improve documentation for flipping and rabi protocols

doc/source/protocols/flipping.rst

@@ -12,7 +12,9 @@ after the initial flip, in the over rotations one the final state will be closer
 By fitting the resulting data with a sinusoidal function, we can determine the delta amplitude, which allows us to refine the
 :math:`\pi` pulse amplitude.
 
-We implemented also a version of the flipping protocol to calibrate the drive pulse amplitude of the :math:`R_x(\pi/2)` rotations, in this case each :math:`R_x(\pi)` rotation is replaced by two math:`R_x(\pi/2)` rotations.
+We implemented also a version of the flipping protocol to calibrate the drive pulse amplitude of the :math:`R_x(\pi/2)` rotations,
+in this case each :math:`R_x(\pi)` rotation is replaced by two :math:`R_x(\pi/2)` rotations.
+The main reasons for implementing protocols to fine tune the `R_x(\pi/2)` rotations are explained in :ref:`rabi`.
 
 Parameters
 ^^^^^^^^^^
@@ -47,7 +49,7 @@ If the same experiment is run setting the `rx90: True` the flipping is performed
 	    delta_amplitude: 0.05
 	    nflips_max: 30
 	    nflips_step: 1
-	    rx90: True
+        rx90: True
 
 Requirements
 ^^^^^^^^^^^^

doc/source/protocols/rabi/rabi.rst

@@ -29,9 +29,17 @@ Rabi rate is larger than the decay and the pure dephasing rate,
 
 where :math:`\Omega_R` is the Rabi frequency and :math:`\tau` the decay time.
 
-In qibocal we implemented also another version of the Rabi experiment which can be used to tune the amplitude (duration) of the drive pulse in order
+
+Since many routines and protocols in quantum computing are based on `R_x(\pi/2)` rotations, in qibocal we implemented
+also another version of the Rabi experiment which can be used to tune the amplitude (duration) of the drive pulse in order
 to excite the qubit from the ground state up to state :math:`\frac{\ket{0}-i\ket{1}}{\sqrt{2}}`.
 
+The possibility to calibrate an `R_x(\pi/2)` rotation as native gate allows us to remove the errors that could arise from assuming that the `R_x(\pi/2)` amplitude (duration)
+is exactly half that of the `R_x(\pi)` amplitude (duration). This assumption presumes a perfectly linear response of the qubit to the drive pulse, which is
+often not the case due to nonlinearities in the qubit's response or imperfections in the pulse shaping :cite:p:`Chen2018MetrologyOQ`.
+
+In this case the pulse sequence is the same as before with the only difference that instad of a single `R_x(\pi)` pulse we use two concatenated `R_x(\pi/2)` pulses.
+
 Parameters
 ^^^^^^^^^^
 
@@ -111,7 +119,7 @@ to excite the qubit from the ground state up to state :math:`\ket{1}`.
 All these example runcards can be modified to calibrate the amplitude (duration) of the drive pulse
 to excite the qubit from the ground state up to state :math:`\frac{\ket{0}-i\ket{1}}{\sqrt{2}}` by simply setting the `rx90` parameter to `True`.
 
-In the following we show an example runcard
+In the following we show an example runcard for the amplitude calibration of the `R_x(\pi/2)`.
 
 .. code-block:: yaml