Cross Resonance Dynamics¶

In [ ]:

import numpy as np

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

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

\(\ket{n}_\mathrm{L} \otimes \ket{n}_\mathrm{H}\)¶

In [ ]:

qubit_L = Transmon(
    label="Q00",
    dimension=4,
    frequency=7.2,
    anharmonicity=-7.2 / 19,
    relaxation_rate=0.00005,
    dephasing_rate=0.00005,
)

qubit_H = Transmon(
    label="Q01",
    dimension=4,
    frequency=8.0,
    anharmonicity=-8.0 / 19,
    relaxation_rate=0.00005,
    dephasing_rate=0.00005,
)

system = QuantumSystem(
    objects=[
        qubit_L,
        qubit_H,
    ],
    couplings=[
        Coupling(
            pair=(qubit_L, qubit_H),
            strength=0.01,
        ),
    ],
)

simulator = QuantumSimulator(system)

qubit_L = Transmon( label="Q00", dimension=4, frequency=7.2, anharmonicity=-7.2 / 19, relaxation_rate=0.00005, dephasing_rate=0.00005, ) qubit_H = Transmon( label="Q01", dimension=4, frequency=8.0, anharmonicity=-8.0 / 19, relaxation_rate=0.00005, dephasing_rate=0.00005, ) system = QuantumSystem( objects=[ qubit_L, qubit_H, ], couplings=[ Coupling( pair=(qubit_L, qubit_H), strength=0.01, ), ], ) simulator = QuantumSimulator(system)

In [ ]:

amplitude = 0.5  # GHz
duration = 200  # ns
ramptime = 30  # ns

pulse = qx.pulse.FlatTop(
    duration=duration,
    amplitude=2 * np.pi * amplitude,
    tau=ramptime,
)

amplitude = 0.5 # GHz duration = 200 # ns ramptime = 30 # ns pulse = qx.pulse.FlatTop( duration=duration, amplitude=2 * np.pi * amplitude, tau=ramptime, )

A. LOW → HIGH¶

• control qubit
  • low frequency
• target qubit
  • high frequency

In [ ]:

control_qubit = qubit_L
target_qubit = qubit_H

control = Control(
    target=control_qubit.label,
    frequency=target_qubit.frequency,
    waveform=pulse,
)
control.plot()

control_qubit = qubit_L target_qubit = qubit_H control = Control( target=control_qubit.label, frequency=target_qubit.frequency, waveform=pulse, ) control.plot()

A.1. \(\ket{0}_\mathrm{L} \otimes \ket{0}_\mathrm{H}\)¶

In [ ]:

result = simulator.mesolve(
    controls=[control],
    initial_state={
        qubit_L.label: "0",
        qubit_H.label: "0",
    },
)

result.plot_bloch_vectors(qubit_L.label)
result.plot_bloch_vectors(qubit_H.label)

result.display_bloch_sphere(qubit_L.label)
result.display_bloch_sphere(qubit_H.label)

result.plot_population_dynamics(qubit_L.label)
result.plot_population_dynamics(qubit_H.label)
result.plot_population_dynamics()

result = simulator.mesolve( controls=[control], initial_state={ qubit_L.label: "0", qubit_H.label: "0", }, ) result.plot_bloch_vectors(qubit_L.label) result.plot_bloch_vectors(qubit_H.label) result.display_bloch_sphere(qubit_L.label) result.display_bloch_sphere(qubit_H.label) result.plot_population_dynamics(qubit_L.label) result.plot_population_dynamics(qubit_H.label) result.plot_population_dynamics()

A.2. \(\ket{1}_\mathrm{L} \otimes \ket{0}_\mathrm{H}\)¶

In [ ]:

result = simulator.mesolve(
    controls=[control],
    initial_state={
        qubit_L.label: "1",
        qubit_H.label: "0",
    },
)

result.plot_bloch_vectors(qubit_L.label)
result.plot_bloch_vectors(qubit_H.label)

result.display_bloch_sphere(qubit_L.label)
result.display_bloch_sphere(qubit_H.label)

result.plot_population_dynamics(qubit_L.label)
result.plot_population_dynamics(qubit_H.label)
result.plot_population_dynamics()

result = simulator.mesolve( controls=[control], initial_state={ qubit_L.label: "1", qubit_H.label: "0", }, ) result.plot_bloch_vectors(qubit_L.label) result.plot_bloch_vectors(qubit_H.label) result.display_bloch_sphere(qubit_L.label) result.display_bloch_sphere(qubit_H.label) result.plot_population_dynamics(qubit_L.label) result.plot_population_dynamics(qubit_H.label) result.plot_population_dynamics()

B. HIGH → LOW¶

• control qubit
  • high frequency
• target qubit
  • low frequency

In [ ]:

control_qubit = qubit_H
target_qubit = qubit_L

control = Control(
    target=control_qubit.label,
    frequency=target_qubit.frequency,
    waveform=pulse,
)
control.plot()

control_qubit = qubit_H target_qubit = qubit_L control = Control( target=control_qubit.label, frequency=target_qubit.frequency, waveform=pulse, ) control.plot()

B.1. \(\ket{0}_\mathrm{L} \otimes \ket{0}_\mathrm{H}\)¶

In [ ]:

result = simulator.mesolve(
    controls=[control],
    initial_state={
        qubit_L.label: "0",
        qubit_H.label: "0",
    },
)

result.plot_bloch_vectors(qubit_L.label)
result.plot_bloch_vectors(qubit_H.label)

result.display_bloch_sphere(qubit_L.label)
result.display_bloch_sphere(qubit_H.label)

result.plot_population_dynamics(qubit_L.label)
result.plot_population_dynamics(qubit_H.label)
result.plot_population_dynamics()

result = simulator.mesolve( controls=[control], initial_state={ qubit_L.label: "0", qubit_H.label: "0", }, ) result.plot_bloch_vectors(qubit_L.label) result.plot_bloch_vectors(qubit_H.label) result.display_bloch_sphere(qubit_L.label) result.display_bloch_sphere(qubit_H.label) result.plot_population_dynamics(qubit_L.label) result.plot_population_dynamics(qubit_H.label) result.plot_population_dynamics()

B.2. \(\ket{0}_\mathrm{L} \otimes \ket{1}_\mathrm{H}\)¶

In [ ]:

result = simulator.mesolve(
    controls=[control],
    initial_state={
        qubit_L.label: "0",
        qubit_H.label: "1",
    },
)

result.plot_bloch_vectors(qubit_L.label)
result.plot_bloch_vectors(qubit_H.label)

result.display_bloch_sphere(qubit_L.label)
result.display_bloch_sphere(qubit_H.label)

result.plot_population_dynamics(qubit_L.label)
result.plot_population_dynamics(qubit_H.label)
result.plot_population_dynamics()

result = simulator.mesolve( controls=[control], initial_state={ qubit_L.label: "0", qubit_H.label: "1", }, ) result.plot_bloch_vectors(qubit_L.label) result.plot_bloch_vectors(qubit_H.label) result.display_bloch_sphere(qubit_L.label) result.display_bloch_sphere(qubit_H.label) result.plot_population_dynamics(qubit_L.label) result.plot_population_dynamics(qubit_H.label) result.plot_population_dynamics()