2 coupled qubits

In [ ]:

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

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

In [ ]:

# Create the quantum system with two coupled transmon qubits (unit: GHz)

qubits = [
    Transmon(
        label="Q0",
        dimension=3,
        frequency=7.648,
        anharmonicity=-0.33,
        relaxation_rate=0.0,
        dephasing_rate=0.0,
    ),
    Transmon(
        label="Q1",
        dimension=3,
        frequency=8.275,
        anharmonicity=-0.33,
        relaxation_rate=0.0,
        dephasing_rate=0.0,
    ),
]

system = QuantumSystem(
    objects=qubits,
    couplings=[
        Coupling(
            pair=(qubits[0], qubits[1]),
            strength=0.01,
        ),
    ],
)

simulator = QuantumSimulator(system)

# Create the quantum system with two coupled transmon qubits (unit: GHz) qubits = [ Transmon( label="Q0", dimension=3, frequency=7.648, anharmonicity=-0.33, relaxation_rate=0.0, dephasing_rate=0.0, ), Transmon( label="Q1", dimension=3, frequency=8.275, anharmonicity=-0.33, relaxation_rate=0.0, dephasing_rate=0.0, ), ] system = QuantumSystem( objects=qubits, couplings=[ Coupling( pair=(qubits[0], qubits[1]), strength=0.01, ), ], ) simulator = QuantumSimulator(system)

In [ ]:

system.hamiltonian

system.hamiltonian

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static_zz = system.get_static_zz(("Q0", "Q1"))
print(f"static_zz: {static_zz * 1e6:.2f} kHz")

static_zz = system.get_static_zz(("Q0", "Q1")) print(f"static_zz: {static_zz * 1e6:.2f} kHz")

In [ ]:

frequency_shift_0 = system.get_frequency_shift("Q0")
print(f"frequency_shift_0: {frequency_shift_0 * 1e6:.2f} kHz")

frequency_shift_1 = system.get_frequency_shift("Q1")
print(f"frequency_shift_1: {frequency_shift_1 * 1e6:.2f} kHz")

frequency_shift_0 = system.get_frequency_shift("Q0") print(f"frequency_shift_0: {frequency_shift_0 * 1e6:.2f} kHz") frequency_shift_1 = system.get_frequency_shift("Q1") print(f"frequency_shift_1: {frequency_shift_1 * 1e6:.2f} kHz")

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effective_frequency_0 = system.get_effective_frequency("Q0")
print(f"effective_frequency_0: {effective_frequency_0:.6f} GHz")

effective_frequency_1 = system.get_effective_frequency("Q1")
print(f"effective_frequency_1: {effective_frequency_1:.6f} GHz")

effective_frequency_0 = system.get_effective_frequency("Q0") print(f"effective_frequency_0: {effective_frequency_0:.6f} GHz") effective_frequency_1 = system.get_effective_frequency("Q1") print(f"effective_frequency_1: {effective_frequency_1:.6f} GHz")

Static ZZ interaction¶

In [ ]:

# Duration for 1 period of the ZZ interaction
duration = abs(1 / static_zz)  # ns

controls = [
    Control(
        target=qubits[0],
        waveform=[0],
        durations=[duration],
        frequency=effective_frequency_0,
    ),
    Control(
        target=qubits[1],
        waveform=[0],
        durations=[duration],
        frequency=effective_frequency_1,
    ),
]

# Duration for 1 period of the ZZ interaction duration = abs(1 / static_zz) # ns controls = [ Control( target=qubits[0], waveform=[0], durations=[duration], frequency=effective_frequency_0, ), Control( target=qubits[1], waveform=[0], durations=[duration], frequency=effective_frequency_1, ), ]

In [ ]:

result = simulator.mesolve(
    controls=controls,
    initial_state={
        qubits[0].label: "0",
        qubits[1].label: "+",
    },
    n_samples=101,
)

result.plot_bloch_vectors(qubits[0].label, frame="drive")
result.plot_bloch_vectors(qubits[1].label, frame="drive")
result.display_bloch_sphere(qubits[0].label, frame="drive")
result.display_bloch_sphere(qubits[1].label, frame="drive")

result = simulator.mesolve( controls=controls, initial_state={ qubits[0].label: "0", qubits[1].label: "+", }, n_samples=101, ) result.plot_bloch_vectors(qubits[0].label, frame="drive") result.plot_bloch_vectors(qubits[1].label, frame="drive") result.display_bloch_sphere(qubits[0].label, frame="drive") result.display_bloch_sphere(qubits[1].label, frame="drive")

In [ ]:

result = simulator.mesolve(
    controls=controls,
    initial_state={
        qubits[0].label: "1",
        qubits[1].label: "+",
    },
    n_samples=101,
)

result.plot_bloch_vectors(qubits[0].label, frame="drive")
result.plot_bloch_vectors(qubits[1].label, frame="drive")
result.display_bloch_sphere(qubits[0].label, frame="drive")
result.display_bloch_sphere(qubits[1].label, frame="drive")

result = simulator.mesolve( controls=controls, initial_state={ qubits[0].label: "1", qubits[1].label: "+", }, n_samples=101, ) result.plot_bloch_vectors(qubits[0].label, frame="drive") result.plot_bloch_vectors(qubits[1].label, frame="drive") result.display_bloch_sphere(qubits[0].label, frame="drive") result.display_bloch_sphere(qubits[1].label, frame="drive")

In [ ]:

result = simulator.mesolve(
    controls=controls,
    initial_state={
        qubits[0].label: "+",
        qubits[1].label: "+",
    },
    n_samples=101,
)

result.plot_bloch_vectors(qubits[0].label, frame="drive")
result.plot_bloch_vectors(qubits[1].label, frame="drive")
result.display_bloch_sphere(qubits[0].label, frame="drive")
result.display_bloch_sphere(qubits[1].label, frame="drive")

result = simulator.mesolve( controls=controls, initial_state={ qubits[0].label: "+", qubits[1].label: "+", }, n_samples=101, ) result.plot_bloch_vectors(qubits[0].label, frame="drive") result.plot_bloch_vectors(qubits[1].label, frame="drive") result.display_bloch_sphere(qubits[0].label, frame="drive") result.display_bloch_sphere(qubits[1].label, frame="drive")