change ^ to \oplus in comparison docs (#1582)

* change ^ to \oplus in comparison docs

* nit

* use proper latex

Author: NoureldinYosri

qualtran/bloqs/arithmetic/comparison.ipynb

@@ -361,7 +361,7 @@
    },
    "source": [
     "## `LessThanConstant`\n",
-    "Applies U_a|x>|z> = |x> |z ^ (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 ^ (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",

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)>"""
+    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 ^ (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.