diff --git a/test/quantization/test_quantize.py b/test/quantization/test_quantize.py
index 9e6379a29cec..07891be5e420 100644
--- a/test/quantization/test_quantize.py
+++ b/test/quantization/test_quantize.py
@@ -1220,6 +1220,49 @@ def checkHooksIsPresent(model, before_convert=True):
         torch.quantization.convert(model, inplace=True)
         checkHooksIsPresent(model, False)
 
+    def test_add_scalar_uses_input_qparams(self):
+        class M(torch.nn.Module):
+            def __init__(self):
+                super().__init__()
+                self.quant = torch.quantization.QuantStub()
+                self.ff = torch.nn.quantized.FloatFunctional()
+
+            def forward(self, x):
+                x = self.quant(x)
+                x = self.ff.add_scalar(x, 1.0)
+                return x
+
+        m = M()
+        m.qconfig = torch.quantization.default_qconfig
+        mp = torch.quantization.prepare_qat(m)
+        mp(torch.randn(4, 4))
+        mq = torch.quantization.convert(mp)
+        res = mq(torch.randn(4, 4))
+        eps = 1e-5
+        self.assertTrue(torch.abs(mq.quant.scale - res.q_scale()) < eps)
+
+    def test_mul_scalar_uses_input_qparams(self):
+        class M(torch.nn.Module):
+            def __init__(self):
+                super().__init__()
+                self.quant = torch.quantization.QuantStub()
+                self.ff = torch.nn.quantized.FloatFunctional()
+
+            def forward(self, x):
+                x = self.quant(x)
+                x = self.ff.mul_scalar(x, 2.0)
+                return x
+
+        m = M()
+        m.qconfig = torch.quantization.default_qconfig
+        mp = torch.quantization.prepare_qat(m)
+        mp(torch.randn(4, 4))
+        mq = torch.quantization.convert(mp)
+        res = mq(torch.randn(4, 4))
+        eps = 1e-5
+        self.assertTrue(torch.abs(mq.quant.scale * 2 - res.q_scale()) < eps)
+
+
 class TestEagerModeOps(QuantizationTestCase):
     def _test_activation_op_impl(
             self, float_module_class, quantized_module_class, extra_module_kwargs):
diff --git a/test/quantization/test_quantize_fx.py b/test/quantization/test_quantize_fx.py
index 7c6c548f2594..11b1d668e844 100644
--- a/test/quantization/test_quantize_fx.py
+++ b/test/quantization/test_quantize_fx.py
@@ -1458,6 +1458,57 @@ def test_quantized_mul_relu(self):
         self._test_quantized_binary_op_relu_impl(
             operator.mul, operator.imul, torch.ops.quantized.mul_relu)
 
+    # TODO(future PR): make more generic
+    def _test_quantized_add_mul_qat(self, model, expected_node_occurrence):
+        qconfig_dict = {'': torch.quantization.get_default_qat_qconfig('fbgemm')}
+        mp = torch.quantization.quantize_fx.prepare_qat_fx(model, qconfig_dict)
+        self.checkGraphModuleNodes(
+            mp, expected_node_occurrence=expected_node_occurrence)
+
+    @skipIfNoFBGEMM
+    def test_quantized_add_qat(self):
+        class M(torch.nn.Module):
+            def __init__(self):
+                super().__init__()
+                self.conv1 = torch.nn.Conv2d(1, 1, 1)
+                self.conv2 = torch.nn.Conv2d(1, 1, 1)
+
+            def forward(self, x):
+                x = torch.add(x, 1.0)
+                x = self.conv1(x)
+                x = torch.add(x, 1.0)
+                x = torch.relu(x)
+                x = self.conv2(x)
+                return x
+
+        m = M()
+        expected_node_occurrence = {
+            ns.call_module(torch.quantization.FakeQuantize): 4,
+        }
+        self._test_quantized_add_mul_qat(m, expected_node_occurrence)
+
+    @skipIfNoFBGEMM
+    def test_quantized_mul_qat(self):
+        class M(torch.nn.Module):
+            def __init__(self):
+                super().__init__()
+                self.conv1 = torch.nn.Conv2d(1, 1, 1)
+                self.conv2 = torch.nn.Conv2d(1, 1, 1)
+
+            def forward(self, x):
+                x = torch.mul(x, 1.0)
+                x = self.conv1(x)
+                x = torch.mul(x, 1.0)
+                x = torch.relu(x)
+                x = self.conv2(x)
+                return x
+
+        m = M()
+        expected_node_occurrence = {
+            ns.call_module(torch.quantization.FakeQuantize): 4,
+        }
+        self._test_quantized_add_mul_qat(m, expected_node_occurrence)
+
     @skipIfNoFBGEMM
     def test_quantized_cat(self):
         """ quantization of the output of cat will be depend on the
diff --git a/torch/nn/quantized/modules/functional_modules.py b/torch/nn/quantized/modules/functional_modules.py
index 959d60f89609..b9fab962d563 100644
--- a/torch/nn/quantized/modules/functional_modules.py
+++ b/torch/nn/quantized/modules/functional_modules.py
@@ -50,7 +50,8 @@ def add(self, x, y):
     def add_scalar(self, x, y):
         # type: (Tensor, float) -> Tensor
         r = torch.add(x, y)
-        r = self.activation_post_process(r)
+        # Note: this operation is not observed because the observation is not
+        # needed for the quantized op.
         return r
 
     r"""Operation equivalent to ``torch.mul(Tensor, Tensor)``"""
@@ -64,7 +65,8 @@ def mul(self, x, y):
     def mul_scalar(self, x, y):
         # type: (Tensor, float) -> Tensor
         r = torch.mul(x, y)
-        r = self.activation_post_process(r)
+        # Note: this operation is not observed because the observation is not
+        # needed for the quantized op.
         return r
 
     r"""Operation equivalent to ``torch.cat``"""
@@ -203,7 +205,8 @@ def add(self, x, y):
     def add_scalar(self, x, y):
         # type: (Tensor, float) -> Tensor
         r = ops.quantized.add_scalar(x, y)
-        r = self.activation_post_process(r)
+        # Note: this operation is not observed because the observation is not
+        # needed for the quantized op.
         return r
 
     r"""Operation equivalent to ``torch.ops.quantized.mul(Tensor, Tensor)``"""
@@ -217,7 +220,8 @@ def mul(self, x, y):
     def mul_scalar(self, x, y):
         # type: (Tensor, float) -> Tensor
         r = ops.quantized.mul_scalar(x, y)
-        r = self.activation_post_process(r)
+        # Note: this operation is not observed because the observation is not
+        # needed for the quantized op.
         return r
 
     r"""Operation equivalent to ``torch.ops.quantized.cat``"""