Hahn Echo Experiment#
This section shows how to perform a Hahn Echo experiment. This experiment can
be easily generated with EchoExperiment.
With the previous Ramsey experiment we showed a way to characterize the decay rate of the coherence between the ground and excited states of the qubit. We now show how to perform a T_2 Hahn Echo experiment to obtain a more precise estimate of the qubit’s decay time. Indeed, unlike the T_2^* previously measured, the T_2 obtained using a Hahn Echo experiement allows to get a measure of the decoherence while eliminating low frequency fluctuations. Here we are following the same process as the Ramsey experiment above with the addition of an additional Z rotation also called a refocusing pulse in between the two \(\frac{\pi}{2}\) pulses. This Z rotation will counteract the natural precession of the qubit’s state and is refocusing any slow noise by doing so.
The experiment therefore follows the following steps:
Initialize the qubit to an equal superposition state between the ground and excited state (in the \(XY\) plane of the Bloch sphere) by applying a \(\frac{\pi}{2}\) gate.
Apply a delay.
Apply a \(Z\) rotation to offset the natural precession.
Apply a second \(\frac{\pi}{2}\) gate to drive the qubit toward either the ground or excited state.
Measure the population of the qubit in the excited state.
Repeat the above steps with varying delay time.
We start again by initializing a qubit and loading a channel mapper to
create a new instance of the EchoExperiment
class. Next, we generate a calibration set for the qubit
using make_calibration_set(). This file includes
the quantum operations and variables we will need to run the experiment.
[2]:
import keysight.qcs as qcs
import numpy as np
from keysight.qcs.experiments import EchoExperiment
from keysight.qcs.experiments import make_calibration_set
# set the following to True when connected to hardware
run_on_hw = False
n_qubits = 1
qubits = qcs.Qudits(range(n_qubits))
calibration_set = make_calibration_set(n_qubits)
# generate an empty channel mapper
mapper = qcs.ChannelMapper("ip_addr")
# create Ramsey experiment
echo_experiment = EchoExperiment(mapper, calibration_set=calibration_set, qubits=qubits)
echo_experiment.draw()
# The program consists of two `X90` gates, with a `X` gate placed between them.
# There are two delays of `d/2` where `d` is variable, one in between the first
# `X90` gates and the `X` gate and one in between the `X` gates and the second
# `X90` gate. The sequence is then followed by a measurement.
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Program
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[3]:
# configure the repetitions for this experiment
start_delay = 40e-9
end_delay = 80e-9
steps = 3
scan_values = np.linspace([start_delay] * n_qubits, [end_delay] * n_qubits, steps)
echo_experiment.configure_repetitions(delays=scan_values, n_shots=1)
Compiling this program to the waveform level using the
ParameterizedLinkers in the calibration set
results in the following program:
[4]:
echo_experiment.compiled_program.render(channel_subplots=False, sample_rate=5e9)
To execute this experiment, we can simply run
[5]:
if run_on_hw:
echo_experiment.execute()
else:
# load in a previously executed version of this experiment
echo_experiment = qcs.load("EchoExperiment_data.hdf5")
The draw and plot methods can then be used just like for the Ramsey experiment.
[6]:
echo_experiment.draw()
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EchoExperiment
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[7]:
echo_experiment.plot_trace(channels=qcs.Qudits(1, "ancilla"))