From 2543e7fe98b754eb208f1bef036900a493f80cda Mon Sep 17 00:00:00 2001
From: Nour Yosri <noureldinyosri@gmail.com>
Date: Tue, 4 Mar 2025 20:26:00 -0800
Subject: [PATCH 1/3] change ^ to \oplus in comparison docs

---
 qualtran/bloqs/arithmetic/comparison.ipynb | 4 ++--
 qualtran/bloqs/arithmetic/comparison.py    | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/qualtran/bloqs/arithmetic/comparison.ipynb b/qualtran/bloqs/arithmetic/comparison.ipynb
index 5183ede00..1a1e8e03c 100644
--- a/qualtran/bloqs/arithmetic/comparison.ipynb
+++ b/qualtran/bloqs/arithmetic/comparison.ipynb
@@ -361,7 +361,7 @@
    },
    "source": [
     "## `LessThanConstant`\n",
-    "Applies U_a|x>|z> = |x> |z ^ (x < a)>"
+    "Applies U_a|x>|z> = |x> |z \\oplus (x < a)>"
    ]
   },
   {
@@ -676,7 +676,7 @@
    },
    "source": [
     "## `LessThanEqual`\n",
-    "Applies U|x>|y>|z> = |x>|y> |z ^ (x <= y)>\n",
+    "Applies U|x>|y>|z> = |x>|y> |z \\oplus (x <= y)>\n",
     "\n",
     "Decomposes the gate in a T-complexity optimal way.\n",
     "\n",
diff --git a/qualtran/bloqs/arithmetic/comparison.py b/qualtran/bloqs/arithmetic/comparison.py
index a47d95cff..61886c10d 100644
--- a/qualtran/bloqs/arithmetic/comparison.py
+++ b/qualtran/bloqs/arithmetic/comparison.py
@@ -67,7 +67,7 @@
 
 @frozen
 class LessThanConstant(GateWithRegisters, cirq.ArithmeticGate):  # type: ignore[misc]
-    """Applies U_a|x>|z> = |x> |z ^ (x < a)>"""
+    """Applies U_a|x>|z> = |x> |z \oplus (x < a)>"""
 
     bitsize: SymbolicInt
     less_than_val: SymbolicInt
@@ -406,7 +406,7 @@ def _equality_with_zero(
 
 @frozen
 class LessThanEqual(GateWithRegisters, cirq.ArithmeticGate):  # type: ignore[misc]
-    """Applies U|x>|y>|z> = |x>|y> |z ^ (x <= y)>
+    """Applies U|x>|y>|z> = |x>|y> |z \oplus (x <= y)>
 
     Decomposes the gate in a T-complexity optimal way.
 

From 88caed86e7892c6c1217cb29c1c28e450cc5a773 Mon Sep 17 00:00:00 2001
From: Nour Yosri <noureldinyosri@gmail.com>
Date: Tue, 4 Mar 2025 20:28:43 -0800
Subject: [PATCH 2/3] nit

---
 qualtran/bloqs/arithmetic/comparison.ipynb | 4 ++--
 qualtran/bloqs/arithmetic/comparison.py    | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/qualtran/bloqs/arithmetic/comparison.ipynb b/qualtran/bloqs/arithmetic/comparison.ipynb
index 1a1e8e03c..535e51145 100644
--- a/qualtran/bloqs/arithmetic/comparison.ipynb
+++ b/qualtran/bloqs/arithmetic/comparison.ipynb
@@ -361,7 +361,7 @@
    },
    "source": [
     "## `LessThanConstant`\n",
-    "Applies U_a|x>|z> = |x> |z \\oplus (x < a)>"
+    "Applies $U_a\\ket{x}\\ket{z} \\rightarrow \\ket{x} \\ket{z \\oplus (x < a)}$"
    ]
   },
   {
@@ -676,7 +676,7 @@
    },
    "source": [
     "## `LessThanEqual`\n",
-    "Applies U|x>|y>|z> = |x>|y> |z \\oplus (x <= y)>\n",
+    "Applies $U\\ket{x}\\ket{y}\\ket{z} \\rightarrow \\ket{x} \\ket{y} \\ket{z \\oplus (x <= y)}$\n",
     "\n",
     "Decomposes the gate in a T-complexity optimal way.\n",
     "\n",
diff --git a/qualtran/bloqs/arithmetic/comparison.py b/qualtran/bloqs/arithmetic/comparison.py
index 61886c10d..1c24f598d 100644
--- a/qualtran/bloqs/arithmetic/comparison.py
+++ b/qualtran/bloqs/arithmetic/comparison.py
@@ -67,7 +67,7 @@
 
 @frozen
 class LessThanConstant(GateWithRegisters, cirq.ArithmeticGate):  # type: ignore[misc]
-    """Applies U_a|x>|z> = |x> |z \oplus (x < a)>"""
+    r"""Applies $U_a\ket{x}\ket{z} \rightarrow \ket{x} \ket{z \oplus (x < a)}$"""
 
     bitsize: SymbolicInt
     less_than_val: SymbolicInt
@@ -406,7 +406,7 @@ def _equality_with_zero(
 
 @frozen
 class LessThanEqual(GateWithRegisters, cirq.ArithmeticGate):  # type: ignore[misc]
-    """Applies U|x>|y>|z> = |x>|y> |z \oplus (x <= y)>
+    r"""Applies $U\ket{x}\ket{y}\ket{z} \rightarrow \ket{x} \ket{y} \ket{z \oplus (x <= y)}$
 
     Decomposes the gate in a T-complexity optimal way.
 

From a0d96aa9fe1b3ff27a27adb75e14d7d409a8556b Mon Sep 17 00:00:00 2001
From: Nour Yosri <noureldinyosri@gmail.com>
Date: Tue, 4 Mar 2025 20:30:05 -0800
Subject: [PATCH 3/3] use proper latex

---
 qualtran/bloqs/arithmetic/comparison.ipynb | 2 +-
 qualtran/bloqs/arithmetic/comparison.py    | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/qualtran/bloqs/arithmetic/comparison.ipynb b/qualtran/bloqs/arithmetic/comparison.ipynb
index 535e51145..62b4053e7 100644
--- a/qualtran/bloqs/arithmetic/comparison.ipynb
+++ b/qualtran/bloqs/arithmetic/comparison.ipynb
@@ -676,7 +676,7 @@
    },
    "source": [
     "## `LessThanEqual`\n",
-    "Applies $U\\ket{x}\\ket{y}\\ket{z} \\rightarrow \\ket{x} \\ket{y} \\ket{z \\oplus (x <= y)}$\n",
+    "Applies $U\\ket{x}\\ket{y}\\ket{z} \\rightarrow \\ket{x} \\ket{y} \\ket{z \\oplus (x \\leq y)}$\n",
     "\n",
     "Decomposes the gate in a T-complexity optimal way.\n",
     "\n",
diff --git a/qualtran/bloqs/arithmetic/comparison.py b/qualtran/bloqs/arithmetic/comparison.py
index 1c24f598d..8b2ba769a 100644
--- a/qualtran/bloqs/arithmetic/comparison.py
+++ b/qualtran/bloqs/arithmetic/comparison.py
@@ -406,7 +406,7 @@ def _equality_with_zero(
 
 @frozen
 class LessThanEqual(GateWithRegisters, cirq.ArithmeticGate):  # type: ignore[misc]
-    r"""Applies $U\ket{x}\ket{y}\ket{z} \rightarrow \ket{x} \ket{y} \ket{z \oplus (x <= y)}$
+    r"""Applies $U\ket{x}\ket{y}\ket{z} \rightarrow \ket{x} \ket{y} \ket{z \oplus (x \leq y)}$
 
     Decomposes the gate in a T-complexity optimal way.