See also

A Jupyter notebook version of this tutorial can be downloaded here.

Echo

The Hahn echo experiment is a modified Ramsey sequence that uses a refocusing π-pulse at the midpoint of the free evolution time (t = τ/2) to invert the phase evolution, which effectively cancels out phase accumulations due to frequency offsets that are constant within the duration of the experiment (low-f noise). The fitted decay time \(T_{2,e}\) can be compared to \(T_2^*\) to estimate low-frequency noise.

from dependencies.analysis_utils import EchoAnalysis
from xarray import open_dataset

from qblox_scheduler import HardwareAgent, Schedule
from qblox_scheduler.operations import (
    X90,
    IdlePulse,
    Measure,
    Reset,
    SetClockFrequency,
    X,
)
from qblox_scheduler.operations.expressions import DType
from qblox_scheduler.operations.loop_domains import arange

Generating hash table for SingleQubitClifford.
Hash table generated.
Generating hash table for TwoQubitCliffordCZ.
Hash table generated.
Generating hash table for TwoQubitCliffordZX.
Hash table generated.
Testing decompositions.
Test passed.

Setup

The hardware agent manages the connection to the instrument and ensures that pulses and acquisitions happen over the appropriate input and output channels of the Cluster. The cell below creates an instance of the HardwareAgent based on the hardware- and device-under-test configuration files in the ./dependencies/configs folder, allowing us to start doing measurements. We also define some convenient aliases to use throughout our measurements. For a more thorough discussion of the hardware- and device-under-test configuration files, check out this tutorial.

# Set up hardware agent, this automatically connects to the instrument
hw_agent = HardwareAgent(
    hardware_configuration="./dependencies/configs/hw_config.json",
    quantum_device_configuration="./dependencies/configs/dut_config.json",
)

# convenience aliases
q0 = hw_agent.quantum_device.get_element("q0")
q2 = hw_agent.quantum_device.get_element("q2")
cluster = hw_agent.get_clusters()["cluster"]
hw_options = hw_agent.hardware_configuration.hardware_options
qubit = q0

/builds/0/.venv/lib/python3.10/site-packages/qblox_scheduler/qblox/hardware_agent.py:460: UserWarning: cluster: Trying to instantiate cluster with ip 'None'.Creating a dummy cluster.
  warnings.warn(

Experiment settings

Note: in order for the second \({\pi/2}\) pulse to have a phase difference \(\Delta \phi = \Delta f \tau\), relative to the first \(X_{\pi/2}\) pulse we offset the clock frequency by \(\Delta f\) for a time \(\tau\). Here, \(\Delta f\) is the frequency_detuning and \(\tau\) is tau.

# Detuning
frequency_detuning = 1e6  # Hz

# Tau settings
tau_start = 1e-6  # s
tau_stop = 100e-6  # s
tau_step = 2e-6  # s

repetitions = 1000

Experiment schedule

echo_sched = Schedule(name="echo_experiment")
echo_sched.add(
    SetClockFrequency(
        clock=qubit.name + ".01", clock_freq_new=qubit.clock_freqs.f01 + frequency_detuning
    )
)
# Update parameters
echo_sched.add(IdlePulse(4e-9))

with (
    echo_sched.loop(arange(0, repetitions, 1, DType.NUMBER)),
    echo_sched.loop(arange(start=tau_start, stop=tau_stop, step=tau_step, dtype=DType.TIME)) as tau,
):
    echo_sched.add(Reset(qubit.name))
    # Play first X/2 pulse
    echo_sched.add(X90(qubit=qubit.name))
    # Add reflecting pi pulse at time tau / 2
    echo_sched.add(X(qubit=qubit.name), rel_time=tau / 2)
    # Play second X/2 pulse tau / 2 seconds after pi pulse
    echo_sched.add(X90(qubit=qubit.name), rel_time=tau / 2)
    echo_sched.add(Measure(qubit.name, coords={"tau": tau}, acq_channel="S_21"))

# Execute the experiment
echo_data = hw_agent.run(echo_sched)
if cluster.is_dummy:
    example_data = open_dataset("./dependencies/datasets/echo.hdf5", engine="h5netcdf")
    echo_data = echo_data.update({"S_21": example_data.S_21})

Analyze the experiment

echo_analysis = EchoAnalysis(echo_data).run()
echo_analysis.display_figs_mpl()

Update the device configuration file

After measurement, we may store the measured device properties inside a new file to use in future experiments. The time-unique identifier ensures that it is easy to find back previously found measurement results.

hw_agent.quantum_device.to_json_file("./dependencies/configs", add_timestamp=True)

'./dependencies/configs/two_flux_tunable_transmons_2025-10-30_00-37-23_UTC.json'