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doc: Hayk review
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Co-authored-by: Hayk Sargsyan <[email protected]>
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andrea-pasquale and hay-k authored Jan 16, 2025
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DRAG experiments
================

In this section we show how to run Ramsey experiments using Qibocal
In this section we show how to run DRAG experiments using Qibocal

.. _drag:


DRAG :cite:p:`Motzoi_2009, Gambetta_2011`: pulses can be used to lower both phase and leakage errors,
it consists in adding a quadrature component to the pulse which is proportional
to the time derivative of the phase component. Given a pulse with a phase component :math:`\Omega_x`
DRAG :cite:p:`Motzoi_2009, Gambetta_2011`: pulses can be used to lower both phase and leakage errors.
It consists of adding a quadrature component to the pulse which is proportional
to the time derivative of the in-phase component. Given a pulse with an in-phase component :math:`\Omega_x`
the quadrature component :math:`\Omega_y` is evaluated as

.. math::
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where :math:`\beta` is a scaling parameter.

Qibocal provides two separate protocols to extract :math:`\beta`.
Qibocal provides two separate protocols to calibrate :math:`\beta`.


Method 1
--------

:math:`\beta` can be extracted by playing the pulse sequence composed by
:math:`\beta` can be extracted by playing the pulse sequence composed of
:math:`[R_X(\pi) - R_X(-\pi)]^N` for different values of :math:`\beta` as shown in :cite:p:`Sheldon_2016`.
The post-processing consists in measuring the probability of :math:`\ket{0}` for every :math:`\beta`
The post-processing consists of measuring the probability of :math:`\ket{0}` for every :math:`\beta`
and fitting the curve with a cosine. The correct :math:`\beta` value is the one which maximizes
the curve.

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Method 2
--------

The second method consists in playing two different sequences
:math:`R_Y(\pi) R_X(\pi/2)` and :math:`R_X(\pi) R_Y(\pi/2)` which are two
of the AllXY pulses which exhibit opposite sign of phase error as highlighted
The second method consists of playing two different sequences
:math:`R_Y(\pi) R_X(\pi/2)` and :math:`R_X(\pi) R_Y(\pi/2)`. These are two
of the AllXY sequences which exhibit opposite sign of phase error as highlighted
in :cite:p:`reed2013entanglementquantumerrorcorrection`.
The post-processing consists in measuring the probability of :math:`\ket{1}` for every :math:`\beta`
The post-processing consists of measuring the probability of :math:`\ket{1}` for every :math:`\beta`
and performing a linear fit for both sequences. The correct :math:`\beta` value is the one where the two lines
cross.

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