From 627eab75ed212b85c19374bb80a9fa839398f305 Mon Sep 17 00:00:00 2001
From: Renato Mello <renato.msf@gmail.com>
Date: Sat, 20 Jan 2024 12:37:25 +0400
Subject: [PATCH 1/3] improved docstrings

---
 src/qibo/noise.py | 21 ++++++++++++++-------
 1 file changed, 14 insertions(+), 7 deletions(-)

diff --git a/src/qibo/noise.py b/src/qibo/noise.py
index e7ed76909e..9cbbee25f6 100644
--- a/src/qibo/noise.py
+++ b/src/qibo/noise.py
@@ -1,6 +1,7 @@
 import collections
 from itertools import combinations
 from math import log2
+from typing import Optional, Union
 
 from qibo import gates
 from qibo.config import raise_error
@@ -211,7 +212,13 @@ def __init__(self):
         self.errors = collections.defaultdict(list)
         self.noise_model = {}
 
-    def add(self, error, gate=None, qubits=None, condition=None):
+    def add(
+        self,
+        error,
+        gate: Optional[gates.Gate] = None,
+        qubits: Optional[Union[int, tuple]] = None,
+        condition=None,
+    ):
         """Add a quantum error for a specific gate and qubit to the noise model.
 
         Args:
@@ -224,13 +231,14 @@ def add(self, error, gate=None, qubits=None, condition=None):
                 :class:`qibo.noise.ReadoutError`,
                 :class:`qibo.noise.ResetError`,
                 :class:`qibo.noise.UnitaryError`,
-                :class:`qibo.noise.KrausError` and
+                :class:`qibo.noise.KrausError`, and
                 :class:`qibo.noise.CustomError`.
-            gate (:class:`qibo.gates.Gate`): gate after which the noise will be added.
+            gate (:class:`qibo.gates.Gate`, optional): gate after which the noise will be added.
                 If ``None``, the noise will be added after each gate except
                 :class:`qibo.gates.Channel` and :class:`qibo.gates.M`.
-            qubits (tuple): qubits where the noise will be applied. If ``None``,
+            qubits (int or tuple, optional): qubits where the noise will be applied. If ``None``,
                 the noise will be added after every instance of the gate.
+                Defaults to ``None``.
             condition (callable, optional): function that takes :class:`qibo.gates.Gate`
                 object as an input and returns ``True`` if noise should be added to it.
 
@@ -306,9 +314,8 @@ def apply(self, circuit):
             circuit (:class:`qibo.models.circuit.Circuit`): quantum circuit
 
         Returns:
-            A (:class:`qibo.models.circuit.Circuit`) which corresponds
-            to the initial circuit with noise gates added according
-            to the noise model.
+            (:class:`qibo.models.circuit.Circuit`): initial circuit with noise gates
+                added according to the noise model.
         """
 
         if isinstance(self.noise_model, CompositeNoiseModel):

From 617fc7a6762f2bb98de3efa45d46a67b05bf3185 Mon Sep 17 00:00:00 2001
From: Renato Mello <renato.msf@gmail.com>
Date: Tue, 23 Jan 2024 15:06:06 +0400
Subject: [PATCH 2/3] another fix

---
 doc/source/api-reference/qibo.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/doc/source/api-reference/qibo.rst b/doc/source/api-reference/qibo.rst
index bbeeda603c..3ee49b39a9 100644
--- a/doc/source/api-reference/qibo.rst
+++ b/doc/source/api-reference/qibo.rst
@@ -849,7 +849,7 @@ U1q
 
     - Pauli-:math:`Z` rotation: :class:`qibo.gates.RZ`
     - Arbitrary :math:`ZZ` rotation: :class:`qibo.gates.RZZ`
-    - Fully-entangling :math:`ZZ`-interaction: :math:`R_{ZZ}(\\pi/2)`
+    - Fully-entangling :math:`ZZ`-interaction: :math:`R_{ZZ}(\pi/2)`
 
 
 _______________________

From d92d4aaf061bd3bd54f35c148028dc5bdb35991f Mon Sep 17 00:00:00 2001
From: Renato Mello <renato.msf@gmail.com>
Date: Tue, 23 Jan 2024 17:42:56 +0400
Subject: [PATCH 3/3] another minor fix

---
 src/qibo/quantum_info/metrics.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/qibo/quantum_info/metrics.py b/src/qibo/quantum_info/metrics.py
index 4d2632fcaa..eb29f1b486 100644
--- a/src/qibo/quantum_info/metrics.py
+++ b/src/qibo/quantum_info/metrics.py
@@ -1176,14 +1176,15 @@ def frame_potential(
 
     .. math::
         \\mathcal{F}_{\\mathcal{U}}^{(t)} = \\int_{U,V \\in \\mathcal{U}} \\,
-            \\text{d}U \\, \\text{d}V \\, \\text{abs}\\bigl[\\text{tr}(U^{\\dagger} \\, V)\\bigr]^{2t} \\, ,
+            \\text{d}U \\, \\text{d}V \\, \\bigl| \\, \\text{tr}(U^{\\dagger} \\, V)
+            \\, \\bigr|^{2t} \\, ,
 
     where :math:`\\mathcal{U}` is the group of unitaries defined by the parametrized circuit.
     The frame potential is approximated by the average
 
     .. math::
         \\mathcal{F}_{\\mathcal{U}}^{(t)} \\approx \\frac{1}{N} \\,
-            \\sum_{k=1}^{N} \\, \\text{abs}\\bigl[ \\text{tr}(U_{k}^{\\dagger} \\, V_{k})\\bigr]^{2t} \\, ,
+            \\sum_{k=1}^{N} \\, \\bigl| \\, \\text{tr}(U_{k}^{\\dagger} \\, V_{k}) \\, \\bigr|^{2t} \\, ,
 
     where :math:`N` is the number of ``samples``.