Address review comments.

qiskit/circuit/classical/types/__init__.py

@@ -40,6 +40,10 @@
 .. autoclass:: Bool
 .. autoclass:: Uint
 
+All types have a :attr:`~Type.const` field to indicate their const-ness. When the result type of
+an expression is constant, the expression is considered a constant expression. Constant
+expressions can be used in certain contexts that aren't valid for runtime-initialized variables.
+
 Note that :class:`Uint` defines a family of types parametrized by their width; it is not one single
 type, which may be slightly different to the 'classical' programming languages you are used to.
 
@@ -59,7 +63,10 @@
 The type system is equipped with a partial ordering, where :math:`a < b` is interpreted as
 ":math:`a` is a strict subtype of :math:`b`".  Note that the partial ordering is a subset of the
 directed graph that describes the allowed explicit casting operations between types.  The partial
-ordering defines when one type may be lossless directly interpreted as another.
+ordering defines when one type may be losslessly directly interpreted as another.
+
+When two types differ only in const-ness, the non-const version is considered to be the
+"greater" of the two.
 
 The low-level interface to querying the subtyping relationship is the :func:`order` function.
 

qiskit/circuit/classical/types/ordering.py

@@ -105,12 +105,12 @@ def order(left: Type, right: Type, /) -> Ordering:
     # If one type is greater (and thus is the only type that can represent
     # both) an ordering is only defined if that type is non-const or both
     # types are const.
-    if left.const is True and right.const is False:
+    if left.const and not right.const:
         if order_ is Ordering.EQUAL:
             return Ordering.LESS
         if order_ is Ordering.GREATER:
             return Ordering.NONE
-    if right.const is True and left.const is False:
+    if right.const and not left.const:
         if order_ is Ordering.EQUAL:
             return Ordering.GREATER
         if order_ is Ordering.LESS:
@@ -251,7 +251,7 @@ def cast_kind(from_: Type, to_: Type, /) -> CastKind:
             >>> types.cast_kind(types.Uint(16), types.Uint(8))
             <CastKind.DANGEROUS: 4>
     """
-    if to_.const is True and from_.const is False:
+    if to_.const and not from_.const:
         # We can't cast to a const type.
         return CastKind.NONE
     if (coercer := _ALLOWED_CASTS.get((from_.kind, to_.kind))) is None:

qiskit/circuit/quantumcircuit.py

@@ -2940,9 +2940,9 @@ def add_input(  # pylint: disable=missing-raises-doc
             if type_ is not None:
                 raise ValueError("cannot give an explicit type with an existing Var")
             if name_or_var.type.const:
-                raise CircuitError("const variables are not supported")
+                raise CircuitError("const variables cannot be input variables")
         elif type_ is not None and type_.const:
-            raise CircuitError("const variables are not supported")
+            raise CircuitError("const variables cannot be input variables")
 
         var = self._prepare_new_var(name_or_var, type_)
         self._vars_input[var.name] = var

qiskit/qpy/binary_io/value.py

@@ -398,7 +398,6 @@ def _write_expr_type_v14(file_obj, type_: types.Type):
     elif type_.kind is types.Uint:
         file_obj.write(type_keys.ExprType.UINT)
         file_obj.write(
-            # TODO: make sure you're calling this correctly
             struct.pack(
                 formats.EXPR_TYPE_UINT_PACK_V14,
                 *formats.EXPR_TYPE_UINT_V14(type_.width, type_.const),

releasenotes/notes/const-expr-397ff09042942b81.yaml

@@ -11,11 +11,11 @@ features_circuits:
       from qiskit.circuit.classical import expr
 
       expr.lift(5, try_const=True)
-      # >>> Value(5, Uint(3, const=True))
+      # Value(5, Uint(3, const=True))
 
     The result type of an operation applied to const types is also const::
 
       from qiskit.circuit.classical import expr
 
       expr.bit_and(expr.lift(5, try_const=True), expr.lift(6, try_const=True)).type.const
-      # >>> True
+      # True

test/python/circuit/test_circuit_vars.py

@@ -119,7 +119,7 @@ def test_initialise_inputs_declarations(self):
 
     def test_initialise_inputs_declarations_rejects_const_vars(self):
         a = expr.Var.new("a", types.Uint(16, const=True))
-        with self.assertRaisesRegex(CircuitError, "const variables.*not supported"):
+        with self.assertRaisesRegex(CircuitError, "const variables cannot be input variables"):
             QuantumCircuit(inputs=[a])
 
     def test_initialise_captures_declarations(self):
@@ -219,9 +219,9 @@ def test_add_input_returns_input(self):
     def test_add_input_rejects_const_var(self):
         a = expr.Var.new("a", types.Bool(const=True))
         qc = QuantumCircuit()
-        with self.assertRaisesRegex(CircuitError, "const variables.*not supported"):
+        with self.assertRaisesRegex(CircuitError, "const variables cannot be input variables"):
             qc.add_input(a)
-        with self.assertRaisesRegex(CircuitError, "const variables.*not supported"):
+        with self.assertRaisesRegex(CircuitError, "const variables cannot be input variables"):
             qc.add_input("a", types.Bool(const=True))
 
     def test_cannot_have_both_inputs_and_captures(self):