6 drag calibration

In [ ]:

import numpy as np

import qubex as qx
from qubex.simulator import Control, QuantumSimulator, QuantumSystem, Transmon

import numpy as np import qubex as qx from qubex.simulator import Control, QuantumSimulator, QuantumSystem, Transmon

In [ ]:

# units: GHz, ns

qubit = Transmon(
    label="Q01",
    dimension=3,
    frequency=7.5,
    anharmonicity=-7.5 / 19,
    relaxation_rate=0.05e-3,
    dephasing_rate=0.05e-3,
)

system = QuantumSystem(objects=[qubit])

simulator = QuantumSimulator(system)

# units: GHz, ns qubit = Transmon( label="Q01", dimension=3, frequency=7.5, anharmonicity=-7.5 / 19, relaxation_rate=0.05e-3, dephasing_rate=0.05e-3, ) system = QuantumSystem(objects=[qubit]) simulator = QuantumSimulator(system)

In [ ]:

def drag_pulse(
    duration: float,
    amplitude: float,
    beta: float,
):
    """Build a DRAG pulse with a Gaussian envelope."""
    pulse = qx.pulse.Drag(
        duration=duration, amplitude=amplitude, beta=beta, type="Gaussian"
    )
    return pulse

def drag_pulse( duration: float, amplitude: float, beta: float, ): """Build a DRAG pulse with a Gaussian envelope.""" pulse = qx.pulse.Drag( duration=duration, amplitude=amplitude, beta=beta, type="Gaussian" ) return pulse

In [ ]:

duration = 24  # ns
alpha = 2 * np.pi * qubit.anharmonicity
beta = -0.5 / alpha

pulse = drag_pulse(
    duration=duration,
    amplitude=1,
    beta=beta,
)
norm_factor = np.pi / float(np.sum(np.abs(pulse.values) * pulse.SAMPLING_PERIOD))
pulse = pulse.scaled(norm_factor)
pulse.plot(divide_by_two_pi=True)

amplitude = np.max(pulse.real).astype(float)
amplitude, beta

duration = 24 # ns alpha = 2 * np.pi * qubit.anharmonicity beta = -0.5 / alpha pulse = drag_pulse( duration=duration, amplitude=1, beta=beta, ) norm_factor = np.pi / float(np.sum(np.abs(pulse.values) * pulse.SAMPLING_PERIOD)) pulse = pulse.scaled(norm_factor) pulse.plot(divide_by_two_pi=True) amplitude = np.max(pulse.real).astype(float) amplitude, beta

In [ ]:

result = simulator.mesolve(
    controls=[
        Control(
            target=qubit.label,
            frequency=qubit.frequency,
            waveform=pulse,
        )
    ],
    initial_state={
        qubit.label: "0",
    },
)
result.show_last_population(qubit.label)
result.plot_population_dynamics(qubit.label)
result.plot_bloch_vectors(qubit.label)
result.display_bloch_sphere(qubit.label)

result = simulator.mesolve( controls=[ Control( target=qubit.label, frequency=qubit.frequency, waveform=pulse, ) ], initial_state={ qubit.label: "0", }, ) result.show_last_population(qubit.label) result.plot_population_dynamics(qubit.label) result.plot_bloch_vectors(qubit.label) result.display_bloch_sphere(qubit.label)

In [ ]:

results = []
beta_range = np.linspace(-1, 1, 51)
for idx, beta in enumerate(beta_range):
    pulse = drag_pulse(
        duration=duration,
        amplitude=amplitude,
        beta=beta,
    )
    result = simulator.mesolve(
        controls=[
            Control(
                target=qubit,
                waveform=qx.PulseArray(
                    [
                        pulse,
                        pulse.scaled(-1),
                    ]
                ),
            )
        ],
    )
    results.append(result)

    if idx % 10 == 0:
        print(f"beta = {beta:.2f}")
        result.display_bloch_sphere(qubit.label)

results = [] beta_range = np.linspace(-1, 1, 51) for idx, beta in enumerate(beta_range): pulse = drag_pulse( duration=duration, amplitude=amplitude, beta=beta, ) result = simulator.mesolve( controls=[ Control( target=qubit, waveform=qx.PulseArray( [ pulse, pulse.scaled(-1), ] ), ) ], ) results.append(result) if idx % 10 == 0: print(f"beta = {beta:.2f}") result.display_bloch_sphere(qubit.label)

In [ ]:

e_x = np.array([result.get_bloch_vectors(qubit.label)[-1][0] for result in results])

qx.viz.plot(
    x=beta_range,
    y=e_x,
    title="Sweeping DRAG beta",
    xlabel="β",
    ylabel="〈X〉",
)

e_x = np.array([result.get_bloch_vectors(qubit.label)[-1][0] for result in results]) qx.viz.plot( x=beta_range, y=e_x, title="Sweeping DRAG beta", xlabel="β", ylabel="〈X〉", )

In [ ]:

from scipy.optimize import root_scalar

e_x_fine = lambda x: np.interp(x, beta_range, e_x)

result = root_scalar(e_x_fine, bracket=[beta_range[0], beta_range[-1]])
beta = result.root
beta

from scipy.optimize import root_scalar e_x_fine = lambda x: np.interp(x, beta_range, e_x) result = root_scalar(e_x_fine, bracket=[beta_range[0], beta_range[-1]]) beta = result.root beta

In [ ]:

pulse = drag_pulse(
    duration=duration,
    amplitude=amplitude,
    beta=beta,
)
pulse.plot(divide_by_two_pi=True)

result = simulator.mesolve(
    controls=[
        Control(
            target=qubit.label,
            frequency=qubit.frequency,
            waveform=pulse,
        )
    ],
    initial_state={
        qubit.label: "0",
    },
)
result.show_last_population(qubit.label)
result.plot_population_dynamics(qubit.label)
result.plot_bloch_vectors(qubit.label)
result.display_bloch_sphere(qubit.label)

pulse = drag_pulse( duration=duration, amplitude=amplitude, beta=beta, ) pulse.plot(divide_by_two_pi=True) result = simulator.mesolve( controls=[ Control( target=qubit.label, frequency=qubit.frequency, waveform=pulse, ) ], initial_state={ qubit.label: "0", }, ) result.show_last_population(qubit.label) result.plot_population_dynamics(qubit.label) result.plot_bloch_vectors(qubit.label) result.display_bloch_sphere(qubit.label)

In [ ]:

def drag_objective_func(x):
    """Objective function for DRAG calibration."""
    amplitude, beta = x
    pulse = drag_pulse(
        duration=duration,
        amplitude=amplitude,
        beta=beta,
    )
    result = simulator.mesolve(
        controls=[
            Control(
                target=qubit,
                waveform=pulse,
            )
        ],
    )
    state = result.get_bloch_vectors(qubit.label)[-1]
    target = np.array([0, 0, -1])
    return np.linalg.norm(state - target)

def drag_objective_func(x): """Objective function for DRAG calibration.""" amplitude, beta = x pulse = drag_pulse( duration=duration, amplitude=amplitude, beta=beta, ) result = simulator.mesolve( controls=[ Control( target=qubit, waveform=pulse, ) ], ) state = result.get_bloch_vectors(qubit.label)[-1] target = np.array([0, 0, -1]) return np.linalg.norm(state - target)

In [ ]:

drag_objective_func([amplitude, beta])

drag_objective_func([amplitude, beta])

In [ ]:

import cma

initial_guess = [
    amplitude,
    beta,
]

es = cma.CMAEvolutionStrategy(
    initial_guess,
    0.01,
    {
        "seed": 42,
        "ftarget": 1e-6,
    },
)

es.optimize(drag_objective_func)

es.result.xbest

import cma initial_guess = [ amplitude, beta, ] es = cma.CMAEvolutionStrategy( initial_guess, 0.01, { "seed": 42, "ftarget": 1e-6, }, ) es.optimize(drag_objective_func) es.result.xbest

In [ ]:

drag_objective_func(es.result.xbest)

drag_objective_func(es.result.xbest)

In [ ]:

pulse = drag_pulse(
    duration=duration,
    amplitude=es.result.xbest[0],
    beta=es.result.xbest[1],
)
pulse.plot(divide_by_two_pi=True)

pulse = drag_pulse( duration=duration, amplitude=es.result.xbest[0], beta=es.result.xbest[1], ) pulse.plot(divide_by_two_pi=True)

In [ ]:

result = simulator.mesolve(
    controls=[
        Control(
            target=qubit.label,
            frequency=qubit.frequency,
            waveform=pulse,
        )
    ],
)
result.display_bloch_sphere(qubit.label)
result.show_last_population(qubit.label)

result = simulator.mesolve( controls=[ Control( target=qubit.label, frequency=qubit.frequency, waveform=pulse, ) ], ) result.display_bloch_sphere(qubit.label) result.show_last_population(qubit.label)

In [ ]:

result = simulator.mesolve(
    controls=[
        Control(
            target=qubit,
            waveform=qx.PulseArray(
                [pulse] * 2,
            ),
        )
    ],
)
result.display_bloch_sphere(qubit.label)
result.show_last_population(qubit.label)

result = simulator.mesolve( controls=[ Control( target=qubit, waveform=qx.PulseArray( [pulse] * 2, ), ) ], ) result.display_bloch_sphere(qubit.label) result.show_last_population(qubit.label)

In [ ]:

result = simulator.mesolve(
    controls=[
        Control(
            target=qubit.label,
            frequency=qubit.frequency,
            waveform=qx.PulseArray(
                [pulse] * 10,
            ),
        )
    ],
)
result.display_bloch_sphere(qubit.label)
result.show_last_population(qubit.label)

result = simulator.mesolve( controls=[ Control( target=qubit.label, frequency=qubit.frequency, waveform=qx.PulseArray( [pulse] * 10, ), ) ], ) result.display_bloch_sphere(qubit.label) result.show_last_population(qubit.label)