 4.60e-04 7.29e+01 -2.5 4.72e-02 0.0 1.00e+00 1.00e+00h 1 + 44 7.0663304e-02 3.41e-04 7.28e+01 -2.5 2.84e-02 -0.5 1.00e+00 1.00e+00h 1 + 45 7.9881071e-02 6.10e-07 3.20e-01 -2.5 1.58e-03 1.8 1.00e+00 1.00e+00h 1 + 46 6.6796267e-02 3.25e-06 8.15e-02 -2.5 4.08e-03 1.3 1.00e+00 1.00e+00f 1 + 47 4.0975600e-02 1.46e-05 6.27e-02 -2.5 9.41e-03 0.8 1.00e+00 1.00e+00f 1 + 48 1.3439429e-02 3.48e-05 3.40e-02 -2.5 1.53e-02 0.3 1.00e+00 1.00e+00h 1 + 49 1.4285231e-02 4.56e-05 7.27e+01 -2.5 1.55e-02 -0.1 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 50 1.7246665e-02 2.09e-04 9.64e+01 -2.5 3.04e-02 -0.6 1.00e+00 1.00e+00h 1 - 51 1.8022397e-02 5.99e-08 1.03e-01 -2.5 5.76e-04 1.6 1.00e+00 1.00e+00h 1 - 52 1.7169751e-02 3.67e-07 1.63e-02 -2.5 1.16e-03 1.1 1.00e+00 1.00e+00h 1 - 53 1.5340291e-02 1.57e-06 1.26e-02 -3.8 2.70e-03 0.7 1.00e+00 1.00e+00h 1 - 54 1.3216567e-02 4.37e-06 8.16e-03 -3.8 4.27e-03 0.2 1.00e+00 1.00e+00h 1 - 55 1.3303181e-02 3.92e-06 9.64e+01 -3.8 3.55e-03 -0.3 1.00e+00 1.00e+00h 1 - 56 1.3094559e-02 2.15e-07 9.64e+01 -3.8 6.71e-04 0.1 1.00e+00 1.00e+00h 1 - 57 1.3096356e-02 2.37e-09 1.73e-02 -3.8 9.65e-05 1.5 1.00e+00 1.00e+00h 1 - 58 1.3067019e-02 1.57e-08 2.29e-03 -3.8 2.32e-04 1.0 1.00e+00 1.00e+00h 1 - 59 1.3011445e-02 7.80e-08 1.62e-03 -3.8 4.94e-04 0.5 1.00e+00 1.00e+00h 1 + 50 1.3191096e-02 5.74e-05 7.27e+01 -2.5 2.30e-02 -0.6 1.00e+00 1.00e+00h 1 + 51 1.3748983e-02 4.19e-08 1.14e-01 -2.5 4.36e-04 1.6 1.00e+00 1.00e+00h 1 + 52 1.3046266e-02 2.70e-07 1.62e-02 -2.5 1.15e-03 1.1 1.00e+00 1.00e+00h 1 + 53 1.1615483e-02 9.70e-07 1.05e-02 -3.8 2.25e-03 0.7 1.00e+00 1.00e+00h 1 + 54 1.0213822e-02 2.15e-06 7.26e+01 -3.8 3.23e-03 0.2 1.00e+00 1.00e+00h 1 + 55 1.1209306e-02 1.34e-06 7.26e+01 -3.8 2.25e-03 -0.3 1.00e+00 1.00e+00h 1 + 56 1.1393618e-02 2.11e-09 2.48e-02 -3.8 9.83e-05 1.9 1.00e+00 1.00e+00h 1 + 57 1.1275511e-02 1.55e-08 7.97e-03 -3.8 2.70e-04 1.5 1.00e+00 1.00e+00h 1 + 58 1.0986690e-02 1.03e-07 6.81e-03 -3.8 6.91e-04 1.0 1.00e+00 1.00e+00h 1 + 59 1.0489449e-02 4.37e-07 4.49e-03 -3.8 1.37e-03 0.5 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 60 1.2965672e-02 1.95e-07 9.64e+01 -3.8 6.70e-04 0.0 1.00e+00 1.00e+00h 1 - 61 1.2970561e-02 4.60e-07 9.64e+01 -3.8 2.24e-03 -0.4 1.00e+00 1.00e+00h 1 - 62 1.2976088e-02 1.42e-10 4.65e-03 -3.8 2.18e-05 1.8 1.00e+00 1.00e+00h 1 - 63 1.2971722e-02 1.20e-09 1.20e-03 -3.8 5.80e-05 1.3 1.00e+00 1.00e+00h 1 - 64 1.2961374e-02 7.84e-09 1.01e-03 -4.0 1.46e-04 0.8 1.00e+00 1.00e+00h 1 - 65 1.2944045e-02 3.50e-08 8.24e-04 -4.0 2.79e-04 0.4 1.00e+00 1.00e+00h 1 - 66 1.2931588e-02 8.28e-08 9.64e+01 -4.0 6.84e-04 -0.1 1.00e+00 1.00e+00h 1 - 67 1.2906983e-02 1.23e-06 9.64e+01 -4.0 3.11e-03 -0.6 1.00e+00 1.00e+00h 1 - 68 1.2907885e-02 1.08e-10 5.08e-03 -4.0 1.53e-05 1.6 1.00e+00 1.00e+00h 1 - 69 1.2906602e-02 4.93e-10 5.94e-04 -4.0 4.07e-05 1.2 1.00e+00 1.00e+00h 1 + 60 1.0244791e-02 7.97e-07 7.25e+01 -3.8 1.68e-03 0.0 1.00e+00 1.00e+00h 1 + 61 1.0351033e-02 5.42e-07 7.25e+01 -3.8 1.88e-03 -0.4 1.00e+00 1.00e+00h 1 + 62 1.0387606e-02 7.72e-10 1.31e-02 -3.8 5.21e-05 1.8 1.00e+00 1.00e+00h 1 + 63 1.0357888e-02 5.49e-09 2.91e-03 -3.8 1.40e-04 1.3 1.00e+00 1.00e+00h 1 + 64 1.0289690e-02 3.42e-08 2.45e-03 -3.8 3.54e-04 0.8 1.00e+00 1.00e+00h 1 + 65 1.0189474e-02 1.26e-07 1.55e-03 -3.8 6.73e-04 0.4 1.00e+00 1.00e+00h 1 + 66 1.0166040e-02 2.11e-07 7.25e+01 -3.8 9.89e-04 -0.1 1.00e+00 1.00e+00h 1 + 67 1.0143407e-02 4.64e-07 7.25e+01 -3.8 2.66e-03 -0.6 1.00e+00 1.00e+00h 1 + 68 1.0148036e-02 2.00e-10 6.80e-03 -3.8 2.67e-05 1.6 1.00e+00 1.00e+00h 1 + 69 1.0143424e-02 1.38e-09 1.06e-03 -3.8 7.28e-05 1.2 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 70 1.2903605e-02 3.12e-09 5.60e-04 -4.0 1.15e-04 0.7 1.00e+00 1.00e+00h 1 - 71 1.2897716e-02 1.45e-08 7.70e-04 -4.0 3.39e-04 0.2 1.00e+00 1.00e+00h 1 - 72 1.2885640e-02 1.24e-07 9.64e+01 -4.0 1.11e-03 -0.3 1.00e+00 1.00e+00h 1 - 73 1.2881467e-02 1.58e-08 9.64e+01 -4.0 3.87e-04 0.2 1.00e+00 1.00e+00h 1 - 74 1.2881371e-02 3.33e-10 1.05e-02 -4.0 2.47e-05 1.5 1.00e+00 1.00e+00h 1 - 75 1.2880628e-02 3.01e-10 6.22e-04 -4.0 6.08e-05 1.0 1.00e+00 1.00e+00h 1 - 76 1.2878553e-02 2.27e-09 5.91e-04 -4.0 1.73e-04 0.5 1.00e+00 1.00e+00h 1 - 77 1.2872819e-02 2.11e-08 1.06e-03 -4.0 5.10e-04 0.1 1.00e+00 1.00e+00h 1 - 78 1.2856044e-02 3.27e-07 3.96e-03 -4.0 1.73e-03 -0.4 1.00e+00 1.00e+00h 1 - 79 1.2849769e-02 2.77e-08 1.18e-03 -4.0 5.73e-04 0.0 1.00e+00 1.00e+00h 1 + 70 1.0133428e-02 7.83e-09 8.62e-04 -4.0 1.77e-04 0.7 1.00e+00 1.00e+00h 1 + 71 1.0119721e-02 2.83e-08 6.70e-04 -4.0 3.90e-04 0.2 1.00e+00 1.00e+00h 1 + 72 1.0109091e-02 6.48e-08 7.25e+01 -4.0 1.03e-03 -0.3 1.00e+00 1.00e+00h 1 + 73 1.0075678e-02 7.74e-07 7.25e+01 -4.0 3.45e-03 -0.7 1.00e+00 1.00e+00h 1 + 74 1.0076570e-02 6.94e-11 4.95e-03 -4.0 2.10e-05 1.5 1.00e+00 1.00e+00h 1 + 75 1.0075406e-02 4.40e-10 5.91e-04 -4.0 5.77e-05 1.0 1.00e+00 1.00e+00h 1 + 76 1.0072622e-02 2.67e-09 5.35e-04 -4.0 1.57e-04 0.5 1.00e+00 1.00e+00h 1 + 77 1.0066541e-02 1.42e-08 5.40e-04 -4.0 4.74e-04 0.1 1.00e+00 1.00e+00h 1 + 78 1.0051075e-02 1.11e-07 7.25e+01 -4.0 1.48e-03 -0.4 1.00e+00 1.00e+00h 1 + 79 1.0001362e-02 3.92e-06 7.25e+01 -4.0 6.30e-03 -0.9 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 80 1.2830970e-02 4.71e-07 4.77e-03 -4.0 2.01e-03 -0.5 1.00e+00 1.00e+00h 1 - 81 1.2823949e-02 3.58e-08 1.28e-03 -4.0 6.46e-04 -0.0 1.00e+00 1.00e+00h 1 - 82 1.2802832e-02 6.97e-07 5.84e-03 -4.0 2.36e-03 -0.5 1.00e+00 1.00e+00h 1 - 83 1.2795017e-02 4.65e-08 1.45e-03 -4.0 7.29e-04 -0.1 1.00e+00 1.00e+00h 1 - 84 1.2771112e-02 1.08e-06 7.32e-03 -4.0 2.81e-03 -0.6 1.00e+00 1.00e+00h 1 - 85 1.2762535e-02 6.06e-08 1.66e-03 -4.0 8.23e-04 -0.1 1.00e+00 1.00e+00h 1 - 86 1.2735846e-02 1.83e-06 9.64e+01 -4.0 3.41e-03 -0.6 1.00e+00 1.00e+00h 1 - 87 1.2726153e-02 9.08e-08 9.64e+01 -4.0 8.69e-04 -0.2 1.00e+00 1.00e+00h 1 - 88 1.2726478e-02 1.03e-11 1.58e-03 -4.0 6.79e-06 2.0 1.00e+00 1.00e+00h 1 - 89 1.2726202e-02 4.34e-11 6.96e-04 -4.0 1.94e-05 1.6 1.00e+00 1.00e+00h 1 + 80 1.0001903e-02 4.54e-10 1.74e-02 -4.0 3.73e-05 1.3 1.00e+00 1.00e+00h 1 + 81 1.0000730e-02 5.06e-10 5.30e-04 -4.0 7.37e-05 0.9 1.00e+00 1.00e+00h 1 + 82 9.9977831e-03 3.58e-09 5.29e-04 -4.0 2.21e-04 0.4 1.00e+00 1.00e+00h 1 + 83 9.9902381e-03 2.55e-08 5.80e-04 -4.0 6.69e-04 -0.1 1.00e+00 1.00e+00h 1 + 84 9.9688387e-03 2.28e-07 7.25e+01 -4.0 2.13e-03 -0.6 1.00e+00 1.00e+00h 1 + 85 9.9610081e-03 3.75e-08 7.25e+01 -4.0 7.36e-04 -0.1 1.00e+00 1.00e+00h 1 + 86 9.9614267e-03 1.76e-12 8.31e-04 -4.0 4.27e-06 2.1 1.00e+00 1.00e+00h 1 + 87 9.9612335e-03 1.51e-11 5.24e-04 -4.0 1.30e-05 1.6 1.00e+00 1.00e+00h 1 + 88 9.9606864e-03 1.28e-10 5.23e-04 -4.0 3.88e-05 1.1 1.00e+00 1.00e+00h 1 + 89 9.9591966e-03 1.00e-09 5.22e-04 -4.0 1.16e-04 0.7 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 90 1.2725485e-02 3.10e-10 6.59e-04 -4.0 5.50e-05 1.1 1.00e+00 1.00e+00h 1 - 91 1.2723695e-02 2.37e-09 6.07e-04 -4.0 1.52e-04 0.6 1.00e+00 1.00e+00h 1 - 92 1.2718965e-02 1.73e-08 9.74e-04 -4.0 4.31e-04 0.1 1.00e+00 1.00e+00h 1 - 93 1.2705298e-02 1.98e-07 3.09e-03 -4.0 1.39e-03 -0.4 1.00e+00 1.00e+00h 1 - 94 1.2700169e-02 2.03e-08 1.05e-03 -4.0 4.73e-04 0.1 1.00e+00 1.00e+00h 1 - 95 1.2684848e-02 2.78e-07 3.66e-03 -4.0 1.60e-03 -0.4 1.00e+00 1.00e+00h 1 - 96 1.2679103e-02 2.47e-08 1.14e-03 -4.0 5.32e-04 0.0 1.00e+00 1.00e+00h 1 - 97 1.2661939e-02 3.95e-07 4.38e-03 -4.0 1.85e-03 -0.5 1.00e+00 1.00e+00h 1 - 98 1.2655519e-02 3.12e-08 1.24e-03 -4.0 6.00e-04 -0.0 1.00e+00 1.00e+00h 1 - 99 1.2636246e-02 5.79e-07 5.33e-03 -4.0 2.17e-03 -0.5 1.00e+00 1.00e+00h 1 + 90 9.9551763e-03 7.44e-09 5.24e-04 -4.0 3.50e-04 0.2 1.00e+00 1.00e+00h 1 + 91 9.9435864e-03 6.11e-08 1.08e-03 -4.0 1.08e-03 -0.3 1.00e+00 1.00e+00h 1 + 92 9.9094353e-03 7.33e-07 7.24e+01 -4.0 3.67e-03 -0.8 1.00e+00 1.00e+00h 1 + 93 9.8963519e-03 9.45e-08 7.24e+01 -4.0 1.20e-03 -0.4 1.00e+00 1.00e+00h 1 + 94 9.8968165e-03 5.01e-12 1.30e-03 -4.0 6.84e-06 1.9 1.00e+00 1.00e+00h 1 + 95 9.8965017e-03 3.84e-11 5.14e-04 -4.0 2.04e-05 1.4 1.00e+00 1.00e+00h 1 + 96 9.8956344e-03 3.16e-10 5.13e-04 -4.0 6.10e-05 0.9 1.00e+00 1.00e+00h 1 + 97 9.8933491e-03 2.39e-09 5.13e-04 -4.0 1.83e-04 0.4 1.00e+00 1.00e+00h 1 + 98 9.8871777e-03 1.79e-08 5.18e-04 -4.0 5.54e-04 -0.0 1.00e+00 1.00e+00h 1 + 99 9.8692933e-03 1.60e-07 7.24e+01 -4.0 1.75e-03 -0.5 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 100 1.2629100e-02 4.05e-08 1.35e-03 -4.0 6.77e-04 -0.1 1.00e+00 1.00e+00h 1 + 100 9.8629890e-03 2.72e-08 7.24e+01 -4.0 6.10e-04 -0.1 1.00e+00 1.00e+00h 1 Number of Iterations....: 100 (scaled) (unscaled) -Objective...............: 1.2629099539928582e-02 1.2629099539928582e-02 -Dual infeasibility......: 1.3520013631410424e-03 1.3520013631410424e-03 -Constraint violation....: 4.0487827354662720e-08 4.0487827354662720e-08 +Objective...............: 9.8629889609505618e-03 9.8629889609505618e-03 +Dual infeasibility......: 7.2435825295257160e+01 7.2435825295257160e+01 +Constraint violation....: 2.7165533059148039e-08 2.7165533059148039e-08 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00 -Complementarity.........: 9.9999999999999964e-05 9.9999999999999964e-05 -Overall NLP error.......: 1.3520013631410424e-03 1.3520013631410424e-03 +Complementarity.........: 9.9999999999979486e-05 9.9999999999979486e-05 +Overall NLP error.......: 7.2435825295257160e+01 7.2435825295257160e+01 -Number of objective function evaluations = 108 +Number of objective function evaluations = 104 Number of objective gradient evaluations = 101 -Number of equality constraint evaluations = 108 +Number of equality constraint evaluations = 104 Number of inequality constraint evaluations = 0 Number of equality constraint Jacobian evaluations = 101 Number of inequality constraint Jacobian evaluations = 0 Number of Lagrangian Hessian evaluations = 100 -Total seconds in IPOPT = 13.372 +Total seconds in IPOPT = 14.911 EXIT: Maximum Number of Iterations Exceeded.

and we can look at the fidelity in the subspace

f = unitary_fidelity(prob; subspace=subspace)
 
-println("Fidelity: $f")
Fidelity: 0.9983739488690163

We can also look at the pulse shapes

transformations = OrderedDict(
+println("Fidelity: $f")
Fidelity: 0.9999402852918097

We can also look at the pulse shapes

transformations = OrderedDict(
     :Ũ⃗ => [
         x -> populations(iso_vec_to_operator(x)[:, 1]),
         x -> populations(iso_vec_to_operator(x)[:, 2]),
@@ -254,7 +254,7 @@
     transformation_labels=transforamtion_labels,
     include_transformation_labels=true,
     transformation_titles=transformation_titles
-)

Leakage suppression

As can bee seen in the plot above, although the fidelity is high, the $f$ level of the transmon is highly populated throughout the evolution. This is suboptimal, but we can account for this by penalizing the leakage elements of the unitary, namely those elements of the form $U_{f, i}$ where $i \neq f$. We utilize an $L_1$ penalty on these elements, which is implemented in the UnitarySmoothPulseProblem type as the leakage_penalty keyword argument.

# get the indices of the leakage subspace of the isomorphic vector representation
+)

Leakage suppression

As can bee seen in the plot above, although the fidelity is high, the $f$ level of the transmon is highly populated throughout the evolution. This is suboptimal, but we can account for this by penalizing the leakage elements of the unitary, namely those elements of the form $U_{f, i}$ where $i \neq f$. We utilize an $L_1$ penalty on these elements, which is implemented in the UnitarySmoothPulseProblem type as the leakage_penalty keyword argument.

# get the indices of the leakage subspace of the isomorphic vector representation
 # of the unitary
 leakage_indices = subspace_leakage_indices(levels)
 
@@ -302,136 +302,136 @@
         inequality constraints with only upper bounds:        0
 
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-   0  4.5721710e+01 1.31e+00 7.55e-04  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
-   1  3.5624894e+01 9.44e-01 9.42e+01  -1.0 2.29e+00  -4.0 3.06e-01 2.78e-01f  1
-   2  3.5787933e+01 9.38e-01 4.86e+00  -1.0 2.87e+01  -4.5 5.51e-02 6.10e-03h  4
-   3  2.4972550e+01 4.03e-01 4.87e+00  -1.0 7.57e-01  -0.4 4.71e-01 5.71e-01f  1
-   4  2.0264802e+01 2.14e-02 2.61e+00  -1.0 3.89e-01  -0.0 1.00e+00 9.65e-01f  1
-   5  1.9284742e+01 1.11e-03 4.03e-01  -1.0 6.14e-02   0.4 1.00e+00 1.00e+00f  1
-   6  1.2135570e+01 2.34e-02 2.16e+00  -1.7 2.23e-01  -0.1 9.43e-01 9.50e-01f  1
-   7  1.1088999e+01 5.29e-03 6.64e-01  -1.7 1.27e-01   0.4 1.00e+00 1.00e+00f  1
-   8  8.9091108e+00 9.64e-02 4.23e+00  -1.7 5.03e-01  -0.1 8.91e-01 7.53e-01f  1
-   9  7.9989019e+00 3.33e-02 9.16e+01  -1.7 1.94e-01   0.3 1.00e+00 7.02e-01f  1
+   0  4.9324784e+01 1.56e+00 8.66e-04  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
+   1  3.2056515e+01 7.71e-01 8.49e+01  -1.0 1.56e+00  -4.0 5.33e-01 5.04e-01f  1
+   2  5.1752525e+01 4.09e-01 6.69e+01  -1.0 9.40e-01   0.0 1.20e-01 4.70e-01h  1
+   3  4.0179696e+01 2.09e-01 3.60e+01  -1.0 3.78e-01   1.4 5.09e-01 4.89e-01f  1
+   4  2.4791795e+01 6.87e-03 8.41e+01  -1.0 2.34e-01   0.9 1.00e+00 1.00e+00f  1
+   5  2.1586753e+01 1.88e-02 8.56e+01  -1.0 1.69e-01   0.4 1.00e+00 1.00e+00f  1
+   6  2.1181389e+01 4.80e-04 1.16e+01  -1.0 3.78e-02   1.7 1.00e+00 1.00e+00h  1
+   7  2.1089030e+01 7.50e-05 5.01e-01  -1.0 2.72e-02   1.3 1.00e+00 1.00e+00f  1
+   8  1.6619614e+01 3.53e-04 3.67e-01  -1.7 5.98e-02   0.8 1.00e+00 1.00e+00f  1
+   9  1.3729580e+01 1.55e-03 2.17e-01  -1.7 1.06e-01   0.3 1.00e+00 1.00e+00f  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  10  8.5161363e+00 3.08e-02 7.20e+00  -1.7 1.34e+00  -0.2 4.02e-01 7.85e-02h  3
-  11  6.9833669e+00 1.71e-02 9.18e+01  -1.7 1.96e-01   0.3 1.00e+00 1.00e+00f  1
-  12  6.7523297e+00 1.76e-02 1.06e+01  -1.7 1.07e+00  -0.2 5.16e-01 1.16e-01f  2
-  13  5.9998727e+00 6.41e-03 9.17e+01  -1.7 1.01e-01   0.2 9.87e-01 1.00e+00f  1
-  14  5.6807919e+00 2.20e-02 4.33e+01  -1.7 5.00e-01  -0.3 6.88e-01 3.55e-01f  1
-  15  5.4347170e+00 5.54e-04 5.30e+00  -1.7 3.18e-02   1.1 1.00e+00 1.00e+00f  1
-  16  5.3871653e+00 3.52e-04 1.77e-01  -1.7 2.64e-02   0.6 1.00e+00 1.00e+00h  1
-  17  3.8661357e+00 3.76e-03 4.93e-01  -2.5 7.73e-02   0.1 8.70e-01 9.26e-01f  1
-  18  3.3875685e+00 9.80e-03 1.11e+00  -2.5 4.16e-01  -0.4 1.00e+00 4.01e-01f  1
-  19  3.2536163e+00 5.35e-03 7.09e-01  -2.5 9.11e-02   0.1 1.00e+00 4.61e-01h  1
+  10  1.2701116e+01 2.95e-02 8.77e+01  -1.7 2.75e-01  -0.2 1.00e+00 1.00e+00f  1
+  11  1.3340572e+01 1.85e-02 1.21e+02  -1.7 3.73e-01   0.3 1.00e+00 6.95e-01h  1
+  12  1.2108332e+01 2.21e-04 6.93e+00  -1.7 3.85e-02   1.6 1.00e+00 1.00e+00f  1
+  13  1.2051293e+01 3.83e-05 2.02e-01  -1.7 1.17e-02   1.1 1.00e+00 1.00e+00h  1
+  14  1.1828863e+01 3.49e-04 1.47e-01  -1.7 3.40e-02   0.6 1.00e+00 1.00e+00f  1
+  15  1.0306696e+01 1.54e-03 2.97e-01  -2.5 1.07e-01   0.2 9.62e-01 8.36e-01f  1
+  16  9.4711204e+00 3.39e-03 4.97e-01  -2.5 3.39e-01  -0.3 6.94e-01 3.66e-01f  1
+  17  8.7033612e+00 2.61e-03 3.41e-01  -2.5 1.05e-01   0.1 1.00e+00 9.52e-01f  1
+  18  8.2206829e+00 4.00e-03 4.94e-01  -2.5 3.77e-01  -0.4 1.86e-01 2.18e-01f  1
+  19  7.7352259e+00 3.35e-03 5.26e-01  -2.5 9.89e-02   0.1 1.00e+00 6.47e-01f  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  20  2.9435769e+00 4.59e-03 7.38e-01  -2.5 2.70e-01  -0.4 1.00e+00 3.45e-01f  1
-  21  2.8188606e+00 2.48e-03 5.06e-01  -2.5 9.61e-02   0.0 9.54e-01 5.19e-01h  1
-  22  2.5414509e+00 3.93e-03 7.64e-01  -2.5 2.66e-01  -0.5 6.94e-01 3.69e-01f  1
-  23  2.4986536e+00 2.06e-03 5.40e-01  -2.5 8.92e-02  -0.0 1.00e+00 5.08e-01h  1
-  24  2.1604298e+00 1.42e-02 9.68e+01  -2.5 2.40e-01  -0.5 5.54e-01 9.42e-01f  1
-  25  2.0686651e+00 1.17e-02 1.89e+01  -2.5 2.48e-01  -0.1 1.69e-01 1.97e-01f  1
-  26  2.0073528e+00 1.06e-02 8.08e+01  -2.5 7.05e-01   0.3 1.09e-01 9.17e-02h  2
-  27  1.9546463e+00 9.54e-03 2.54e+01  -2.5 1.91e-01  -0.1 1.54e-01 1.02e-01h  1
-  28  2.0316229e+00 1.66e-04 2.14e+00  -2.5 1.99e-02   1.2 4.57e-01 1.00e+00h  1
-  29  2.0212155e+00 9.80e-05 1.68e+00  -2.5 1.27e-02   0.7 1.00e+00 4.09e-01h  1
+  20  7.4185584e+00 4.46e-03 7.29e-01  -2.5 4.43e-01  -0.4 2.78e-01 1.31e-01f  1
+  21  7.1061911e+00 3.79e-03 5.05e-01  -2.5 1.27e-01   0.0 4.88e-01 3.81e-01f  1
+  22  6.4961905e+00 5.79e-03 5.09e-01  -2.5 4.78e-01  -0.5 1.32e-01 2.29e-01f  1
+  23  6.0732334e+00 4.65e-03 4.14e-01  -2.5 1.45e-01  -0.0 6.14e-01 4.33e-01f  1
+  24  5.7569768e+00 4.60e-03 6.51e-01  -2.5 5.85e-01  -0.5 2.62e-01 1.06e-01f  1
+  25  5.4201196e+00 3.39e-03 8.97e+01  -2.5 1.92e-01  -0.1 2.43e-01 5.83e-01f  1
+  26  5.3226396e+00 3.09e-03 1.22e+01  -2.5 5.45e-01  -0.6 2.78e-01 1.36e-01f  1
+  27  5.2393175e+00 5.86e-05 7.85e-01  -2.5 1.93e-02   0.8 7.05e-01 1.00e+00f  1
+  28  5.0858572e+00 3.98e-04 1.15e-01  -2.5 6.10e-02   0.3 1.00e+00 1.00e+00f  1
+  29  4.9722811e+00 4.34e-04 6.77e-01  -2.5 1.90e-01  -0.2 8.19e-01 2.61e-01f  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  30  1.9853504e+00 1.18e-04 1.25e-01  -2.5 2.55e-02   0.2 1.00e+00 1.00e+00f  1
-  31  1.8904322e+00 5.90e-04 2.60e-01  -2.5 7.39e-02  -0.3 1.00e+00 8.29e-01h  1
-  32  1.7837722e+00 1.18e-03 8.15e-01  -2.5 4.40e-01  -0.7 5.45e-01 2.26e-01f  1
-  33  1.7577856e+00 1.17e-03 2.66e-01  -2.5 8.97e-02  -0.3 1.00e+00 1.00e+00f  1
-  34  1.5476156e+00 5.20e-03 7.69e-01  -2.5 3.08e-01  -0.8 6.37e-01 7.12e-01h  1
-  35  1.4689243e+00 1.83e-03 4.05e-01  -2.5 1.05e-01  -0.4 1.00e+00 7.70e-01h  1
-  36  1.4212120e+00 5.75e-03 9.80e+01  -2.5 5.37e-01  -0.8 1.98e-01 2.50e-01f  2
-  37  1.4360418e+00 3.72e-03 3.70e+01  -2.5 3.90e-01  -0.4 5.11e-01 3.78e-01H  1
-  38  1.2810050e+00 4.41e-05 1.55e+00  -2.5 1.09e-02   0.9 1.00e+00 1.00e+00f  1
-  39  1.2703778e+00 4.63e-05 4.80e-02  -2.5 1.50e-02   0.4 1.00e+00 1.00e+00h  1
+  30  4.8520516e+00 2.16e-02 9.26e-01  -2.5 3.94e+00  -0.7 7.92e-02 3.61e-02f  1
+  31  4.5523897e+00 1.21e-02 6.08e-01  -2.5 1.44e-01  -0.3 1.00e+00 9.11e-01h  1
+  32  4.3559976e+00 1.58e-03 1.46e-01  -2.5 5.53e-02   0.2 1.00e+00 1.00e+00h  1
+  33  4.0120573e+00 1.63e-02 7.43e-01  -2.5 1.86e-01  -0.3 1.00e+00 7.64e-01f  1
+  34  3.8551384e+00 3.26e-03 1.27e+00  -2.5 6.73e-02   0.1 5.75e-01 1.00e+00h  1
+  35  3.7085153e+00 6.61e-03 1.20e+00  -2.5 2.12e-01  -0.4 1.00e+00 3.64e-01f  1
+  36  3.5865666e+00 3.16e-03 2.88e-01  -2.5 6.47e-02   0.1 1.00e+00 8.94e-01f  1
+  37  3.2090824e+00 4.58e-02 1.82e+00  -2.5 2.71e-01  -0.4 5.87e-01 8.91e-01f  1
+  38  3.2360500e+00 4.25e-03 4.20e-01  -2.5 8.83e-02   0.0 1.00e+00 1.00e+00h  1
+  39  2.8071305e+00 1.63e-02 7.97e-01  -2.5 3.00e-01  -0.5 7.48e-01 5.36e-01f  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  40  1.2068059e+00 3.82e-04 1.43e-01  -2.5 4.73e-02  -0.0 1.00e+00 9.35e-01h  1
-  41  1.0912223e+00 1.05e-03 9.73e+01  -2.5 1.32e-01  -0.5 1.00e+00 9.07e-01f  1
-  42  1.0817915e+00 1.98e-03 2.96e+01  -2.5 3.48e-01  -1.0 3.98e-01 3.05e-01f  1
-  43  1.0888089e+00 6.23e-06 5.93e-01  -2.5 4.17e-03   1.2 1.00e+00 1.00e+00f  1
-  44  1.0809845e+00 7.61e-06 3.01e-02  -2.5 4.40e-03   0.8 1.00e+00 1.00e+00h  1
-  45  1.0701311e+00 1.89e-05 4.30e-02  -2.5 1.34e-02   0.3 1.00e+00 1.00e+00h  1
-  46  1.0470979e+00 1.73e-04 1.21e-01  -2.5 3.84e-02  -0.2 1.00e+00 1.00e+00h  1
-  47  9.9188854e-01 1.42e-03 4.00e-01  -2.5 9.97e-02  -0.7 1.00e+00 1.00e+00h  1
-  48  9.8936317e-01 1.64e-04 1.30e-01  -2.5 3.67e-02  -0.2 1.00e+00 1.00e+00h  1
-  49  9.4063687e-01 1.73e-03 5.80e-01  -2.5 1.10e-01  -0.7 1.00e+00 9.95e-01h  1
+  40  2.6546751e+00 6.94e-03 5.50e-01  -2.5 8.63e-02  -0.0 9.27e-01 6.35e-01h  1
+  41  2.2104816e+00 1.61e-02 1.01e+00  -2.5 2.95e-01  -0.5 5.98e-01 6.15e-01f  1
+  42  2.0840323e+00 7.92e-03 7.37e-01  -2.5 1.57e-01  -0.1 8.23e-01 5.08e-01h  1
+  43  1.8580830e+00 8.10e-03 7.41e-01  -2.5 3.64e-01  -0.6 5.00e-01 3.73e-01f  1
+  44  1.6253286e+00 1.23e-03 2.58e-01  -2.5 1.33e-01  -0.1 1.00e+00 1.00e+00f  1
+  45  1.4582332e+00 1.92e-03 8.75e-01  -2.5 4.12e-01  -0.6 7.73e-01 3.13e-01h  1
+  46  1.3259984e+00 1.01e-03 1.82e-01  -2.5 1.29e-01  -0.2 1.00e+00 9.95e-01f  1
+  47  1.2663984e+00 1.73e-03 9.16e+01  -2.5 4.19e-01  -0.7 6.09e-01 2.57e-01f  1
+  48  1.2027220e+00 1.29e-03 2.56e+01  -2.5 2.03e-01  -0.2 1.00e+00 2.80e-01f  1
+  49  1.2058859e+00 1.71e-04 1.53e+00  -2.5 1.77e-02   1.1 5.40e-01 1.00e+00f  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  50  9.4154116e-01 9.56e-05 1.16e-01  -2.5 3.20e-02  -0.3 1.00e+00 1.00e+00f  1
-  51  9.0975256e-01 9.33e-04 5.28e-01  -2.5 1.11e-01  -0.8 1.00e+00 1.00e+00h  1
-  52  8.9769761e-01 9.47e-05 1.38e-01  -2.5 3.04e-02  -0.3 1.00e+00 1.00e+00h  1
-  53  8.5716088e-01 1.51e-03 6.25e-01  -2.5 1.31e-01  -0.8 1.00e+00 1.00e+00h  1
-  54  8.5620613e-01 7.81e-05 1.11e-01  -2.5 2.50e-02  -0.4 1.00e+00 1.00e+00h  1
-  55  8.2908966e-01 8.23e-04 9.66e+01  -2.5 2.08e-01  -0.9 1.00e+00 5.00e-01h  2
-  56  8.4588178e-01 8.18e-04 9.65e+01  -2.5 8.00e-02  -0.4 1.00e+00 1.00e+00h  1
-  57  8.7518792e-01 2.03e-06 1.03e+00  -2.5 2.22e-03   1.8 1.00e+00 1.00e+00h  1
-  58  8.6716131e-01 4.79e-06 5.45e-02  -2.5 2.64e-03   1.3 1.00e+00 1.00e+00h  1
-  59  8.5594432e-01 1.34e-05 5.13e-02  -2.5 7.44e-03   0.8 1.00e+00 1.00e+00h  1
+  50  1.1926151e+00 1.31e-04 1.47e+00  -2.5 1.71e-02   0.6 1.00e+00 3.53e-01h  1
+  51  1.1451288e+00 2.64e-04 8.84e-02  -2.5 6.40e-02   0.1 1.00e+00 1.00e+00f  1
+  52  1.0156290e+00 1.81e-03 9.28e+01  -2.5 1.63e-01  -0.3 1.00e+00 1.00e+00f  1
+  53  9.6176421e-01 7.84e-04 9.27e+01  -2.5 8.08e-02   0.1 1.00e+00 1.00e+00h  1
+  54  9.5602262e-01 1.88e-07 3.29e-01  -2.5 8.63e-04   2.3 1.00e+00 1.00e+00h  1
+  55  9.5407603e-01 4.38e-07 8.16e-02  -2.5 1.17e-03   1.8 1.00e+00 1.00e+00h  1
+  56  9.4927388e-01 1.37e-06 7.20e-02  -2.5 3.09e-03   1.4 1.00e+00 1.00e+00f  1
+  57  9.3920171e-01 8.07e-06 7.37e-02  -2.5 9.51e-03   0.9 1.00e+00 1.00e+00f  1
+  58  9.1352410e-01 5.97e-05 7.30e-02  -2.5 2.83e-02   0.4 1.00e+00 1.00e+00h  1
+  59  8.4867274e-01 4.01e-04 9.35e+01  -2.5 7.80e-02  -0.1 1.00e+00 1.00e+00h  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  60  8.4273640e-01 2.94e-05 3.92e-02  -2.5 1.61e-02   0.4 1.00e+00 1.00e+00h  1
-  61  8.2971486e-01 4.80e-05 9.32e-02  -2.5 2.63e-02  -0.1 1.00e+00 1.00e+00h  1
-  62  8.1259571e-01 1.94e-04 2.01e-01  -2.5 5.50e-02  -0.6 1.00e+00 1.00e+00h  1
-  63  8.1449537e-01 2.87e-05 5.76e-02  -2.5 1.96e-02  -0.2 1.00e+00 1.00e+00h  1
-  64  8.0128235e-01 3.62e-04 1.54e-01  -2.5 6.85e-02  -0.6 1.00e+00 1.00e+00h  1
-  65  7.9846851e-01 3.35e-05 5.91e-02  -2.5 2.25e-02  -0.2 1.00e+00 1.00e+00h  1
-  66  7.8442160e-01 5.81e-04 1.85e-01  -2.5 8.26e-02  -0.7 1.00e+00 1.00e+00h  1
-  67  7.8170339e-01 4.10e-05 6.52e-02  -2.5 2.56e-02  -0.3 1.00e+00 1.00e+00h  1
-  68  7.6562627e-01 9.35e-04 2.31e-01  -2.5 9.95e-02  -0.7 1.00e+00 1.00e+00h  1
-  69  7.6371129e-01 5.08e-05 7.42e-02  -2.5 2.84e-02  -0.3 1.00e+00 1.00e+00h  1
+  60  7.0757276e-01 2.20e-03 8.75e+01  -2.5 1.95e-01  -0.5 1.00e+00 9.35e-01h  1
+  61  7.2416075e-01 1.07e-05 1.24e+00  -2.5 6.13e-03   1.7 5.88e-01 1.00e+00f  1
+  62  7.1605103e-01 3.75e-06 6.09e-02  -2.5 3.73e-03   1.2 1.00e+00 1.00e+00h  1
+  63  7.0650033e-01 1.38e-05 3.99e-02  -2.5 7.32e-03   0.7 1.00e+00 1.00e+00h  1
+  64  6.8834498e-01 3.54e-05 9.41e+01  -2.5 1.95e-02   0.3 1.00e+00 1.00e+00h  1
+  65  6.6397484e-01 3.42e-04 9.42e+01  -2.5 4.66e-02  -0.2 1.00e+00 1.00e+00h  1
+  66  6.7177821e-01 3.52e-07 3.97e-01  -2.5 1.03e-03   2.0 1.00e+00 1.00e+00h  1
+  67  6.6984479e-01 1.20e-06 6.81e-02  -2.5 1.98e-03   1.5 1.00e+00 1.00e+00h  1
+  68  6.6499857e-01 4.96e-06 4.83e-02  -2.5 4.21e-03   1.1 1.00e+00 1.00e+00h  1
+  69  6.5587356e-01 1.40e-05 3.16e-02  -2.5 8.26e-03   0.6 1.00e+00 1.00e+00h  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  70  7.4249185e-01 1.57e-03 3.19e-01  -2.5 1.21e-01  -0.8 1.00e+00 1.00e+00h  1
-  71  7.4354657e-01 6.91e-05 8.35e-02  -2.5 3.01e-02  -0.4 1.00e+00 1.00e+00h  1
-  72  7.2830717e-01 3.16e-03 9.83e+01  -2.5 1.48e-01  -0.8 1.00e+00 1.00e+00h  1
-  73  7.1795881e-01 2.14e-03 2.46e+01  -2.5 1.17e-01  -0.4 1.00e+00 2.50e-01h  3
-  74  7.2237758e-01 1.30e-05 4.24e-01  -2.5 3.33e-03   0.9 1.00e+00 1.00e+00h  1
-  75  7.2443862e-01 4.58e-06 1.61e-02  -2.5 6.01e-03   0.4 1.00e+00 1.00e+00h  1
-  76  5.3175915e-01 6.84e-05 1.03e-01  -3.8 2.98e-02  -0.0 1.00e+00 7.93e-01f  1
-  77  4.6064574e-01 7.35e-04 4.02e-01  -3.8 7.81e-02  -0.5 1.00e+00 9.14e-01f  1
-  78  4.4792398e-01 9.31e-05 1.78e-01  -3.8 3.37e-02  -0.1 1.00e+00 1.00e+00h  1
-  79  4.3266341e-01 2.35e-04 2.93e-01  -3.8 7.44e-02  -0.6 1.00e+00 5.47e-01h  1
+  70  6.4360488e-01 6.04e-05 9.48e+01  -2.5 1.97e-02   0.1 1.00e+00 1.00e+00h  1
+  71  6.2067132e-01 4.03e-04 9.49e+01  -2.5 4.74e-02  -0.4 1.00e+00 1.00e+00h  1
+  72  6.2610276e-01 9.76e-07 6.50e-01  -2.5 1.47e-03   1.9 1.00e+00 1.00e+00h  1
+  73  6.2442850e-01 1.11e-06 4.99e-02  -2.5 2.06e-03   1.4 1.00e+00 1.00e+00h  1
+  74  6.2027435e-01 4.46e-06 3.56e-02  -2.5 4.42e-03   0.9 1.00e+00 1.00e+00h  1
+  75  6.1163113e-01 2.04e-05 2.26e-02  -2.5 8.42e-03   0.4 1.00e+00 1.00e+00h  1
+  76  4.0210750e-01 1.09e-04 9.56e+01  -3.8 4.35e-02  -0.0 9.95e-01 8.49e-01f  1
+  77  3.4109668e-01 5.20e-04 6.11e+01  -3.8 9.33e-02  -0.5 9.73e-01 6.38e-01f  1
+  78  3.3884713e-01 4.58e-07 2.71e-01  -3.8 1.42e-03   1.7 1.00e+00 1.00e+00h  1
+  79  3.3600132e-01 1.27e-06 4.87e-02  -3.8 2.87e-03   1.2 1.00e+00 1.00e+00h  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  80  4.2379473e-01 6.90e-05 1.33e-01  -3.8 2.46e-02  -0.2 1.00e+00 1.00e+00f  1
-  81  3.9883507e-01 7.60e-04 3.38e-01  -3.8 8.34e-02  -0.6 1.00e+00 8.46e-01h  1
-  82  3.9577316e-01 3.08e-04 2.06e-01  -3.8 2.57e-02  -0.2 1.00e+00 6.49e-01f  1
-  83  3.7060015e-01 1.57e-03 3.79e-01  -3.8 9.57e-02  -0.7 1.00e+00 1.00e+00f  1
-  84  3.6648715e-01 3.01e-04 1.79e-01  -3.8 3.14e-02  -0.3 1.00e+00 8.30e-01h  1
-  85  3.5635398e-01 3.28e-04 2.75e-01  -3.8 1.12e-01  -0.7 1.00e+00 4.78e-01f  1
-  86  3.4986442e-01 6.80e-05 1.01e-01  -3.8 3.52e-02  -0.3 1.00e+00 9.65e-01f  1
-  87  3.4441717e-01 1.04e-04 1.93e-01  -3.8 9.12e-02  -0.8 9.73e-01 2.68e-01f  1
-  88  3.3985191e-01 7.17e-05 1.08e-01  -3.8 2.44e-02  -0.4 1.00e+00 1.00e+00f  1
-  89  3.1739264e-01 1.24e-03 9.81e+01  -3.8 1.66e-01  -0.8 5.81e-01 8.90e-01h  1
+  80  3.2919370e-01 7.34e-06 4.15e-02  -3.8 7.33e-03   0.8 1.00e+00 1.00e+00h  1
+  81  3.1592775e-01 2.68e-05 3.21e-02  -3.8 1.22e-02   0.3 1.00e+00 9.06e-01h  1
+  82  3.0558702e-01 6.64e-05 9.63e+01  -3.8 2.65e-02  -0.2 1.00e+00 6.44e-01f  1
+  83  2.7964872e-01 8.50e-04 7.56e+01  -3.8 1.70e-01  -0.7 1.00e+00 7.84e-01f  1
+  84  2.8586320e-01 1.35e-06 4.51e-01  -3.8 2.57e-03   1.6 1.00e+00 1.00e+00h  1
+  85  2.8379281e-01 1.72e-06 2.74e-02  -3.8 2.29e-03   1.1 1.00e+00 1.00e+00h  1
+  86  2.7881775e-01 8.81e-06 2.46e-02  -3.8 6.18e-03   0.6 1.00e+00 1.00e+00h  1
+  87  2.6744587e-01 3.61e-05 2.31e-02  -3.8 1.50e-02   0.1 1.00e+00 1.00e+00h  1
+  88  2.6117114e-01 2.76e-04 9.72e+01  -3.8 4.33e-02  -0.4 1.00e+00 1.00e+00h  1
+  89  2.4152851e-01 3.83e-04 7.44e+01  -3.8 1.61e-01  -0.8 7.83e-01 2.34e-01h  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  90  3.2637543e-01 1.19e-03 6.73e+01  -3.8 9.47e-02  -0.4 4.48e-01 6.86e-01h  1
-  91  3.2617296e-01 6.52e-07 1.84e-01  -3.8 1.76e-03   1.8 1.00e+00 1.00e+00f  1
-  92  3.2572274e-01 4.10e-07 3.49e-02  -3.8 1.56e-03   1.3 1.00e+00 1.00e+00h  1
-  93  3.2414517e-01 2.28e-06 3.11e-02  -3.8 4.18e-03   0.9 1.00e+00 1.00e+00h  1
-  94  3.2122013e-01 8.82e-06 3.02e-02  -3.8 9.12e-03   0.4 1.00e+00 1.00e+00h  1
-  95  3.1642333e-01 3.69e-05 7.71e-02  -3.8 1.37e-02  -0.1 1.00e+00 1.00e+00h  1
-  96  3.0643474e-01 2.42e-04 2.11e-01  -3.8 4.26e-02  -0.6 1.00e+00 1.00e+00h  1
-  97  3.0440411e-01 3.20e-05 7.07e-02  -3.8 1.64e-02  -0.1 1.00e+00 1.00e+00h  1
-  98  2.9211920e-01 3.80e-04 2.39e-01  -3.8 5.55e-02  -0.6 1.00e+00 1.00e+00h  1
-  99  2.8806267e-01 4.49e-05 8.29e-02  -3.8 1.97e-02  -0.2 1.00e+00 1.00e+00h  1
+  90  1.8202576e-01 8.80e-03 3.49e+01  -3.8 1.33e+00  -1.3 2.75e-01 1.62e-01f  1
+  91  1.8300238e-01 7.45e-03 2.95e+01  -3.8 2.07e-02   0.9 2.88e-01 1.54e-01h  1
+  92  1.8603713e-01 6.30e-03 2.49e+01  -3.8 1.61e-02   1.3 1.54e-01 1.54e-01h  1
+  93  1.9780102e-01 4.82e-05 1.71e+00  -3.8 1.35e-02   0.9 5.62e-01 1.00e+00h  1
+  94  1.9305007e-01 3.21e-05 1.07e+00  -3.8 1.79e-02   0.4 6.57e-01 3.73e-01h  1
+  95  1.8779375e-01 2.42e-05 7.69e-01  -3.8 2.93e-02  -0.1 1.00e+00 3.24e-01f  1
+  96  1.6960856e-01 2.02e-04 9.76e+01  -3.8 7.58e-02  -0.6 1.00e+00 6.81e-01f  1
+  97  1.5309574e-01 5.14e-04 2.90e+01  -3.8 3.12e-01  -1.0 9.61e-01 2.97e-01f  1
+  98  1.6064261e-01 5.29e-07 1.01e-01  -3.8 1.36e-03   1.2 1.00e+00 1.00e+00h  1
+  99  1.5875407e-01 2.05e-06 2.33e-02  -3.8 4.46e-03   0.7 1.00e+00 1.00e+00h  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
- 100  2.7354126e-01 3.49e-04 2.76e-01  -3.8 6.24e-02  -0.7 1.00e+00 8.25e-01h  1
+ 100  1.5378022e-01 1.35e-05 2.80e-02  -3.8 1.31e-02   0.2 1.00e+00 1.00e+00h  1
 
 Number of Iterations....: 100
 
                                    (scaled)                 (unscaled)
-Objective...............:   2.7354126368711773e-01    2.7354126368711773e-01
-Dual infeasibility......:   2.7563401247938490e-01    2.7563401247938490e-01
-Constraint violation....:   3.4884623638093185e-04    3.4884623638093185e-04
+Objective...............:   1.5378022069371172e-01    1.5378022069371172e-01
+Dual infeasibility......:   2.7994924266236922e-02    2.7994924266236922e-02
+Constraint violation....:   1.3518769914067086e-05    1.3518769914067086e-05
 Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
-Complementarity.........:   1.5180217214689554e-04    1.5180217214689554e-04
-Overall NLP error.......:   2.7563401247938490e-01    2.7563401247938490e-01
+Complementarity.........:   1.5042429381314576e-04    1.5042429381314576e-04
+Overall NLP error.......:   2.7994924266236922e-02    2.7994924266236922e-02
 
 
-Number of objective function evaluations             = 124
+Number of objective function evaluations             = 101
 Number of objective gradient evaluations             = 101
-Number of equality constraint evaluations            = 124
+Number of equality constraint evaluations            = 101
 Number of inequality constraint evaluations          = 0
 Number of equality constraint Jacobian evaluations   = 101
 Number of inequality constraint Jacobian evaluations = 0
 Number of Lagrangian Hessian evaluations             = 100
-Total seconds in IPOPT                               = 2.989
+Total seconds in IPOPT                               = 3.915
 
-EXIT: Maximum Number of Iterations Exceeded.

This page was generated using Literate.jl.

+EXIT: Maximum Number of Iterations Exceeded.

This page was generated using Literate.jl.

diff --git a/dev/generated/man/problem_templates/index.html b/dev/generated/man/problem_templates/index.html index ef25234b..88037281 100644 --- a/dev/generated/man/problem_templates/index.html +++ b/dev/generated/man/problem_templates/index.html @@ -10,4 +10,4 @@ & \quad |\ddot{a}_t| \leq \ddot{a}_{\text{bound}} \\ & \quad \Delta t_{\text{min}} \leq \Delta t_t \leq \Delta t_{\text{max}} \\ \end{aligned}\]

where, for $U \in SU(N)$,

\[\ell\qty(\vec{\tilde{U}}_T, \vec{\tilde{U}}_{\text{goal}}) = -\abs{1 - \frac{1}{N} \abs{ \tr \qty(U_{\text{goal}}, U_T)} }\]

is the infidelity objective function, $Q$ is a weight, $R_a$, $R_{\dot{a}}$, and $R_{\ddot{a}}$ are weights on the regularization terms, and $\vb{P}^{(n)}$ is the $n$th-order Pade integrator.

Arguments

or

with

Keyword Arguments

source

Unitary Minimum Time Problem

This page was generated using Literate.jl.

+\abs{1 - \frac{1}{N} \abs{ \tr \qty(U_{\text{goal}}, U_T)} }\]

is the infidelity objective function, $Q$ is a weight, $R_a$, $R_{\dot{a}}$, and $R_{\ddot{a}}$ are weights on the regularization terms, and $\vb{P}^{(n)}$ is the $n$th-order Pade integrator.

Arguments

or

with

Keyword Arguments

source

Unitary Minimum Time Problem

This page was generated using Literate.jl.

diff --git a/dev/generated/man/utils/index.html b/dev/generated/man/utils/index.html index cc1d1d1a..9dda2ea4 100644 --- a/dev/generated/man/utils/index.html +++ b/dev/generated/man/utils/index.html @@ -1,2 +1,2 @@ -Utilities · QuantumCollocation.jl
Edit on GitHub
+Utilities · QuantumCollocation.jl
Edit on GitHub
diff --git a/dev/generated/quickstart/index.html b/dev/generated/quickstart/index.html index 60ee7e42..8bec91ca 100644 --- a/dev/generated/quickstart/index.html +++ b/dev/generated/quickstart/index.html @@ -56,62 +56,62 @@ inequality constraints with only upper bounds: 0 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 0 3.5802114e-03 1.79e+00 3.80e-05 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0 - 1 8.7198916e+01 2.61e-01 4.72e+01 -1.0 2.37e+00 - 2.03e-02 1.00e+00h 1 - 2 8.7343471e+01 1.09e-01 9.07e+02 -1.0 9.69e-01 2.0 5.68e-01 5.79e-01h 1 - 3 8.3446398e+01 4.09e-02 2.33e+02 -1.0 8.86e-01 1.5 9.45e-01 6.33e-01f 1 - 4 8.3977719e+01 3.68e-02 2.02e+02 -1.0 1.61e+00 1.0 1.46e-01 1.24e-01h 1 - 5 8.0030666e+01 3.93e-03 1.67e+02 -1.0 2.82e-01 1.5 1.00e+00 1.00e+00f 1 - 6 7.1383831e+01 4.81e-04 1.13e+01 -1.0 1.20e-01 1.0 1.00e+00 1.00e+00f 1 - 7 2.6114842e+01 7.07e-03 5.77e+00 -1.0 4.58e-01 0.5 1.00e+00 1.00e+00f 1 - 8 1.3033741e+01 1.44e-02 9.88e+01 -1.0 8.38e-01 0.0 9.96e-01 5.00e-01f 2 - 9 4.3030156e+00 1.68e-02 5.86e+01 -1.0 1.32e+00 -0.4 4.60e-01 5.82e-01F 1 + 0 2.8847853e-03 1.91e+00 2.34e-05 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0 + 1 6.9343461e+01 2.34e-01 4.18e+01 -1.0 1.71e+00 - 2.40e-02 1.00e+00h 1 + 2 5.5358766e+01 5.99e-03 3.75e+02 -1.0 5.72e-01 2.0 8.92e-01 1.00e+00f 1 + 3 4.3114104e+01 7.52e-02 4.15e+02 -1.0 3.31e+00 1.5 3.40e-01 2.64e-01f 1 + 4 2.6016989e+01 1.49e-02 3.83e+02 -1.0 2.87e-01 1.9 8.12e-02 1.00e+00f 1 + 5 3.1641794e+01 1.36e-03 5.51e+01 -1.0 1.92e-01 1.5 1.00e+00 1.00e+00h 1 + 6 2.7093087e+01 2.26e-04 5.12e+00 -1.0 8.82e-02 1.0 1.00e+00 1.00e+00f 1 + 7 1.1449299e+01 1.44e-03 2.04e+00 -1.0 1.79e-01 0.5 1.00e+00 1.00e+00f 1 + 8 2.9519925e+00 3.24e-03 9.98e+01 -1.0 2.98e-01 0.0 1.00e+00 1.00e+00f 1 + 9 6.8556401e+00 1.97e-03 1.00e+02 -1.0 3.21e-01 -0.4 9.92e-01 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 10 4.6447287e+00 5.53e-04 1.29e+01 -1.0 5.16e-01 0.9 1.00e+00 1.00e+00f 1 - 11 1.2177214e+00 4.09e-04 1.71e+00 -1.0 1.24e-01 0.4 9.84e-01 1.00e+00f 1 - 12 7.6997639e-01 9.65e-04 1.00e+02 -1.0 2.53e-01 -0.1 1.00e+00 1.00e+00f 1 - 13 6.4116966e-01 4.71e-03 1.00e+02 -1.0 4.12e-01 - 1.00e+00 1.00e+00f 1 - 14 6.3844791e-01 1.40e-04 3.78e+00 -1.0 4.70e-02 1.3 1.00e+00 1.00e+00h 1 - 15 7.3144602e-01 7.01e-03 1.00e+02 -1.0 2.68e-01 - 1.00e+00 1.00e+00f 1 - 16 9.0171618e-01 3.22e-04 9.99e+01 -1.0 6.72e-02 0.8 1.00e+00 1.00e+00h 1 - 17 3.6960638e-02 1.72e-06 1.79e-01 -1.0 8.69e-03 1.2 1.00e+00 1.00e+00f 1 - 18 8.5384647e-04 9.50e-04 3.86e-01 -2.5 5.13e-02 - 9.34e-01 1.00e+00F 1 - 19 6.2477835e-03 7.01e-06 5.70e-02 -2.5 1.04e-02 0.7 1.00e+00 1.00e+00h 1 + 10 4.5779924e+00 1.30e-04 4.98e+00 -1.0 6.97e-02 0.9 1.00e+00 1.00e+00f 1 + 11 1.8028562e-01 3.51e-03 9.99e+01 -1.0 7.72e-01 - 1.00e+00 4.58e-01f 2 + 12 1.3782122e+00 3.64e-03 1.26e+01 -1.0 1.11e+00 - 7.20e-01 1.25e-01h 4 + 13 1.3148736e+00 5.30e-03 1.02e+01 -1.0 2.13e+00 - 1.00e+00 1.87e-01f 3 + 14 6.7917479e-01 4.21e-03 9.49e+01 -1.0 3.59e-01 - 1.00e+00 5.00e-01f 2 + 15 6.7302285e-01 4.35e-03 8.51e+00 -1.0 3.21e+00 - 4.08e-01 3.58e-02f 5 + 16 2.4179225e-01 6.05e-03 9.23e+01 -1.0 1.59e+00 - 7.29e-01 9.29e-02f 4 + 17 3.4149156e-01 6.03e-03 8.93e+00 -1.0 3.17e+00 - 3.14e-01 1.30e-02h 6 + 18 3.7662461e+00 7.11e-03 1.00e+02 -1.0 3.75e-01 - 1.00e+00 1.00e+00h 1 + 19 6.3171684e-01 2.67e-04 9.99e+01 -1.0 6.94e-02 0.4 1.00e+00 1.00e+00f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 20 6.7911483e-04 4.12e-08 2.18e-03 -2.5 1.19e-03 0.3 1.00e+00 1.00e+00h 1 - 21 7.3238572e-04 1.60e-08 1.00e+02 -3.8 8.53e-04 -0.2 1.00e+00 1.00e+00h 1 - 22 7.0077269e-04 5.38e-09 1.00e+02 -3.8 3.09e-04 -0.7 1.00e+00 1.00e+00h 1 - 23 6.8018328e-04 2.73e-09 1.00e+02 -3.8 3.58e-04 0.6 1.00e+00 1.00e+00h 1 - 24 6.8738195e-04 7.34e-10 1.00e+02 -3.8 1.61e-04 0.2 1.00e+00 1.00e+00h 1 - 25 6.7738392e-04 7.20e-13 4.33e-02 -3.8 3.91e-04 0.6 1.00e+00 1.00e+00H 1 - 26 6.7554352e-04 5.96e-10 1.00e+02 -3.8 1.35e-04 0.1 1.00e+00 1.00e+00h 1 - 27 4.7491733e-04 9.36e-03 1.00e+02 -3.8 3.17e-01 - 1.00e+00 1.00e+00f 1 - 28 9.6921980e-04 9.35e-03 1.78e+01 -3.8 2.77e-01 0.5 1.00e+00 1.22e-04h 14 - 29 9.6909795e-04 9.28e-03 1.00e+02 -3.8 5.51e-02 1.0 1.00e+00 7.81e-03h 8 + 20 1.1607881e-02 2.92e-06 6.28e-01 -1.0 7.85e-03 0.8 1.00e+00 1.00e+00f 1 + 21 1.3304919e-02 1.51e-04 1.00e+02 -1.7 5.81e-02 - 1.00e+00 1.00e+00f 1 + 22 1.4844113e-02 2.13e-03 2.50e+01 -1.7 8.08e-01 - 1.00e+00 2.50e-01h 3 + 23 4.7871300e-03 1.80e-05 2.92e-01 -1.7 2.05e-02 0.4 1.00e+00 1.00e+00h 1 + 24 2.7272138e-03 2.20e-06 1.00e+02 -1.7 7.30e-03 -0.1 1.00e+00 1.00e+00h 1 + 25 8.5254326e-04 1.17e-03 1.00e+02 -1.7 1.83e-01 - 1.00e+00 1.00e+00f 1 + 26 3.9591191e-03 4.81e-06 1.00e+02 -1.7 1.75e-02 1.2 1.00e+00 1.00e+00h 1 + 27 1.1117366e-02 7.77e-06 1.00e+02 -1.7 4.78e-02 - 1.00e+00 1.00e+00H 1 + 28 6.1843930e-03 3.29e-06 1.00e+02 -1.7 8.71e-03 0.7 1.00e+00 1.00e+00h 1 + 29 3.0106776e-03 1.05e-04 1.00e+02 -1.7 4.38e-02 - 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls - 30 6.7817481e-04 9.28e-03 1.77e+01 -3.8 4.94e-01 0.5 1.00e+00 1.22e-04h 14 + 30 2.7852949e-03 5.75e-08 1.24e-01 -1.7 1.38e-03 1.2 1.00e+00 1.00e+00h 1 Number of Iterations....: 30 (scaled) (unscaled) -Objective...............: 6.7817480943690122e-04 6.7817480943690122e-04 -Dual infeasibility......: 1.7684743822899918e+01 1.7684743822899918e+01 -Constraint violation....: 9.2797904649121465e-03 9.2797904649121465e-03 +Objective...............: 2.7852948712949444e-03 2.7852948712949444e-03 +Dual infeasibility......: 1.2403431937574055e-01 1.2403431937574055e-01 +Constraint violation....: 5.7474296752402232e-08 5.7474296752402232e-08 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00 -Complementarity.........: 1.9627710623146906e-04 1.9627710623146906e-04 -Overall NLP error.......: 1.7684743822899918e+01 1.7684743822899918e+01 +Complementarity.........: 2.0000015612416343e-02 2.0000015612416343e-02 +Overall NLP error.......: 1.2403431937574055e-01 1.2403431937574055e-01 -Number of objective function evaluations = 74 +Number of objective function evaluations = 64 Number of objective gradient evaluations = 31 -Number of equality constraint evaluations = 74 +Number of equality constraint evaluations = 64 Number of inequality constraint evaluations = 0 Number of equality constraint Jacobian evaluations = 31 Number of inequality constraint Jacobian evaluations = 0 Number of Lagrangian Hessian evaluations = 30 -Total seconds in IPOPT = 1.955 +Total seconds in IPOPT = 2.952 -EXIT: Maximum Number of Iterations Exceeded.

The above output comes from the Ipopt.jl solver. To see the final fidelity we can use the unitary_fidelity function exported by QuantumCollocation.jl.

println("Final fidelity: ", unitary_fidelity(prob))
Final fidelity: 0.9706491514856868

We can also easily plot the solutions using the plot function exported by NamedTrajectories.jl.

plot(prob.trajectory, [:Ũ⃗, :a])

Minimum Time Problems

We can also easily set up and solve a minimum time problem, where we enforce a constraint on the final fidelity:

\[\mathcal{F}(U_T, U_{\text{goal}}) \geq \mathcal{F}_{\text{min}}\]

Using the problem we just solved we can do the following:

# final fidelity constraint
+EXIT: Maximum Number of Iterations Exceeded.

The above output comes from the Ipopt.jl solver. To see the final fidelity we can use the unitary_fidelity function exported by QuantumCollocation.jl.

println("Final fidelity: ", unitary_fidelity(prob))
Final fidelity: 0.9999764862210143

We can also easily plot the solutions using the plot function exported by NamedTrajectories.jl.

plot(prob.trajectory, [:Ũ⃗, :a])

Minimum Time Problems

We can also easily set up and solve a minimum time problem, where we enforce a constraint on the final fidelity:

\[\mathcal{F}(U_T, U_{\text{goal}}) \geq \mathcal{F}_{\text{min}}\]

Using the problem we just solved we can do the following:

# final fidelity constraint
 final_fidelity = 0.99
 
 # weight on the minimum time objective
@@ -147,66 +147,66 @@
         inequality constraints with only upper bounds:        0
 
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-   0  1.0195758e+02 9.28e-03 3.04e-01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
-   1  9.7917111e+01 3.07e-04 1.44e+01  -1.0 5.85e-02   2.0 1.00e+00 1.00e+00f  1
-   2  9.7042161e+01 7.66e-06 9.99e+01  -1.0 8.89e-03   1.5 1.00e+00 1.00e+00f  1
-   3  9.5035638e+01 4.26e-05 2.51e+00  -1.0 2.98e-02   1.0 1.00e+00 1.00e+00f  1
-   4  9.0377208e+01 3.00e-04 2.84e-01  -1.0 7.75e-02   0.6 1.00e+00 1.00e+00f  1
-   5  7.7780719e+01 3.07e-03 4.50e-01  -1.7 2.21e-01   0.1 9.75e-01 1.00e+00f  1
-   6  7.3656366e+01 3.97e-04 6.80e-01  -1.7 9.29e-02   0.5 1.00e+00 1.00e+00f  1
-   7  6.5755331e+01 1.23e-03 7.16e-01  -1.7 1.59e-01   0.0 1.00e+00 1.00e+00f  1
-   8  5.5560151e+01 3.17e-03 3.97e-01  -1.7 3.21e-01  -0.4 1.00e+00 1.00e+00f  1
-   9  5.5838040e+01 3.62e-05 1.27e-01  -1.7 1.30e-01  -0.0 1.00e+00 1.00e+00h  1
+   0  1.0174325e+02 5.75e-08 3.08e-01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
+   1  8.5501422e+01 6.29e-03 1.12e+00  -1.0 3.43e-01   0.0 8.86e-01 1.00e+00f  1
+   2  8.1454406e+01 1.16e-03 1.38e+00  -1.0 1.06e-01   0.4 1.00e+00 8.73e-01f  1
+   3  7.2475115e+01 1.56e-03 2.34e-01  -1.0 1.75e-01  -0.1 1.00e+00 1.00e+00f  1
+   4  6.1758634e+01 6.17e-02 1.11e+01  -1.7 2.39e+00  -0.5 2.84e-01 4.05e-01f  1
+   5  5.1041042e+01 1.39e-02 1.21e+01  -1.7 4.62e-01  -0.1 2.40e-01 9.53e-01f  1
+   6  5.4596495e+01 1.84e-03 2.85e+00  -1.7 3.37e-01    -  8.00e-01 1.00e+00f  1
+   7  5.3069856e+01 1.62e-03 8.89e+00  -1.7 3.53e-01    -  7.05e-01 1.00e+00f  1
+   8  5.2242870e+01 5.78e-04 1.00e+02  -1.7 3.74e-01    -  1.00e+00 1.00e+00f  1
+   9  5.2099247e+01 6.81e-04 7.50e+01  -1.7 5.51e-01    -  1.00e+00 2.50e-01h  3
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  10  5.2037331e+01 9.43e-04 2.24e-01  -2.5 2.48e-01  -0.5 9.76e-01 1.00e+00f  1
-  11  5.0035123e+01 1.71e-02 1.00e+02  -2.5 1.09e+00  -1.0 7.62e-01 6.60e-01f  1
-  12  5.1016042e+01 1.68e-02 6.35e+00  -2.5 1.17e+00  -0.5 1.25e-01 2.34e-02h  1
-  13  5.1164844e+01 4.24e-03 5.46e+00  -2.5 2.95e-01  -1.0 2.17e-01 1.00e+00f  1
-  14  5.0360324e+01 1.63e-03 1.00e+02  -2.5 5.29e-01    -  1.00e+00 1.00e+00f  1
-  15  5.0444458e+01 2.11e-03 1.32e+00  -2.5 1.93e+01    -  2.47e-02 1.32e-02f  3
-  16  5.0564561e+01 2.06e-04 6.34e-02  -2.5 2.20e-01  -1.5 1.00e+00 1.00e+00h  1
-  17  5.0286903e+01 7.52e-04 6.21e-02  -2.5 3.28e-01    -  1.00e+00 1.00e+00f  1
-  18  5.0309772e+01 7.00e-04 6.43e-02  -2.5 3.08e-01    -  1.00e+00 5.00e-01h  2
-  19  5.0305977e+01 1.49e-04 7.34e-03  -2.5 1.39e-01    -  1.00e+00 1.00e+00h  1
+  10  5.1957118e+01 3.29e-03 4.68e+01  -1.7 1.10e+00    -  8.32e-01 3.76e-01f  2
+  11  5.2038016e+01 3.20e-03 5.45e+01  -1.7 2.52e-01  -0.6 1.00e+00 2.76e-02h  4
+  12  5.2079683e+01 3.00e-03 4.89e+01  -1.7 3.01e-01  -1.1 1.90e-01 6.25e-02h  5
+  13  5.2073893e+01 3.00e-03 5.12e+01  -1.7 1.52e+01  -1.5 4.22e-02 3.38e-03f  3
+  14  5.2004170e+01 2.96e-03 4.96e+01  -1.7 1.17e+00  -1.1 8.18e-02 1.63e-02f  6
+  15  5.2134925e+01 2.81e-03 5.28e+01  -1.7 3.37e-01  -0.7 1.00e+00 4.80e-02h  3
+  16  5.2930855e+01 2.60e-03 4.93e+01  -1.7 1.00e+00  -1.2 4.69e-01 6.65e-02H  1
+  17  5.2904901e+01 2.78e-03 4.91e+01  -1.7 7.92e+01    -  1.11e-02 2.55e-03f  3
+  18  5.2810945e+01 1.41e-03 4.91e+01  -1.7 1.18e+00  -1.6 1.76e-01 8.26e-01H  1
+  19  5.2984206e+01 1.38e-03 6.18e+01  -1.7 1.80e+00  -1.2 1.00e+00 3.72e-02H  1
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  20  5.0014901e+01 2.45e-06 1.00e+02  -3.8 9.04e-03    -  1.00e+00 1.00e+00f  1
-  21  5.0015884e+01 4.73e-05 1.00e+02  -3.8 6.91e-02    -  1.00e+00 1.00e+00h  1
-  22  5.0015750e+01 2.63e-09 2.14e-02  -3.8 7.33e-04   0.7 1.00e+00 1.00e+00h  1
-  23  5.0015810e+01 1.61e-06 1.00e+02  -3.8 2.83e-02    -  1.00e+00 1.00e+00h  1
-  24  5.0015793e+01 3.29e-06 5.00e+01  -3.8 3.48e-02    -  1.00e+00 5.00e-01h  2
-  25  5.0015790e+01 1.51e-10 3.47e-03  -3.8 8.61e-05   0.3 1.00e+00 1.00e+00h  1
-  26  5.0015784e+01 2.03e-05 1.02e-03  -3.8 3.31e-02    -  1.00e+00 1.00e+00h  1
-  27  5.0010739e+01 2.47e-06 1.00e+02  -4.0 1.22e-02    -  1.00e+00 1.00e+00h  1
-  28  5.0010765e+01 2.02e-06 5.00e+01  -4.0 8.61e-02    -  1.00e+00 5.00e-01h  2
-  29  5.0010740e+01 3.79e-10 1.00e+02  -4.0 1.58e-04  -0.2 1.00e+00 1.00e+00h  1
+  20  5.2968270e+01 1.69e-03 5.76e+01  -1.7 1.50e+00    -  1.18e-01 1.63e-01f  3
+  21  5.5479917e+01 1.32e-03 9.66e+01  -1.7 5.41e-01  -1.7 1.00e+00 5.00e-01h  2
+  22  5.3121106e+01 1.90e-03 6.80e+01  -1.7 5.31e-01    -  1.00e+00 6.69e-01f  1
+  23  5.2758531e+01 9.07e-05 1.02e+02  -1.7 5.48e-02  -0.4 2.75e-01 1.00e+00h  1
+  24  5.2958756e+01 8.16e-05 1.49e+02  -1.7 8.70e-01  -0.8 7.08e-01 6.50e-03H  1
+  25  5.2981103e+01 3.31e-04 1.06e+02  -1.7 1.67e-01  -1.3 3.14e-01 1.00e+00f  1
+  26  5.2422976e+01 3.78e-04 1.01e+02  -1.7 6.81e-01  -0.9 6.83e-03 1.25e-01f  4
+  27  5.2288104e+01 3.91e-04 9.98e+01  -1.7 2.37e+00  -1.4 4.22e-01 1.71e-02f  2
+  28  5.2185453e+01 3.91e-04 9.83e+01  -1.7 1.10e+00  -0.9 3.74e-02 2.19e-02f  6
+  29  5.2113914e+01 3.92e-04 9.89e+01  -1.7 3.24e+00  -1.4 1.00e+00 4.87e-03f  3
 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
-  30  5.0010740e+01 1.72e-06 1.00e+02  -4.0 4.15e-02    -  1.00e+00 1.00e+00h  1
+  30  5.2447485e+01 3.78e-04 9.79e+01  -1.7 3.98e+00  -1.9 2.34e-02 1.48e-02h  6
 
 Number of Iterations....: 30
 
                                    (scaled)                 (unscaled)
-Objective...............:   5.0010739653239270e+01    5.0010739653239270e+01
-Dual infeasibility......:   9.9999999977078105e+01    9.9999999977078105e+01
-Constraint violation....:   1.7189509157189420e-06    1.7189509157189420e-06
+Objective...............:   5.2447484706303236e+01    5.2447484706303236e+01
+Dual infeasibility......:   9.7874961331494234e+01    9.7874961331494234e+01
+Constraint violation....:   3.7786267946626761e-04    3.7786267946626761e-04
 Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
-Complementarity.........:   1.0000000000000002e-04    1.0000000000000002e-04
-Overall NLP error.......:   9.9999999977078105e+01    9.9999999977078105e+01
+Complementarity.........:   7.1220656666454607e-02    7.1220656666454607e-02
+Overall NLP error.......:   9.7874961331494234e+01    9.7874961331494234e+01
 
 
-Number of objective function evaluations             = 41
+Number of objective function evaluations             = 98
 Number of objective gradient evaluations             = 31
-Number of equality constraint evaluations            = 41
-Number of inequality constraint evaluations          = 41
+Number of equality constraint evaluations            = 98
+Number of inequality constraint evaluations          = 98
 Number of equality constraint Jacobian evaluations   = 31
 Number of inequality constraint Jacobian evaluations = 31
 Number of Lagrangian Hessian evaluations             = 30
-Total seconds in IPOPT                               = 5.535
+Total seconds in IPOPT                               = 8.367
 
-EXIT: Maximum Number of Iterations Exceeded.

We can see that the final fidelity is indeed greater than the minimum fidelity we set.

println("Final fidelity:    ", unitary_fidelity(prob_min_time))
Final fidelity:    0.9999999579469339

and that the duration of the pulse has decreased.

initial_dur = times(prob.trajectory)[end]
+EXIT: Maximum Number of Iterations Exceeded.

We can see that the final fidelity is indeed greater than the minimum fidelity we set.

println("Final fidelity:    ", unitary_fidelity(prob_min_time))
Final fidelity:    0.984453125542833

and that the duration of the pulse has decreased.

initial_dur = times(prob.trajectory)[end]
 min_time_dur = times(prob_min_time.trajectory)[end]
 
 println("Initial duration:  ", initial_dur)
 println("Minimum duration:  ", min_time_dur)
-println("Duration decrease: ", initial_dur - min_time_dur)
Initial duration:  10.093733429381277
-Minimum duration:  4.950989294849908
-Duration decrease: 5.14274413453137

We can also plot the solutions for the minimum time problem.

plot(prob_min_time.trajectory, [:Ũ⃗, :a])

This page was generated using Literate.jl.

+println("Duration decrease: ", initial_dur - min_time_dur)
Initial duration:  10.072306376823661
+Minimum duration:  5.14824548458331
+Duration decrease: 4.924060892240352

We can also plot the solutions for the minimum time problem.

plot(prob_min_time.trajectory, [:Ũ⃗, :a])

This page was generated using Literate.jl.

diff --git a/dev/index.html b/dev/index.html index c8e7eacb..fd687975 100644 --- a/dev/index.html +++ b/dev/index.html @@ -6,4 +6,4 @@ f(U_{t+1}, U_t, a_t) &= U_{t+1} - \exp(-i H(a_t)) U_t \\ &\approx U_{t+1} - B^{-1}(a_t) F(a_t) U_t \\ &= B(a_t) U_{t+1} - F(a_t) U_t \\ -\end{aligned}\]

where $B(a_t)$ and $F(a_t)$ are the backward and forward Pade operators, and are just polynomials in $H(a_t)$.

This implementation is possible because direct collocation allows for the dynamics to be implicit. Since numerically calculating matrix exponentials inherently requires an approximation – the Padé approximant is commonly used – utilizing this formulation significantly improves performance, as, at least here, no matrix inversion is required.

Index

+\end{aligned}\]

where $B(a_t)$ and $F(a_t)$ are the backward and forward Pade operators, and are just polynomials in $H(a_t)$.

This implementation is possible because direct collocation allows for the dynamics to be implicit. Since numerically calculating matrix exponentials inherently requires an approximation – the Padé approximant is commonly used – utilizing this formulation significantly improves performance, as, at least here, no matrix inversion is required.

Index

diff --git a/dev/lib/index.html b/dev/lib/index.html index 43c87e4c..1321c95e 100644 --- a/dev/lib/index.html +++ b/dev/lib/index.html @@ -3,12 +3,12 @@ levels::Vector{Int}, gate_name::Symbol, qubit::Union{Int, Vector{Int}} -)

Get a unitary matrix for a gate acting on a subspace of a multilevel system.

TODO: reimplement this as embed_operator with more methods.

source

QuantumSystems

QuantumCollocation.QuantumSystems.AbstractSystem — Type
AbstractSystem

Abstract type for defining systems.

source
QuantumCollocation.QuantumSystems.QuantumSystem — Type
QuantumSystemNew <: AbstractSystem

A struct for storing the isomorphisms of the system's drift and drive Hamiltonians, as well as the system's parameters.

source
QuantumCollocation.QuantumSystems.QuantumSystem — Method
QuantumSystem(
+)

Get a unitary matrix for a gate acting on a subspace of a multilevel system.

TODO: reimplement this as embed_operator with more methods.

source

QuantumSystems

QuantumCollocation.QuantumSystems.AbstractSystem — Type
AbstractSystem

Abstract type for defining systems.

source
QuantumCollocation.QuantumSystems.QuantumSystem — Type
QuantumSystemNew <: AbstractSystem

A struct for storing the isomorphisms of the system's drift and drive Hamiltonians, as well as the system's parameters.

source
QuantumCollocation.QuantumSystems.QuantumSystem — Method
QuantumSystem(
     H_drift::Matrix{<:Number},
     H_drives::Vector{Matrix{<:Number}};
     params=Dict{Symbol, Any}(),
     kwargs...
-)::QuantumSystem

Constructs a QuantumSystem object from the drift and drive Hamiltonian terms.

source
QuantumCollocation.QuantumSystems.G — Method
G(H::AbstractMatrix)::Matrix{Float64}

Returns the isomorphism of $-iH$:

\[G(H) = \widetilde{- i H} = \mqty(1 & 0 \\ 0 & 1) \otimes \Im(H) - \mqty(0 & -1 \\ 1 & 0) \otimes \Re(H)\]

where $\Im(H)$ and $\Re(H)$ are the imaginary and real parts of $H$ and the tilde indicates the standard isomorphism of a complex valued matrix:

\[\widetilde{H} = \mqty(1 & 0 \\ 0 & 1) \otimes \Re(H) + \mqty(0 & -1 \\ 1 & 0) \otimes \Im(H)\]

source
QuantumCollocation.QuantumSystems.H — Method
H(G::AbstractMatrix{<:Number})::Matrix{ComplexF64}

Returns the inverse of G(H) = iso(-iH), i.e. returns H

source
QuantumCollocation.QuantumSystems.MultiModeSystem — Method
MultiModeSystem(
+)::QuantumSystem

Constructs a QuantumSystem object from the drift and drive Hamiltonian terms.

source
QuantumCollocation.QuantumSystems.G — Method
G(H::AbstractMatrix)::Matrix{Float64}

Returns the isomorphism of $-iH$:

\[G(H) = \widetilde{- i H} = \mqty(1 & 0 \\ 0 & 1) \otimes \Im(H) - \mqty(0 & -1 \\ 1 & 0) \otimes \Re(H)\]

where $\Im(H)$ and $\Re(H)$ are the imaginary and real parts of $H$ and the tilde indicates the standard isomorphism of a complex valued matrix:

\[\widetilde{H} = \mqty(1 & 0 \\ 0 & 1) \otimes \Re(H) + \mqty(0 & -1 \\ 1 & 0) \otimes \Im(H)\]

source
QuantumCollocation.QuantumSystems.H — Method
H(G::AbstractMatrix{<:Number})::Matrix{ComplexF64}

Returns the inverse of G(H) = iso(-iH), i.e. returns H

source
QuantumCollocation.QuantumSystems.MultiModeSystem — Method
MultiModeSystem(
     transmon_levels::Int,
     cavity_levels::Int;
     χ=2π * -0.5459e-3,
@@ -23,4 +23,4 @@
         \epsilon_{c}(t) +
         \epsilon_{q}(t) +
         \mathrm{c.c.}
-    \right)\]
source
QuantumCollocation.QuantumSystems.lie_subalgebra_dim — Method
lie_subalgebra_dim(Hs::Vector{<:AbstractMatrix})

Returns the dimension of the Lie subalgebra generated by the operators in Hs.

source

Integrators

QuantumCollocation.Integrators.UnitaryPadeIntegrator — Type
source
+ \right)\]

source
QuantumCollocation.QuantumSystems.lie_subalgebra_dim — Method
lie_subalgebra_dim(Hs::Vector{<:AbstractMatrix})

Returns the dimension of the Lie subalgebra generated by the operators in Hs.

source

Integrators

QuantumCollocation.Integrators.UnitaryPadeIntegrator — Type
source
diff --git a/dev/search/index.html b/dev/search/index.html index 9db97732..f9b3723f 100644 --- a/dev/search/index.html +++ b/dev/search/index.html @@ -1,2 +1,2 @@ -Search · QuantumCollocation.jl

Loading search...

    +Search · QuantumCollocation.jl

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