Constrain piece-wise constant pulses to vary smoothly

import numpy as np
import matplotlib.pyplot as plt

from paraqeet.quantity import Quantity
from paraqeet.signal.envelopes import GaussEnvelope
from paraqeet.signal.pwc_generator import PWCGenerator
from paraqeet.measurement.smoothness import Smoothness
from paraqeet.optimisation_map import OptimisationMap
from paraqeet.optimisers.scipy_optimiser_gradient import ScipyOptimiserGradient

delta_sampling = 33e-9
n_pwc = 40  # number of piecewise constants in the pulse
t_final = n_pwc * delta_sampling  # for now just set up for trying
tlist = np.linspace(0, t_final, n_pwc + 1)
eps_qubit = 2 * np.pi * 1.0  # initial amplitude of the qubit (in MHz)
eps_max_qubit = 5 * eps_qubit  # maximum amplitude of the resonator (in MHz)
tone_qubit = GaussEnvelope(
    amplitude=Quantity(eps_qubit * 1e6, -eps_max_qubit * 1e6, eps_max_qubit * 1e6),
    t_final=Quantity(t_final, 1 / 2 * t_final, 2 * t_final),
)
gen_qubit = PWCGenerator(envelopes=[tone_qubit], max_amplitude=eps_max_qubit * 1e6, tlist=tlist)

from plotting import plot_signal

ts = np.linspace(0, t_final, 501)
fig, ax = plt.subplots(1, figsize=(5, 3))
plot_signal(tone_qubit, ts, ax, linestyle="-", label="Smooth")
plot_signal(gen_qubit, ts, ax, linestyle="--", label="PWC")
ax.legend(loc=1, frameon=True)
plt.show()

optmap = OptimisationMap()
optmap.add(gen_qubit, gen_qubit.get_parameters())

# We add dummy parameters to check if the gradient is computed
# correctly by padding zeros
# optmap.add(tone_qubit, tone_qubit.get_parameters())

optmap.register_params_with_optimisables()

smoothness = Smoothness(pwc_generator=gen_qubit)

We can check that the gradient has the correct shape

print(smoothness.measure_with_gradient()[1].shape)

(80,)

opt = ScipyOptimiserGradient(smoothness, optimisation_map=optmap)
max_iter = 200
opt.set_options({"maxiter": max_iter})

opt.optimise()

{'status': 1, 'value': 1.8438155335864792e-08, 'iterations': 15, 'message': 'CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL'}

smoothness.measure()

0.9999999815618447

smoothness.measure_with_gradient()

(0.9999999815618447,
 Array([ 9.29053612e-14,  2.07661214e-13, -1.98912979e-13, -5.70798606e-14,
        -8.65882301e-14, -9.38920408e-14,  5.79057140e-14,  4.16652832e-14,
         1.73505745e-13, -2.70482385e-14,  7.20441408e-14, -1.86976502e-13,
        -2.12695167e-14, -7.15428687e-14,  1.95900735e-15,  6.48107118e-14,
         8.08025679e-14,  4.28865051e-14, -2.21246235e-14, -7.07113902e-14,
        -7.07113902e-14, -2.21246235e-14,  4.28865051e-14,  8.08025679e-14,
         6.48107118e-14,  1.95900735e-15, -7.15428687e-14, -2.12695167e-14,
        -1.86976502e-13,  7.20441408e-14, -2.70482385e-14,  1.73505745e-13,
         4.16652832e-14,  5.79057140e-14, -9.38920408e-14, -8.65882301e-14,
        -5.70798606e-14, -1.98912979e-13,  2.07661214e-13,  9.29053612e-14,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,
        -0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00],      dtype=float64))

plot_signal(gen_qubit, ts, linestyle="--", label="PWC");

As expected obtain a flat pulse.