diff --git a/cirq-core/cirq/study/resolver.py b/cirq-core/cirq/study/resolver.py
index e2f82cce1c7..35c3889348c 100644
--- a/cirq-core/cirq/study/resolver.py
+++ b/cirq-core/cirq/study/resolver.py
@@ -55,6 +55,9 @@ class ParamResolver:
     Attributes:
         param_dict: A dictionary from the ParameterValue key (str) to its
             assigned value.
+
+    Raises:
+        TypeError if formulas are passed as keys.
     """
 
     def __new__(cls, param_dict: 'cirq.ParamResolverOrSimilarType' = None):
@@ -68,6 +71,9 @@ def __init__(self, param_dict: 'cirq.ParamResolverOrSimilarType' = None) -> None
 
         self._param_hash: Optional[int] = None
         self.param_dict = cast(ParamDictType, {} if param_dict is None else param_dict)
+        for key in self.param_dict:
+            if isinstance(key, sympy.Expr) and not isinstance(key, sympy.Symbol):
+                raise TypeError(f'ParamResolver keys cannot be (non-symbol) formulas ({key})')
         self._deep_eval_map: ParamDictType = {}
 
     def value_of(
diff --git a/cirq-core/cirq/study/resolver_test.py b/cirq-core/cirq/study/resolver_test.py
index c612448b7c9..8e26abd9d7e 100644
--- a/cirq-core/cirq/study/resolver_test.py
+++ b/cirq-core/cirq/study/resolver_test.py
@@ -156,27 +156,13 @@ def test_param_dict_iter():
 
 
 def test_formulas_in_param_dict():
-    """Test formulas in a `param_dict`.
-
-    Param dicts are allowed to have str or sympy.Symbol as keys and
-    floats or sympy.Symbol as values.  This should not be a common use case,
-    but this tests makes sure something reasonable is returned when
-    mixing these types and using formulas in ParamResolvers.
-
-    Note that sympy orders expressions for deterministic resolution, so
-    depending on the operands sent to sub(), the expression may not fully
-    resolve if it needs to take several iterations of resolution.
-    """
+    """Tests that formula keys are rejected in a `param_dict`."""
     a = sympy.Symbol('a')
     b = sympy.Symbol('b')
     c = sympy.Symbol('c')
     e = sympy.Symbol('e')
-    r = cirq.ParamResolver({a: b + 1, b: 2, b + c: 101, 'd': 2 * e})
-    assert sympy.Eq(r.value_of('a'), 3)
-    assert sympy.Eq(r.value_of('b'), 2)
-    assert sympy.Eq(r.value_of(b + c), 101)
-    assert sympy.Eq(r.value_of('c'), c)
-    assert sympy.Eq(r.value_of('d'), 2 * e)
+    with pytest.raises(TypeError, match='formula'):
+        _ = cirq.ParamResolver({a: b + 1, b: 2, b + c: 101, 'd': 2 * e})
 
 
 def test_recursive_evaluation():
diff --git a/cirq-google/cirq_google/api/v2/sweeps.py b/cirq-google/cirq_google/api/v2/sweeps.py
index da540da4b74..83210e86315 100644
--- a/cirq-google/cirq_google/api/v2/sweeps.py
+++ b/cirq-google/cirq_google/api/v2/sweeps.py
@@ -61,11 +61,9 @@ def sweep_to_proto(
         sweep_dict: Dict[str, List[float]] = {}
         for param_resolver in sweep:
             for key in param_resolver:
-                if isinstance(key, sympy.Expr):
-                    raise ValueError(f'cannot convert to v2 Sweep proto: {sweep}')
                 if key not in sweep_dict:
-                    sweep_dict[key] = []
-                sweep_dict[key].append(cast(float, param_resolver.value_of(key)))
+                    sweep_dict[cast(str, key)] = []
+                sweep_dict[cast(str, key)].append(cast(float, param_resolver.value_of(key)))
         out.sweep_function.function_type = run_context_pb2.SweepFunction.ZIP
         for key in sweep_dict:
             sweep_to_proto(cirq.Points(key, sweep_dict[key]), out=out.sweep_function.sweeps.add())
diff --git a/cirq-google/cirq_google/api/v2/sweeps_test.py b/cirq-google/cirq_google/api/v2/sweeps_test.py
index 6acc3264d07..d4d1c2b8cbe 100644
--- a/cirq-google/cirq_google/api/v2/sweeps_test.py
+++ b/cirq-google/cirq_google/api/v2/sweeps_test.py
@@ -73,9 +73,20 @@ def test_sweep_to_proto_linspace():
 
 
 def test_list_sweep_bad_expression():
-    sweep = cirq.ListSweep([cirq.ParamResolver({sympy.Symbol('a') + sympy.Symbol('b'): 4.0})])
-    with pytest.raises(ValueError, match='cannot convert'):
-        v2.sweep_to_proto(sweep)
+    with pytest.raises(TypeError, match='formula'):
+        _ = cirq.ListSweep([cirq.ParamResolver({sympy.Symbol('a') + sympy.Symbol('b'): 4.0})])
+
+
+def test_symbol_to_string_conversion():
+    sweep = cirq.ListSweep([cirq.ParamResolver({sympy.Symbol('a'): 4.0})])
+    proto = v2.sweep_to_proto(sweep)
+    assert isinstance(proto, v2.run_context_pb2.Sweep)
+    expected = v2.run_context_pb2.Sweep()
+    expected.sweep_function.function_type = v2.run_context_pb2.SweepFunction.ZIP
+    p1 = expected.sweep_function.sweeps.add()
+    p1.single_sweep.parameter_key = 'a'
+    p1.single_sweep.points.points.extend([4.0])
+    assert proto == expected
 
 
 def test_sweep_to_proto_points():