diff --git a/src/diffusers/quantizers/quantization_config.py b/src/diffusers/quantizers/quantization_config.py
index 3078be310719..a6e4dd9ff5e5 100644
--- a/src/diffusers/quantizers/quantization_config.py
+++ b/src/diffusers/quantizers/quantization_config.py
@@ -481,8 +481,15 @@ def __init__(self, quant_type: str, modules_to_not_convert: Optional[List[str]]
 
         TORCHAO_QUANT_TYPE_METHODS = self._get_torchao_quant_type_to_method()
         if self.quant_type not in TORCHAO_QUANT_TYPE_METHODS.keys():
+            is_floating_quant_type = self.quant_type.startswith("float") or self.quant_type.startswith("fp")
+            if is_floating_quant_type and not self._is_cuda_capability_atleast_8_9():
+                raise ValueError(
+                    f"Requested quantization type: {self.quant_type} is not supported on GPUs with CUDA capability <= 8.9. You "
+                    f"can check the CUDA capability of your GPU using `torch.cuda.get_device_capability()`."
+                )
+
             raise ValueError(
-                f"Requested quantization type: {self.quant_type} is not supported yet or is incorrect. If you think the "
+                f"Requested quantization type: {self.quant_type} is not supported or is an incorrect `quant_type` name. If you think the "
                 f"provided quantization type should be supported, please open an issue at https://github.com/huggingface/diffusers/issues."
             )
 
@@ -652,13 +659,13 @@ def get_apply_tensor_subclass(self):
 
     def __repr__(self):
         r"""
-        Example of how this looks for `TorchAoConfig("uint_a16w4", group_size=32)`:
+        Example of how this looks for `TorchAoConfig("uint4wo", group_size=32)`:
 
         ```
         TorchAoConfig {
             "modules_to_not_convert": null,
             "quant_method": "torchao",
-            "quant_type": "uint_a16w4",
+            "quant_type": "uint4wo",
             "quant_type_kwargs": {
                 "group_size": 32
             }