1 rabi oscillation

In [ ]:

# Install qubex library if not installed
# !pip install git+https://github.com/amachino/qubex.git

# Install qubex library if not installed # !pip install git+https://github.com/amachino/qubex.git

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 [ ]:

# Define the transmon qubit (unit: GHz, ns)
qubit = Transmon(
    label="Q01",
    dimension=3,
    frequency=7.648,
    anharmonicity=-0.333,
    relaxation_rate=0.00005,
    dephasing_rate=0.00005,
)

# Define the quantum system with the qubit
system = QuantumSystem(objects=[qubit])

# Define the quantum simulator with the system
simulator = QuantumSimulator(system)

# Define the transmon qubit (unit: GHz, ns) qubit = Transmon( label="Q01", dimension=3, frequency=7.648, anharmonicity=-0.333, relaxation_rate=0.00005, dephasing_rate=0.00005, ) # Define the quantum system with the qubit system = QuantumSystem(objects=[qubit]) # Define the quantum simulator with the system simulator = QuantumSimulator(system)

In [ ]:

# Check the Hamiltonian of the system
system.hamiltonian

# Check the Hamiltonian of the system system.hamiltonian

In [ ]:

# Define the drive pulse

# Rectangular pulse with amplitude 4π/100 and duration 100 ns
# Rabi frequency will be 2/100 = 0.02 GHz = 20 MHz
duration = 100
drive = qx.pulse.Rect(
    duration=duration,
    amplitude=2 * (2 * np.pi) / duration,
)

# Plot the drive pulse
drive.plot()

# Define the drive pulse # Rectangular pulse with amplitude 4π/100 and duration 100 ns # Rabi frequency will be 2/100 = 0.02 GHz = 20 MHz duration = 100 drive = qx.pulse.Rect( duration=duration, amplitude=2 * (2 * np.pi) / duration, ) # Plot the drive pulse drive.plot()

On-resonant Rabi oscillation¶

In [ ]:

# Define the control with the target qubit and the drive pulse
control = Control(
    target=qubit,
    waveform=drive,
)

# Run the simulation by solving the master equation
result = simulator.mesolve(
    controls=[control],  # List of controls
    initial_state={"Q01": "0"},  # Initial states of the qubits
    n_samples=101,  # Number of samples
)

# Define the control with the target qubit and the drive pulse control = Control( target=qubit, waveform=drive, ) # Run the simulation by solving the master equation result = simulator.mesolve( controls=[control], # List of controls initial_state={"Q01": "0"}, # Initial states of the qubits n_samples=101, # Number of samples )

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# Show the last population of the qubit
result.show_last_population(qubit.label)

# Plot the population dynamics of the qubit
result.plot_population_dynamics(qubit.label)

# Plot the Bloch vectors of the qubit
result.plot_bloch_vectors(qubit.label)

# Display the Bloch sphere of the qubit
result.display_bloch_sphere(qubit.label)

# Show the last population of the qubit result.show_last_population(qubit.label) # Plot the population dynamics of the qubit result.plot_population_dynamics(qubit.label) # Plot the Bloch vectors of the qubit result.plot_bloch_vectors(qubit.label) # Display the Bloch sphere of the qubit result.display_bloch_sphere(qubit.label)

Off-resonant Rabi oscillation¶

In [ ]:

detuning = 0.01

control = Control(
    target=qubit,
    frequency=qubit.frequency + detuning,
    waveform=drive,
)

result = simulator.mesolve(
    controls=[control],
    initial_state={"Q01": "0"},
    n_samples=101,
)

result.show_last_population(qubit.label)
result.plot_population_dynamics(qubit.label)

# qubit frame
result.plot_bloch_vectors(qubit.label, frame="qubit")
result.display_bloch_sphere(qubit.label, frame="qubit")

# drive frame
result.plot_bloch_vectors(qubit.label, frame="drive")
result.display_bloch_sphere(qubit.label, frame="drive")

detuning = 0.01 control = Control( target=qubit, frequency=qubit.frequency + detuning, waveform=drive, ) result = simulator.mesolve( controls=[control], initial_state={"Q01": "0"}, n_samples=101, ) result.show_last_population(qubit.label) result.plot_population_dynamics(qubit.label) # qubit frame result.plot_bloch_vectors(qubit.label, frame="qubit") result.display_bloch_sphere(qubit.label, frame="qubit") # drive frame result.plot_bloch_vectors(qubit.label, frame="drive") result.display_bloch_sphere(qubit.label, frame="drive")