diff --git a/neural_compressor/torch/quantization/config.py b/neural_compressor/torch/quantization/config.py
index 71b01353d5a..5e794a81bd1 100644
--- a/neural_compressor/torch/quantization/config.py
+++ b/neural_compressor/torch/quantization/config.py
@@ -71,9 +71,26 @@ class OperatorConfig(NamedTuple):
     valid_func_list: List[Callable] = []
 
 
+class TorchBaseConfig(BaseConfig):
+    # re-write func _get_op_name_op_type_config to fallback op_type with string
+    # because there are some special op_types for IPEX backend: `Linear&Relu`, `Linear&add`, ...
+    def _get_op_name_op_type_config(self):
+        op_type_config_dict = dict()
+        op_name_config_dict = dict()
+        for name, config in self.local_config.items():
+            if self._is_op_type(name):
+                # Convert the Callable to String.
+                new_name = self._op_type_to_str(name)
+                op_type_config_dict[new_name] = config
+            else:
+                op_name_config_dict[name] = config
+                op_type_config_dict[name] = config
+        return op_type_config_dict, op_name_config_dict
+
+
 ######################## RNT Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=RTN, priority=PRIORITY_RTN)
-class RTNConfig(BaseConfig):
+class RTNConfig(TorchBaseConfig):
     """Config class for round-to-nearest weight-only quantization."""
 
     name = RTN
@@ -238,7 +255,7 @@ def get_default_double_quant_config(type="BNB_NF4"):
 
 ######################## GPTQ Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=GPTQ, priority=PRIORITY_GPTQ)
-class GPTQConfig(BaseConfig):
+class GPTQConfig(TorchBaseConfig):
     """Config class for GPTQ.
 
     GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers.
@@ -390,7 +407,7 @@ def get_default_gptq_config() -> GPTQConfig:
 
 ######################## AWQ Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=AWQ, priority=PRIORITY_AWQ)
-class AWQConfig(BaseConfig):
+class AWQConfig(TorchBaseConfig):
     """Config class for AWQ.
 
     AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration.
@@ -532,7 +549,7 @@ def get_default_awq_config() -> AWQConfig:
 
 ######################## TEQ Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=TEQ, priority=PRIORITY_TEQ)
-class TEQConfig(BaseConfig):
+class TEQConfig(TorchBaseConfig):
     """Config class for TEQ.
 
     TEQ: Activation-aware Weight Quantization for LLM Compression and Acceleration.
@@ -670,7 +687,7 @@ def get_default_teq_config() -> TEQConfig:
 
 ######################## AUTOROUND Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=AUTOROUND, priority=PRIORITY_AUTOROUND)
-class AutoRoundConfig(BaseConfig):
+class AutoRoundConfig(TorchBaseConfig):
     """Config class for AUTOROUND.
 
     AUTOROUND: Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs.
@@ -815,7 +832,7 @@ def get_default_AutoRound_config() -> AutoRoundConfig:
 
 ######################## MX Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=MX_QUANT)
-class MXQuantConfig(BaseConfig):
+class MXQuantConfig(TorchBaseConfig):
     """Config class for MX quantization."""
 
     supported_configs: List[OperatorConfig] = []
@@ -928,7 +945,7 @@ def get_default_mx_config() -> MXQuantConfig:
 
 ######################## Dynamic Quant Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=PT2E_DYNAMIC_QUANT)
-class DynamicQuantConfig(BaseConfig):
+class DynamicQuantConfig(TorchBaseConfig):
     """Config class for dynamic quantization."""
 
     name = PT2E_DYNAMIC_QUANT
@@ -1002,7 +1019,7 @@ def get_default_dynamic_config() -> DynamicQuantConfig:
 
 ######################## Static Quant Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=STATIC_QUANT)
-class StaticQuantConfig(BaseConfig):
+class StaticQuantConfig(TorchBaseConfig):
     """Config class for static quantization."""
 
     name = STATIC_QUANT
@@ -1091,7 +1108,7 @@ def get_default_static_config() -> StaticQuantConfig:
 
 ######################## Smooth Quant Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=SMOOTH_QUANT)
-class SmoothQuantConfig(BaseConfig):
+class SmoothQuantConfig(TorchBaseConfig):
     """Config class for smooth quantization."""
 
     name = SMOOTH_QUANT
@@ -1205,7 +1222,7 @@ def get_default_sq_config() -> SmoothQuantConfig:
 
 ######################## HQQ Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=HQQ, priority=PRIORITY_HQQ)
-class HQQConfig(BaseConfig):
+class HQQConfig(TorchBaseConfig):
     # Half-Quadratic Quantization (HQQ), more details:
     # Blog: https://mobiusml.github.io/hqq_blog/
     # Code: https://github.com/mobiusml/hqq
@@ -1286,7 +1303,7 @@ def get_default_hqq_config() -> HQQConfig:
 
 ######################## FP8 Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=FP8_QUANT)
-class FP8Config(BaseConfig):
+class FP8Config(TorchBaseConfig):
     """Config class for FP8 quantization."""
 
     name = FP8_QUANT
@@ -1381,7 +1398,7 @@ def get_default_fp8_config_set() -> FP8Config:
 
 ######################## MixPrecision Config ###############################
 @register_config(framework_name=FRAMEWORK_NAME, algo_name=MIX_PRECISION)
-class MixPrecisionConfig(BaseConfig):
+class MixPrecisionConfig(TorchBaseConfig):
     """Config class for mix-precision."""
 
     name = MIX_PRECISION
diff --git a/test/3x/torch/quantization/test_static_quant.py b/test/3x/torch/quantization/test_static_quant.py
index 46e791aa52f..cae22ff79ab 100644
--- a/test/3x/torch/quantization/test_static_quant.py
+++ b/test/3x/torch/quantization/test_static_quant.py
@@ -76,7 +76,7 @@ def test_static_quant_fallback(self):
         quant_config = get_default_static_config()
         example_inputs = self.input
         # fallback by op_type
-        quant_config.set_local(torch.nn.Linear, StaticQuantConfig(w_dtype="fp32", act_dtype="fp32"))
+        quant_config.set_local([torch.nn.Linear, "Linear&add"], StaticQuantConfig(w_dtype="fp32", act_dtype="fp32"))
         prepared_model = prepare(fp32_model, quant_config=quant_config, example_inputs=example_inputs)
         run_fn(prepared_model)
         q_model = convert(prepared_model)