diff --git a/vllm/model_executor/layers/quantization/awq.py b/vllm/model_executor/layers/quantization/awq.py
index f4fc7ce020e95..a3854f70bb4fa 100644
--- a/vllm/model_executor/layers/quantization/awq.py
+++ b/vllm/model_executor/layers/quantization/awq.py
@@ -43,7 +43,8 @@ def get_name(self) -> str:
     def get_supported_act_dtypes(self) -> List[torch.dtype]:
         return [torch.half]
 
-    def get_min_capability(self) -> int:
+    @classmethod
+    def get_min_capability(cls) -> int:
         # The AWQ kernel only supports Turing or newer GPUs.
         return 75
 
diff --git a/vllm/model_executor/layers/quantization/base_config.py b/vllm/model_executor/layers/quantization/base_config.py
index e7de283b562a6..c23b66161d9b8 100644
--- a/vllm/model_executor/layers/quantization/base_config.py
+++ b/vllm/model_executor/layers/quantization/base_config.py
@@ -44,8 +44,9 @@ def get_supported_act_dtypes(self) -> List[torch.dtype]:
         """List of supported activation dtypes."""
         raise NotImplementedError
 
+    @classmethod
     @abstractmethod
-    def get_min_capability(self) -> int:
+    def get_min_capability(cls) -> int:
         """Minimum GPU capability to support the quantization method.
 
         E.g., 70 for Volta, 75 for Turing, 80 for Ampere.
diff --git a/vllm/model_executor/layers/quantization/bitsandbytes.py b/vllm/model_executor/layers/quantization/bitsandbytes.py
index 969958d9b5448..e76714a7b460c 100644
--- a/vllm/model_executor/layers/quantization/bitsandbytes.py
+++ b/vllm/model_executor/layers/quantization/bitsandbytes.py
@@ -38,7 +38,7 @@ def get_supported_act_dtypes(self) -> List[torch.dtype]:
         return [torch.float32, torch.float16, torch.bfloat16]
 
     @classmethod
-    def get_min_capability(self) -> int:
+    def get_min_capability(cls) -> int:
         return 70
 
     @staticmethod
diff --git a/vllm/model_executor/layers/quantization/compressed_tensors/compressed_tensors.py b/vllm/model_executor/layers/quantization/compressed_tensors/compressed_tensors.py
index 0cf224cc05479..a451427ec93f2 100644
--- a/vllm/model_executor/layers/quantization/compressed_tensors/compressed_tensors.py
+++ b/vllm/model_executor/layers/quantization/compressed_tensors/compressed_tensors.py
@@ -33,10 +33,9 @@ def get_scaled_act_names(self) -> List[str]:
     def get_supported_act_dtypes(cls) -> List[torch.dtype]:
         return [torch.float16, torch.bfloat16]
 
-    # Need to figure it out
     @classmethod
     def get_min_capability(cls) -> int:
-        return 60
+        return 75
 
     def get_name(self) -> str:
         return "compressed_tensors"
@@ -84,6 +83,14 @@ def from_config(cls, config: Dict[str, Any]) -> "CompressedTensorsConfig":
     def get_config_filenames(cls) -> List[str]:
         return []
 
+    def _check_gptq_and_marlin_can_run(self):
+        capability = torch.cuda.get_device_capability()
+        capability = capability[0] * 10 + capability[1]
+        if capability < 80:
+            raise RuntimeError("The quantization config is not supported for ",
+                               "the current GPU. Minimum capability: 80. ",
+                               f"Current capability: {capability}.")
+
     def _is_static_tensor_w8a8(self, weight_quant: BaseModel,
                                input_quant: BaseModel) -> bool:
         is_8_bits = weight_quant.num_bits == input_quant.num_bits == 8
@@ -126,6 +133,7 @@ def _get_schema(self, weight_quant: BaseModel,
                     input_quant: BaseModel) -> "CompressedTensorsScheme":
 
         if self._is_wNa16_group_channel(weight_quant, input_quant):
+            self._check_gptq_and_marlin_can_run()
             if (self.quant_format == CompressionFormat.marlin_24.value
                     and weight_quant.num_bits in W4A16SPARSE24_SUPPORTED_BITS):
                 return CompressedTensorsW4A16Sparse24(
diff --git a/vllm/model_executor/layers/quantization/squeezellm.py b/vllm/model_executor/layers/quantization/squeezellm.py
index 207dbcee8afc5..72ba55eb1740d 100644
--- a/vllm/model_executor/layers/quantization/squeezellm.py
+++ b/vllm/model_executor/layers/quantization/squeezellm.py
@@ -39,7 +39,8 @@ def get_name(self) -> str:
     def get_supported_act_dtypes(self) -> List[torch.dtype]:
         return [torch.half]
 
-    def get_min_capability(self) -> int:
+    @classmethod
+    def get_min_capability(cls) -> int:
         return 70
 
     @staticmethod