Single qubit Rabi flopping¶

First, let's implement a single-qubit Rabi flopping experiment. Here, a two-level system, initialized in the $\ket{0}$ basis state, oscillates between $\ket{0}$ and $\ket{1}$ during evolution. The Hamiltonian under which the state evolves is, $$ H = -\frac{\pi}{4}\sigma^x $$

Building the quantum program¶

We will go through how to specify this quantum program using OQD's analog interface. First import the relevant modules,

Imports

import numpy as np

from oqd_core.interface.analog.operator import PauliI, PauliX, PauliZ, PauliY
from oqd_core.interface.analog.operation import *
from oqd_core.backend.metric import *
from oqd_core.backend.task import Task
from oqd_analog_emulator.qutip_backend import QutipBackend

Then we construct an AnalogGate object,

X = PauliX()
gate = AnalogGate(hamiltonian= -(np.pi / 4) * X)

The AnalogCircuit represents a sequence of Hamiltonians which the quantum system evolves under for a fixed duration. Let's construct a circuit and add the gate from above and then measure,

circuit = AnalogCircuit()
circuit.evolve(duration=3, gate=gate)
circuit.measure()

Setting up the backend¶

Now, let's emulate the time dynamics of our quantum system. We use one of the provided backends, here the QutipBackend, to solve the evolution of the quantum state through the circuit. We first initialize the backend and a [TaskArgsAnalog][oqd_core.backend.task.TaskArgsAnalog] object with the settings for the emulation, such as the number of shots, the metrics to track through the evolution (e.g., an expectation value), and the time step.

backend = QutipBackend()
args = TaskArgsAnalog(
    n_shots=100,
    metrics={
        "Z": Expectation(operator=Z),
    },
    dt=1e-3,
)

Running the backend emulation¶

Now, we simply use the .run() method of the backend to run the emulation of the time dynamics of the circuit.

results = backend.run(task = task)