Fitting

In [ ]:

import numpy as np

import qubex as qx

import numpy as np import qubex as qx

In [ ]:

t = np.linspace(0, 200, 20)

A = 1.0
f = 12.5e-3
phi = np.pi / 2
C = 0.5
noise = 0.1

data = qx.fit.func_cos(
    t=t,
    A=A,
    omega=2 * np.pi * f,
    phi=phi,
    C=C,
) + np.random.default_rng().normal(0, noise, len(t))

qx.viz.plot(
    x=t,
    y=data,
    title="Cosine data",
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

result = qx.fit.fit_cosine(
    t,
    data,
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

t = np.linspace(0, 200, 20) A = 1.0 f = 12.5e-3 phi = np.pi / 2 C = 0.5 noise = 0.1 data = qx.fit.func_cos( t=t, A=A, omega=2 * np.pi * f, phi=phi, C=C, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.plot( x=t, y=data, title="Cosine data", xlabel="Time (ns)", ylabel="Amplitude", ) result = qx.fit.fit_cosine( t, data, xlabel="Time (ns)", ylabel="Amplitude", )

In [ ]:

t = np.linspace(0, 200, 20)

A = 1.0
f = 12.5e-3
phi = np.pi / 2
C = 0.5
tau = 100
noise = 0.1

data = qx.fit.func_damped_cos(
    t=t,
    A=A,
    omega=2 * np.pi * f,
    phi=phi,
    C=C,
    tau=tau,
) + np.random.default_rng().normal(0, noise, len(t))

qx.viz.plot(
    x=t,
    y=data,
    title="Cosine data",
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

result = qx.fit.fit_cosine(
    t,
    data,
    is_damped=True,
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

t = np.linspace(0, 200, 20) A = 1.0 f = 12.5e-3 phi = np.pi / 2 C = 0.5 tau = 100 noise = 0.1 data = qx.fit.func_damped_cos( t=t, A=A, omega=2 * np.pi * f, phi=phi, C=C, tau=tau, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.plot( x=t, y=data, title="Cosine data", xlabel="Time (ns)", ylabel="Amplitude", ) result = qx.fit.fit_cosine( t, data, is_damped=True, xlabel="Time (ns)", ylabel="Amplitude", )

In [ ]:

t = np.linspace(0, 200, 20)

A = 1.0
C = 0.5
tau = 100
noise = 0.1

data = qx.fit.func_exp_decay(
    t=t,
    A=A,
    C=C,
    tau=tau,
) + np.random.default_rng().normal(0, noise, len(t))

qx.viz.plot(
    x=t,
    y=data,
    title="Exponential decay data",
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

result = qx.fit.fit_exp_decay(
    t,
    data,
    xlabel="Time (ns)",
    ylabel="Amplitude",
    xaxis_type="linear",
)

t = np.linspace(0, 200, 20) A = 1.0 C = 0.5 tau = 100 noise = 0.1 data = qx.fit.func_exp_decay( t=t, A=A, C=C, tau=tau, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.plot( x=t, y=data, title="Exponential decay data", xlabel="Time (ns)", ylabel="Amplitude", ) result = qx.fit.fit_exp_decay( t, data, xlabel="Time (ns)", ylabel="Amplitude", xaxis_type="linear", )

In [ ]:

f = np.linspace(7.0, 8.0, 100)

A = 1.0
f0 = 7.5
gamma = 0.1
C = -0.5
noise = 0.1

data = qx.fit.func_lorentzian(
    f=f,
    A=A,
    f0=f0,
    gamma=gamma,
    C=C,
) + np.random.default_rng().normal(0, noise, len(f))

qx.viz.plot(
    x=f,
    y=data,
    title="Lorentzian data",
    xlabel="Frequency (GHz)",
    ylabel="Amplitude",
)

result = qx.fit.fit_lorentzian(
    f,
    data,
    xlabel="Frequency (GHz)",
    ylabel="Amplitude",
)

f = np.linspace(7.0, 8.0, 100) A = 1.0 f0 = 7.5 gamma = 0.1 C = -0.5 noise = 0.1 data = qx.fit.func_lorentzian( f=f, A=A, f0=f0, gamma=gamma, C=C, ) + np.random.default_rng().normal(0, noise, len(f)) qx.viz.plot( x=f, y=data, title="Lorentzian data", xlabel="Frequency (GHz)", ylabel="Amplitude", ) result = qx.fit.fit_lorentzian( f, data, xlabel="Frequency (GHz)", ylabel="Amplitude", )

In [ ]:

f = np.linspace(7.0, 8.0, 100)

A = -1.0
f0 = 7.5
Omega = 0.1
C = -0.5
noise = 0.1

data = qx.fit.func_sqrt_lorentzian(
    f=f,
    A=A,
    f0=f0,
    Omega=Omega,
    C=C,
) + np.random.default_rng().normal(0, noise, len(f))

qx.viz.plot(
    x=f,
    y=data,
    title="Square root Lorentzian data",
    xlabel="Frequency (GHz)",
    ylabel="Amplitude",
)

result = qx.fit.fit_sqrt_lorentzian(
    f,
    data,
    xlabel="Frequency (GHz)",
    ylabel="Amplitude",
)

f = np.linspace(7.0, 8.0, 100) A = -1.0 f0 = 7.5 Omega = 0.1 C = -0.5 noise = 0.1 data = qx.fit.func_sqrt_lorentzian( f=f, A=A, f0=f0, Omega=Omega, C=C, ) + np.random.default_rng().normal(0, noise, len(f)) qx.viz.plot( x=f, y=data, title="Square root Lorentzian data", xlabel="Frequency (GHz)", ylabel="Amplitude", ) result = qx.fit.fit_sqrt_lorentzian( f, data, xlabel="Frequency (GHz)", ylabel="Amplitude", )

In [ ]:

t = np.linspace(0, 200, 20)

A = -1.0 + 0.5j
f = 12.5e-3
phi = 0.1
C = 0.5 + 0.5j
noise = 0.1

data = qx.fit.func_cos(
    t=t,
    A=A,
    omega=2 * np.pi * f,
    phi=phi,
    C=C,
) + np.random.default_rng().normal(0, noise, len(t))


qx.viz.scatter_iq_data(data)
qx.viz.plot_waveform(data)

result = qx.fit.fit_rabi(
    target="Q00",
    times=t,
    data=data,
)

t = np.linspace(0, 200, 20) A = -1.0 + 0.5j f = 12.5e-3 phi = 0.1 C = 0.5 + 0.5j noise = 0.1 data = qx.fit.func_cos( t=t, A=A, omega=2 * np.pi * f, phi=phi, C=C, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.scatter_iq_data(data) qx.viz.plot_waveform(data) result = qx.fit.fit_rabi( target="Q00", times=t, data=data, )

In [ ]:

t = np.linspace(0, 200, 20)

A = -1.0 + 0.5j
f = 12.5e-3
phi = 0.1
C = 0.5 + 0.5j
tau = 100
noise = 0.1

data = qx.fit.func_damped_cos(
    t=t,
    A=A,
    omega=2 * np.pi * f,
    phi=phi,
    C=C,
    tau=tau,
) + np.random.default_rng().normal(0, noise, len(t))


qx.viz.scatter_iq_data(data)
qx.viz.plot_waveform(data)

result = qx.fit.fit_rabi(
    target="Q00",
    times=t,
    data=data,
    is_damped=True,
)

t = np.linspace(0, 200, 20) A = -1.0 + 0.5j f = 12.5e-3 phi = 0.1 C = 0.5 + 0.5j tau = 100 noise = 0.1 data = qx.fit.func_damped_cos( t=t, A=A, omega=2 * np.pi * f, phi=phi, C=C, tau=tau, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.scatter_iq_data(data) qx.viz.plot_waveform(data) result = qx.fit.fit_rabi( target="Q00", times=t, data=data, is_damped=True, )

In [ ]:

f_control = np.linspace(7.0, 8.0, 20)
f_resonance = 7.5
f_rabi = 0.1
noise = 0.01

data = np.sqrt(
    f_rabi**2 + (f_control - f_resonance) ** 2,
) + np.random.default_rng().normal(0, noise, len(f_control))


qx.viz.plot(
    x=f_control,
    y=data,
    title="Detuned Rabi data",
    xlabel="Frequency (GHz)",
    ylabel="Amplitude",
)

result = qx.fit.fit_detuned_rabi(
    target="Q00",
    control_frequencies=f_control,
    rabi_frequencies=data,
)

f_control = np.linspace(7.0, 8.0, 20) f_resonance = 7.5 f_rabi = 0.1 noise = 0.01 data = np.sqrt( f_rabi**2 + (f_control - f_resonance) ** 2, ) + np.random.default_rng().normal(0, noise, len(f_control)) qx.viz.plot( x=f_control, y=data, title="Detuned Rabi data", xlabel="Frequency (GHz)", ylabel="Amplitude", ) result = qx.fit.fit_detuned_rabi( target="Q00", control_frequencies=f_control, rabi_frequencies=data, )

In [ ]:

t = np.linspace(0, 200, 50)

A = 1.0
f = 0.05
phi = np.pi / 2
C = 0.5
tau = 100
noise = 0.1

data = qx.fit.func_damped_cos(
    t=t,
    A=A,
    omega=2 * np.pi * f,
    phi=phi,
    C=C,
    tau=tau,
) + np.random.default_rng().normal(0, noise, len(t))

qx.viz.plot(
    x=t,
    y=data,
    title="Cosine data",
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

result = qx.fit.fit_ramsey(
    target="Q00",
    times=t,
    data=data,
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

t = np.linspace(0, 200, 50) A = 1.0 f = 0.05 phi = np.pi / 2 C = 0.5 tau = 100 noise = 0.1 data = qx.fit.func_damped_cos( t=t, A=A, omega=2 * np.pi * f, phi=phi, C=C, tau=tau, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.plot( x=t, y=data, title="Cosine data", xlabel="Time (ns)", ylabel="Amplitude", ) result = qx.fit.fit_ramsey( target="Q00", times=t, data=data, xlabel="Time (ns)", ylabel="Amplitude", )

In [ ]:

n = np.arange(0, 1000, 100)

A = 1.0
p = 0.99
C = 0
noise = 0.1
data = A * p**n + C + np.random.default_rng().normal(0, noise, len(n))

qx.viz.plot(
    x=n,
    y=data,
    title="Randomized benchmarking data",
    xlabel="Number of Cliffords",
    ylabel="Survival probability",
)

result = qx.fit.fit_rb(
    target="Q00",
    x=n,
    y=data,
)

n = np.arange(0, 1000, 100) A = 1.0 p = 0.99 C = 0 noise = 0.1 data = A * p**n + C + np.random.default_rng().normal(0, noise, len(n)) qx.viz.plot( x=n, y=data, title="Randomized benchmarking data", xlabel="Number of Cliffords", ylabel="Survival probability", ) result = qx.fit.fit_rb( target="Q00", x=n, y=data, )

In [ ]:

amplitude_range = np.linspace(0.0, 1.0, 20)

A = 1.0
f = 1.0
phi = np.pi
C = 0.1
noise = 0.1

data = qx.fit.func_cos(
    t=amplitude_range,
    A=A,
    omega=2 * np.pi * f,
    phi=phi,
    C=C,
) + np.random.default_rng().normal(0, noise, len(amplitude_range))

qx.viz.plot(
    x=amplitude_range,
    y=data,
    title="Amplitude calibration data",
    xlabel="Amplitude (arb. units)",
    ylabel="Signal (arb. units)",
)

result = qx.fit.fit_ampl_calib_data(
    target="Q00",
    amplitude_range=amplitude_range,
    data=data,
)

amplitude_range = np.linspace(0.0, 1.0, 20) A = 1.0 f = 1.0 phi = np.pi C = 0.1 noise = 0.1 data = qx.fit.func_cos( t=amplitude_range, A=A, omega=2 * np.pi * f, phi=phi, C=C, ) + np.random.default_rng().normal(0, noise, len(amplitude_range)) qx.viz.plot( x=amplitude_range, y=data, title="Amplitude calibration data", xlabel="Amplitude (arb. units)", ylabel="Signal (arb. units)", ) result = qx.fit.fit_ampl_calib_data( target="Q00", amplitude_range=amplitude_range, data=data, )

In [ ]:

f = np.linspace(7.0, 8.0, 100)

f_r = 7.5
kappa_ex = 0.1
kappa_in = 0.05
A = -1.0
tau = 0.0
phi = np.pi
noise = 0.1

data = (
    qx.fit.func_resonator_reflection(
        f=f,
        f_r=f_r,
        kappa_ex=kappa_ex,
        kappa_in=kappa_in,
        A=A,
        tau=tau,
        phi=phi,
    )
    + np.random.default_rng().normal(0, noise, len(f))
    + 1j * np.random.default_rng().normal(0, noise, len(f))
)

qx.viz.plot(
    x=f,
    y=np.abs(data),
    title="Resonance data",
    xlabel="Frequency (GHz)",
    ylabel="Amplitude",
)

qx.viz.plot_waveform(data)

result = qx.fit.fit_reflection_coefficient(
    target="Q00",
    freq_range=f,
    data=data,
)

f = np.linspace(7.0, 8.0, 100) f_r = 7.5 kappa_ex = 0.1 kappa_in = 0.05 A = -1.0 tau = 0.0 phi = np.pi noise = 0.1 data = ( qx.fit.func_resonator_reflection( f=f, f_r=f_r, kappa_ex=kappa_ex, kappa_in=kappa_in, A=A, tau=tau, phi=phi, ) + np.random.default_rng().normal(0, noise, len(f)) + 1j * np.random.default_rng().normal(0, noise, len(f)) ) qx.viz.plot( x=f, y=np.abs(data), title="Resonance data", xlabel="Frequency (GHz)", ylabel="Amplitude", ) qx.viz.plot_waveform(data) result = qx.fit.fit_reflection_coefficient( target="Q00", freq_range=f, data=data, )

In [ ]:

import numpy as np

import qubex as qx


def delayed_cosine(t, t_start, A, f, offset):
    """Return a delayed cosine waveform."""
    return np.where(
        t < t_start,
        A + offset,
        A * np.cos(2 * np.pi * f * (t - t_start)) + offset,
    )


t = np.arange(0, 1000, 2)
t0 = 160
A = 1.0
f = 0.01
C = 0.0
noise = 0.1

data = qx.fit.func_delayed_cos(
    t,
    t0=t0,
    A=A,
    omega=2 * np.pi * f,
    C=C,
) + np.random.default_rng().normal(0, noise, len(t))

qx.viz.plot(
    x=t,
    y=data,
    title="Delayed cosine signal",
    xlabel="Time (ns)",
    ylabel="Signal (arb. units)",
)

result = qx.fit.fit_delayed_cosine(
    t,
    data,
    xlabel="Time (ns)",
    ylabel="Amplitude",
)

import numpy as np import qubex as qx def delayed_cosine(t, t_start, A, f, offset): """Return a delayed cosine waveform.""" return np.where( t < t_start, A + offset, A * np.cos(2 * np.pi * f * (t - t_start)) + offset, ) t = np.arange(0, 1000, 2) t0 = 160 A = 1.0 f = 0.01 C = 0.0 noise = 0.1 data = qx.fit.func_delayed_cos( t, t0=t0, A=A, omega=2 * np.pi * f, C=C, ) + np.random.default_rng().normal(0, noise, len(t)) qx.viz.plot( x=t, y=data, title="Delayed cosine signal", xlabel="Time (ns)", ylabel="Signal (arb. units)", ) result = qx.fit.fit_delayed_cosine( t, data, xlabel="Time (ns)", ylabel="Amplitude", )