One qubit Rabi flopping¶

Rabi flopping is the oscillation of a qubit in the presence of a driving field. The qubit, initialized in the $|0\rangle$ state, will precess around the XY-plane of the Bloch sphere.

The driving Hamiltonian here is simply the Pauli $X$ operator, $$ X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} $$

In this example, we implement a single-qubit Rabi flopping and emulate the qubit oscillation using the classical backend.

In [1]:

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

import warnings
warnings.filterwarnings("ignore")

from oqd_core.interface.analog.operator import *
from oqd_core.interface.analog.operation import *
from oqd_core.backend.metric import *
from oqd_core.backend.task import Task, TaskArgsAnalog

from oqd_analog_emulator.qutip_backend import QutipBackend

import numpy as np import matplotlib.pyplot as plt import seaborn as sns import warnings warnings.filterwarnings("ignore") from oqd_core.interface.analog.operator import * from oqd_core.interface.analog.operation import * from oqd_core.backend.metric import * from oqd_core.backend.task import Task, TaskArgsAnalog from oqd_analog_emulator.qutip_backend import QutipBackend

In [2]:

X = PauliX()
Z = PauliZ()

Hx = AnalogGate(hamiltonian=X)

circuit = AnalogCircuit()
circuit.evolve(duration=10, gate=Hx)
circuit.measure()

X = PauliX() Z = PauliZ() Hx = AnalogGate(hamiltonian=X) circuit = AnalogCircuit() circuit.evolve(duration=10, gate=Hx) circuit.measure()

In [3]:

# define task args
args = TaskArgsAnalog(
    n_shots=1000,
    fock_cutoff=4,
    metrics={
        "Z": Expectation(operator=Z),
    },
    dt=1e-3,
)

task = Task(program=circuit, args=args)

# define task args args = TaskArgsAnalog( n_shots=1000, fock_cutoff=4, metrics={ "Z": Expectation(operator=Z), }, dt=1e-3, ) task = Task(program=circuit, args=args)

In [4]:

backend = QutipBackend()
results = backend.run(task=task)

backend = QutipBackend() results = backend.run(task=task)

In [5]:

fig, ax = plt.subplots(1, 1, figsize=[6, 3])
colors = sns.color_palette(palette="crest", n_colors=4)

for k, (name, metric) in enumerate(results.metrics.items()):
    ax.plot(results.times, metric, label=f"$\\langle {name} \\rangle$", color=colors[k])
ax.legend();

fig, ax = plt.subplots(1, 1, figsize=[6, 3]) colors = sns.color_palette(palette="crest", n_colors=4) for k, (name, metric) in enumerate(results.metrics.items()): ax.plot(results.times, metric, label=f"$\\langle {name} \\rangle$", color=colors[k]) ax.legend();

In [6]:

fig, axs = plt.subplots(4, 1, sharex=True, figsize=[5, 9])

state = np.array([basis.real + 1j * basis.imag for basis in results.state])
bases = ["0", "1"]
counts = {basis: results.counts.get(basis, 0) for basis in bases}

ax = axs[0]
ax.bar(x=bases, height=np.abs(state) ** 2, color=colors[0])
ax.set(ylabel="Probability")

ax = axs[1]
ax.bar(x=bases, height=list(counts.values()), color=colors[1])
ax.set(ylabel="Count")

ax = axs[2]
ax.bar(x=bases, height=state.real, color=colors[2])
ax.set(ylabel="Amplitude (real)")

ax = axs[3]
ax.bar(x=bases, height=state.imag, color=colors[3])
ax.set(xlabel="Basis state", ylabel="Amplitude (imag)", ylim=[-np.pi, np.pi]);

fig, axs = plt.subplots(4, 1, sharex=True, figsize=[5, 9]) state = np.array([basis.real + 1j * basis.imag for basis in results.state]) bases = ["0", "1"] counts = {basis: results.counts.get(basis, 0) for basis in bases} ax = axs[0] ax.bar(x=bases, height=np.abs(state) ** 2, color=colors[0]) ax.set(ylabel="Probability") ax = axs[1] ax.bar(x=bases, height=list(counts.values()), color=colors[1]) ax.set(ylabel="Count") ax = axs[2] ax.bar(x=bases, height=state.real, color=colors[2]) ax.set(ylabel="Amplitude (real)") ax = axs[3] ax.bar(x=bases, height=state.imag, color=colors[3]) ax.set(xlabel="Basis state", ylabel="Amplitude (imag)", ylim=[-np.pi, np.pi]);