Emulating device noise

In this notebook, you will learn how to:

fetch a device from a connection and use its noise model,
emulate a program with the device noise model,
compare ideal and noisy results, through occupations and bitstrings.

Fetching a device with a noise model

Here, we fetch a device from PasqalCloudConnection which has a noise model.

from pasqal_cloud import PasqalCloudConnection

from qoolqit import Device

device = Device.from_connection(connection=PasqalCloudConnection(), name="FRESNEL_CAN1")

<string>:26: DeprecationWarning: Defining the number of emulation trajectories via 'NoiseModel.runs' is deprecated since pulser v1.7. Please favour using 'EmulationConfig.n_trajectories' instead.

Rabi oscillations of a blockaded pair

We drive two qubits placed at the minimum distance of the device, where their interaction energy is \(J = 1\) in dimensionless units, with a constant amplitude \(\Omega = 0.1\).

Since \(J \gg \Omega\), the pair is in the blockade regime: the doubly excited state \(|11\rangle\) is strongly suppressed. Neglecting it, the global drive couples \(|00\rangle\) only to the symmetric state \(|\Psi^+\rangle = (|01\rangle + |10\rangle)/\sqrt{2}\).

In this approximation, the pair behaves as a two-level system oscillating at the collective Rabi frequency \(\sqrt{2}\,\Omega\):

\[ P_{\Psi^+}(t) \simeq \sin^2\left(\frac{\sqrt{2}\,\Omega\, t}{2}\right), \]

and the occupation of each qubit, \(P_{\Psi^+}/2\), oscillates between \(0\) and \(1/2\) with period \(T_\text{Rabi} \simeq 2\pi / (\sqrt{2}\,\Omega)\).

This is the leading order in \(\Omega / J\): the residual coupling to \(|11\rangle\) shifts the frequency by corrections of order \(\Omega^2 / J\), so over many periods the exact dynamics slowly drifts from this estimate.

We choose the drive duration as a number of Rabi periods, long enough for the noise to build up.

import numpy as np

from qoolqit import ConstantWaveform, Drive, QuantumProgram, Register

omega = 0.1 # much smaller than the interaction energy (1.0 at distance 1): blockade regime
n_oscillations = 7
# approximate duration of n_oscillations Rabi periods, valid in the blockade regime
duration = n_oscillations * 2 * np.pi / (np.sqrt(2) * omega)

register = Register.from_coordinates([(0.0, 0.0), (1.0, 0.0)])
drive = Drive(amplitude=ConstantWaveform(duration, omega))
program = QuantumProgram(register, drive)

program.compile_to(device)
print(program)

Quantum Program:
| Register(n_qubits = 2)
| Drive(duration = 311.002)
| Compiled: True
| Device: FRESNEL_CAN1

Switching on the device noise

We ask the emulator for the Rydberg Occupation of each qubit along the pulse. Starting from an ideal configuration, the noisy one is obtained by setting prefer_device_noise_model=True.

Since the device noise is stochastic, the emulation averages over n_trajectories random realizations of the noise.

from qoolqit.execution import EmulationConfig, LocalEmulator, Occupation

rel_times = np.linspace(0, 1, 201)  # relative evaluation times, between 0 and 1
observables = (Occupation(evaluation_times=rel_times),)

ideal_config = EmulationConfig(observables=observables)
# same configuration, with the device noise switched on
noisy_config = EmulationConfig(
    observables=observables, prefer_device_noise_model=True, n_trajectories=64
)

ideal_results = LocalEmulator(emulation_config=ideal_config).run(program).results()
noisy_results = LocalEmulator(emulation_config=noisy_config).run(program).results()

/opt/hostedtoolcache/Python/3.14.8/x64/lib/python3.14/site-packages/pulser_simulation/qutip_backend.py:149: UserWarning: 'sequence.device.noise_model.runs=1' is being ignored; 'config.n_trajectories=64' will be used instead.
  super().__init__(sequence, config=config, mimic_qpu=mimic_qpu)

import matplotlib.pyplot as plt

# evaluation times are relative to the drive duration
times = rel_times * duration

fig, axes = plt.subplots(1, 2, figsize=(10, 4), sharey=True)
for qubit, ax in enumerate(axes):
    ax.plot(times, [occ[qubit] for occ in ideal_results.occupation], label="ideal")
    ax.plot(
        times,
        [occ[qubit] for occ in noisy_results.occupation],
        "-o",
        ms=4,
        markevery=4,
        label="noisy",
    )
    ax.set_title(f"qubit {qubit}")
    ax.set_xlabel("$t$")
    ax.legend(loc="upper right")
axes[0].set_ylabel("Rydberg occupation")
plt.show()

png

Without noise, the two qubits oscillate in phase with full contrast, between \(0\) and \(1/2\). With noise, the oscillation damps: the maxima decrease and the minima lift from zero.

Noise also shows up in the bitstrings sampled at the end of the pulse: the noisy counts deviate from the ideal ones, partly because of state preparation and measurement (SPAM) errors. Note that the noisy counter collects the shots of every trajectory.

print("Ideal:", ideal_results.final_bitstrings)
print("Noisy:", noisy_results.final_bitstrings)

print("Number of ideal results (n_shots):", sum(ideal_results.final_bitstrings.values()))
print(
    "Number of noisy results (n_trajectories x n_shots):",
    sum(noisy_results.final_bitstrings.values()),
)

Ideal: Counter({'00': 999, '10': 1})
Noisy: Counter({'00': 53673, '10': 5708, '01': 4352, '11': 267})
Number of ideal results (n_shots): 1000
Number of noisy results (n_trajectories x n_shots): 64000