Correcting documentation of Drag/LiftedDrag (#7659) (#7856)

* Correct documentation of Drag/LiftedDrag

As discussed in qiskit-terra issue #7659, the definition of the LiftedDrag pulse was not consistent with its implementation in qiskit.pulse.library.continuous.py.
One error is fixed by this PR.
A remaining problem is the explicit definition of the sampler strategy. This should be fixed after/with the update of parametric pulses, qiskit-terra issue  #7821.

* Implement review update of #7856

- Removal of f'(x)
- Added definition of g'(x)
- Typos corrected 'gaussian' -> 'Gaussian'
- Link to `qiskit.pulse.library.Gaussian` added

* Fixing linting errors #7856

Fixed the linting errors (line too long) in lines 353, 356, and 358 of qiskit/pulse/library/parametric_pulses.py.

* Replace URL link to Gaussian

Co-authored-by: Naoki Kanazawa <nkanazawa1989@gmail.com>

* Removal of trailing whitespace in line 357

Moved link to Gaussian via :class: from line 358 to 357.

Co-authored-by: Naoki Kanazawa <nkanazawa1989@gmail.com>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
(cherry picked from commit c90c176)

qiskit/pulse/library/parametric_pulses.py

@@ -341,23 +341,23 @@ class Drag(ParametricPulse):
     """The Derivative Removal by Adiabatic Gate (DRAG) pulse is a standard Gaussian pulse
     with an additional Gaussian derivative component and lifting applied.
 
-    It is designed to reduce the frequency spectrum of a normal gaussian pulse near
+    It is designed to reduce the frequency spectrum of a standard Gaussian pulse near
     the :math:`|1\\rangle\\leftrightarrow|2\\rangle` transition,
     reducing the chance of leakage to the :math:`|2\\rangle` state.
 
     .. math::
 
         g(x) &= \\exp\\Bigl(-\\frac12 \\frac{(x - \\text{duration}/2)^2}{\\text{sigma}^2}\\Bigr)\\\\
-        f'(x) &= g(x) + 1j \\times \\text{beta} \\times \\frac{\\mathrm d}{\\mathrm{d}x} g(x)\\\\
-              &= g(x) + 1j \\times \\text{beta} \\times\
-                    \\Bigl(-\\frac{x - \\text{duration}/2}{\\text{sigma}^2}\\Bigr)g(x)\\\\
-        f(x) &= \\text{amp}\\times\\frac{f'(x)-f'(-1)}{1-f'(-1)}, \\quad 0 \\le x < \\text{duration}
+        g'(x) &= \\text{amp}\\times\\frac{g(x)-g(-1)}{1-g(-1)}\\\\
+        f(x) &=  g'(x) \\times \\Bigl(1 + 1j \\times \\text{beta} \\times\
+            \\Bigl(-\\frac{x - \\text{duration}/2}{\\text{sigma}^2}\\Bigr)  \\Bigr),
+            \\quad 0 \\le x < \\text{duration}
 
-    where :math:`g(x)` is a standard unlifted gaussian waveform and
-    :math:`f'(x)` is the DRAG waveform without lifting or amplitude scaling.
+    where :math:`g(x)` is a standard unlifted Gaussian waveform and
+    :math:`g'(x)` is the lifted :class:`~qiskit.pulse.library.Gaussian` waveform.
 
-    This pulse would be more accurately named as ``LiftedDrag``, however, for historical
-    and practical DSP reasons it has the name ``Drag``.
+    This pulse, defined by :math:`f(x)`, would be more accurately named as ``LiftedDrag``, however,
+    for historical and practical DSP reasons it has the name ``Drag``.
 
     References:
         1. |citation1|_