diff --git a/cirq-core/cirq/devices/grid_qubit.py b/cirq-core/cirq/devices/grid_qubit.py
index 01f77e3d636..6cc55574e6b 100644
--- a/cirq-core/cirq/devices/grid_qubit.py
+++ b/cirq-core/cirq/devices/grid_qubit.py
@@ -33,6 +33,7 @@ class _BaseGridQid(ops.Qid):
     _row: int
     _col: int
     _dimension: int
+    _comp_key: Optional[Tuple[int, int]] = None
     _hash: Optional[int] = None
 
     def __hash__(self) -> int:
@@ -40,7 +41,7 @@ def __hash__(self) -> int:
             self._hash = hash((self._row, self._col, self._dimension))
         return self._hash
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         # Explicitly implemented for performance (vs delegating to Qid).
         if isinstance(other, _BaseGridQid):
             return self is other or (
@@ -50,7 +51,7 @@ def __eq__(self, other):
             )
         return NotImplemented
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         # Explicitly implemented for performance (vs delegating to Qid).
         if isinstance(other, _BaseGridQid):
             return self is not other and (
@@ -60,8 +61,38 @@ def __ne__(self, other):
             )
         return NotImplemented
 
+    def __lt__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseGridQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 < k1 or (k0 == k1 and self._dimension < other._dimension)
+        return super().__lt__(other)
+
+    def __le__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseGridQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 < k1 or (k0 == k1 and self._dimension <= other._dimension)
+        return super().__le__(other)
+
+    def __ge__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseGridQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 > k1 or (k0 == k1 and self._dimension >= other._dimension)
+        return super().__ge__(other)
+
+    def __gt__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseGridQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 > k1 or (k0 == k1 and self._dimension > other._dimension)
+        return super().__gt__(other)
+
     def _comparison_key(self):
-        return self._row, self._col
+        if self._comp_key is None:
+            self._comp_key = self._row, self._col
+        return self._comp_key
 
     @property
     def row(self) -> int:
@@ -359,11 +390,6 @@ def __getnewargs__(self):
     def _with_row_col(self, row: int, col: int) -> 'GridQubit':
         return GridQubit(row, col)
 
-    def _cmp_tuple(self):
-        cls = GridQid if type(self) is GridQubit else type(self)
-        # Must be same as Qid._cmp_tuple but with cls in place of type(self).
-        return (cls.__name__, repr(cls), self._comparison_key(), self.dimension)
-
     @staticmethod
     def square(diameter: int, top: int = 0, left: int = 0) -> List['GridQubit']:
         """Returns a square of GridQubits.
diff --git a/cirq-core/cirq/devices/line_qubit.py b/cirq-core/cirq/devices/line_qubit.py
index 71d292b5e3d..c1634d86297 100644
--- a/cirq-core/cirq/devices/line_qubit.py
+++ b/cirq-core/cirq/devices/line_qubit.py
@@ -37,13 +37,13 @@ def __hash__(self) -> int:
             self._hash = hash((self._x, self._dimension))
         return self._hash
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         # Explicitly implemented for performance (vs delegating to Qid).
         if isinstance(other, _BaseLineQid):
             return self is other or (self._x == other._x and self._dimension == other._dimension)
         return NotImplemented
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         # Explicitly implemented for performance (vs delegating to Qid).
         if isinstance(other, _BaseLineQid):
             return self is not other and (
@@ -51,6 +51,38 @@ def __ne__(self, other):
             )
         return NotImplemented
 
+    def __lt__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseLineQid):
+            return self._x < other._x or (
+                self._x == other._x and self._dimension < other._dimension
+            )
+        return super().__lt__(other)
+
+    def __le__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseLineQid):
+            return self._x < other._x or (
+                self._x == other._x and self._dimension <= other._dimension
+            )
+        return super().__le__(other)
+
+    def __ge__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseLineQid):
+            return self._x > other._x or (
+                self._x == other._x and self._dimension >= other._dimension
+            )
+        return super().__ge__(other)
+
+    def __gt__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseLineQid):
+            return self._x > other._x or (
+                self._x == other._x and self._dimension > other._dimension
+            )
+        return super().__gt__(other)
+
     def _comparison_key(self):
         return self._x
 
@@ -279,12 +311,6 @@ def __getnewargs__(self):
     def _with_x(self, x: int) -> 'LineQubit':
         return LineQubit(x)
 
-    def _cmp_tuple(self):
-        cls = LineQid if type(self) is LineQubit else type(self)
-        # Must be the same as Qid._cmp_tuple but with cls in place of
-        # type(self).
-        return (cls.__name__, repr(cls), self._comparison_key(), self._dimension)
-
     @staticmethod
     def range(*range_args) -> List['LineQubit']:
         """Returns a range of line qubits.
diff --git a/cirq-core/cirq/ops/named_qubit.py b/cirq-core/cirq/ops/named_qubit.py
index 7f7bccaf516..3c91b8bdf6f 100644
--- a/cirq-core/cirq/ops/named_qubit.py
+++ b/cirq-core/cirq/ops/named_qubit.py
@@ -37,7 +37,7 @@ def __hash__(self) -> int:
             self._hash = hash((self._name, self._dimension))
         return self._hash
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         # Explicitly implemented for performance (vs delegating to Qid).
         if isinstance(other, _BaseNamedQid):
             return self is other or (
@@ -45,7 +45,7 @@ def __eq__(self, other):
             )
         return NotImplemented
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         # Explicitly implemented for performance (vs delegating to Qid).
         if isinstance(other, _BaseNamedQid):
             return self is not other and (
@@ -53,6 +53,34 @@ def __ne__(self, other):
             )
         return NotImplemented
 
+    def __lt__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseNamedQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 < k1 or (k0 == k1 and self._dimension < other._dimension)
+        return super().__lt__(other)
+
+    def __le__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseNamedQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 < k1 or (k0 == k1 and self._dimension <= other._dimension)
+        return super().__le__(other)
+
+    def __ge__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseNamedQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 > k1 or (k0 == k1 and self._dimension >= other._dimension)
+        return super().__ge__(other)
+
+    def __gt__(self, other) -> bool:
+        # Explicitly implemented for performance (vs delegating to Qid).
+        if isinstance(other, _BaseNamedQid):
+            k0, k1 = self._comparison_key(), other._comparison_key()
+            return k0 > k1 or (k0 == k1 and self._dimension > other._dimension)
+        return super().__gt__(other)
+
     def _comparison_key(self):
         if self._comp_key is None:
             self._comp_key = _pad_digits(self._name)
@@ -174,11 +202,6 @@ def __getnewargs__(self):
         """Returns a tuple of args to pass to __new__ when unpickling."""
         return (self._name,)
 
-    def _cmp_tuple(self):
-        cls = NamedQid if type(self) is NamedQubit else type(self)
-        # Must be same as Qid._cmp_tuple but with cls in place of type(self).
-        return (cls.__name__, repr(cls), self._comparison_key(), self._dimension)
-
     def __str__(self) -> str:
         return self._name