diff --git a/torchquantum/graph/graphs.py b/torchquantum/graph/graphs.py
index 0dd7baa1..45bb13fc 100644
--- a/torchquantum/graph/graphs.py
+++ b/torchquantum/graph/graphs.py
@@ -238,11 +238,11 @@ def build_static_matrix(self):
         # for wire_modules in self.wire_module_list:
         for module in self.flat_module_list:
             name = module.name
-            if name in tq.Operator.fixed_ops:
+            if name in tq.operator.fixed_ops:
                 if name not in self.static_matrix_dict.keys():
                     # fixed operator, all share one static matrix
                     self.static_matrix_dict[module.name] = module.matrix.to(self.device)
-            elif name in tq.Operator.parameterized_ops and name not in [
+            elif name in tq.operator.parameterized_ops and name not in [
                 "QubitUnitary",
                 "QubitUnitaryFast",
                 "TrainableUnitary",
@@ -281,9 +281,9 @@ def build_static_matrix(self):
         # for wire_modules in self.wire_module_list:
         for module in self.flat_module_list:
             name = module.name
-            if name in tq.Operator.fixed_ops:
+            if name in tq.operator.fixed_ops:
                 module.static_matrix = self.static_matrix_dict[name]
-            elif name in tq.Operator.parameterized_ops and name not in [
+            elif name in tq.operator.parameterized_ops and name not in [
                 "QubitUnitary",
                 "QubitUnitaryFast",
                 "TrainableUnitary",
diff --git a/torchquantum/layer/layers.py b/torchquantum/layer/layers.py
index bd88fb13..9f129acc 100644
--- a/torchquantum/layer/layers.py
+++ b/torchquantum/layer/layers.py
@@ -391,7 +391,7 @@ def build_random_layer(self):
                     )
                 else:
                     operation = op(n_wires=n_op_wires, wires=op_wires)
-            elif op().name in tq.Operator.parameterized_ops:
+            elif op().name in tq.operator.parameterized_ops:
                 operation = op(has_params=True, trainable=True, wires=op_wires)
             else:
                 operation = op(wires=op_wires)
diff --git a/torchquantum/operator/op_types.py b/torchquantum/operator/op_types.py
index 786214a9..bdf35337 100644
--- a/torchquantum/operator/op_types.py
+++ b/torchquantum/operator/op_types.py
@@ -53,79 +53,6 @@ class NParamsEnum(IntEnum):
 class Operator(tq.QuantumModule):
     """The class for quantum operators."""
 
-    fixed_ops = [
-        "Hadamard",
-        "SHadamard",
-        "PauliX",
-        "PauliY",
-        "PauliZ",
-        "I",
-        "S",
-        "T",
-        "SX",
-        "CNOT",
-        "CZ",
-        "CY",
-        "SWAP",
-        "SSWAP",
-        "CSWAP",
-        "Toffoli",
-        "MultiCNOT",
-        "MultiXCNOT",
-        "Reset",
-        "EchoedCrossResonance",
-        "QFT",
-        "SDG",
-        "TDG",
-        "SXDG",
-        "CH",
-        "CCZ",
-        "ISWAP",
-        "CS",
-        "CSDG",
-        "CSX",
-        "CHadamard",
-        "DCX",
-        "C3X",
-        "C3SX",
-        "RCCX",
-        "RC3X",
-        "C4X",
-    ]
-
-    parameterized_ops = [
-        "RX",
-        "RY",
-        "RZ",
-        "RXX",
-        "RYY",
-        "RZZ",
-        "RZX",
-        "PhaseShift",
-        "Rot",
-        "MultiRZ",
-        "CRX",
-        "CRY",
-        "CRZ",
-        "CRot",
-        "U1",
-        "U2",
-        "U3",
-        "CU",
-        "CU1",
-        "CU2",
-        "CU3",
-        "QubitUnitary",
-        "QubitUnitaryFast",
-        "TrainableUnitary",
-        "TrainableUnitaryStrict",
-        "SingleExcitation",
-        "XXMINYY",
-        "XXPLUSYY",
-        "R",
-        "GlobalPhase",
-    ]
-
     @property
     def name(self):
         """String for the name of the operator."""
diff --git a/torchquantum/operator/standard_gates/__init__.py b/torchquantum/operator/standard_gates/__init__.py
index b6bcaf12..98f55997 100644
--- a/torchquantum/operator/standard_gates/__init__.py
+++ b/torchquantum/operator/standard_gates/__init__.py
@@ -133,7 +133,7 @@
 __all__.extend(["U", "CH", "QubitUnitary", "QubitUnitaryFast"])
 
 # add the dictionary
-__all__.append("op_name_dict")
+__all__.extend(["op_name_dict", "fixed_ops", "parameterized_ops"])
 
 # create the operations dictionary
 op_name_dict = {x.op_name: x for x in all_variables}
@@ -160,3 +160,6 @@
         "cr": CU1,
     }
 )
+
+fixed_ops = [a().__class__.__name__ for a in all_variables if a.num_params == 0]
+parameterized_ops = [a().__class__.__name__ for a in all_variables if a.num_params > 0]