diff --git a/quafu/circuits/quantum_circuit.py b/quafu/circuits/quantum_circuit.py
index 684e3cb..075e447 100644
--- a/quafu/circuits/quantum_circuit.py
+++ b/quafu/circuits/quantum_circuit.py
@@ -182,15 +182,11 @@ def layered_circuit(self) -> np.ndarray:
         gateQlist = [[] for i in range(num)]
         used_qubits = []
         for gate in gatelist:
-            if (
-                isinstance(gate, SingleQubitGate)
-                or isinstance(gate, Delay)
-                or isinstance(gate, QuantumPulse)
-            ):
-                gateQlist[gate.pos].append(gate)
+            if len(gate.pos) == 1:
+                p = gate.pos[0]
+                gateQlist[p].append(gate)
                 if gate.pos not in used_qubits:
                     used_qubits.append(gate.pos)
-
             elif (
                 isinstance(gate, Barrier)
                 or isinstance(gate, MultiQubitGate)
@@ -202,7 +198,7 @@ def layered_circuit(self) -> np.ndarray:
                 for j in range(pos1 + 1, pos2 + 1):
                     gateQlist[j].append(None)
 
-                if isinstance(gate, MultiQubitGate) or isinstance(gate, XYResonance):
+                if isinstance(gate, (MultiQubitGate, XYResonance)):
                     for pos in gate.pos:
                         if pos not in used_qubits:
                             used_qubits.append(pos)
diff --git a/quafu/elements/instruction.py b/quafu/elements/instruction.py
index 7994fcb..d86f682 100644
--- a/quafu/elements/instruction.py
+++ b/quafu/elements/instruction.py
@@ -13,21 +13,29 @@
 #  limitations under the License.
 
 from abc import ABC, abstractmethod
-from typing import Dict, List, Optional, Union
+from typing import Dict, List, Optional, Union, Any
 
 from .parameters import ParameterType
 
 __all__ = ["Instruction", "Barrier", "Measure", "PosType", "Reset"]
 
-PosType = Union[int, List[int]]
+PosType = Union[int]  # TODO: include qubits
 
 
 class Instruction(ABC):
     """Base class for ALL the possible instructions on Quafu superconducting quantum circuits.
 
     Attributes:
-        pos: Qubit position(s) of the instruction on the circuit.
-        paras: Parameters of the instruction.
+        pos: Qubit position(s) list of the instruction on the circuit.
+        paras: Parameter list of the instruction.
+
+    Properties:
+        symbol: Text symbolic representation of this gate.
+
+    Functions:
+        register_gate: Register a new gate class.
+        to_qasm: Convert this gate to QASM format.
+        update_paras: Update the parameters of this gate.
 
     """
 
@@ -35,14 +43,32 @@ class Instruction(ABC):
 
     def __init__(
         self,
-        pos: PosType,
+        pos: Union[PosType, List[PosType]],
         paras: Optional[Union[ParameterType, List[ParameterType]]] = None,
         *args,
         **kwargs,
     ):
+        self.__init_pos__(pos)
+        self.__init_paras__(paras)
+        self._symbol = None
+
+    def __init_pos__(self, pos: Any):
+        """If pos is not a list of PoseType objects, make it so."""
+        if isinstance(pos, PosType):
+            pos = [pos]
+        elif not isinstance(pos, List):
+            raise ValueError('pos must be in PoseType or a list of PoseType objects')
         self.pos = pos
+
+    def __init_paras__(self, paras: Any):
+        """If paras is not a list of ParameterType objects, make it so."""
+        if paras is None:
+            paras = []
+        elif not isinstance(paras, List):
+            if not isinstance(paras, ParameterType):
+                raise ValueError('paras must be in ParameterType or a list of ParameterType objects')
+            paras = [paras]
         self.paras = paras
-        self._symbol = None
 
     @property
     @abstractmethod
@@ -95,6 +121,7 @@ def to_qasm(self):
         pass
 
 
+@Instruction.register('barrier')
 class Barrier(Instruction):
     """
     Barrier instruction.
@@ -137,6 +164,7 @@ def to_qasm(self):
         )
 
 
+@Instruction.register('reset')
 class Reset(Instruction):
     name = "reset"
 
@@ -168,6 +196,7 @@ def to_qasm(self):
         )
 
 
+@Instruction.register('measure')
 class Measure(Instruction):
     """
     Measure instruction.
@@ -195,7 +224,3 @@ def to_qasm(self):
         ]
         qasm = "".join(lines)
         return qasm
-
-
-Instruction.register_ins(Barrier)
-Instruction.register_ins(Measure)
diff --git a/quafu/elements/oracle.py b/quafu/elements/oracle.py
index 070bf0e..82aad6c 100644
--- a/quafu/elements/oracle.py
+++ b/quafu/elements/oracle.py
@@ -88,8 +88,19 @@ def named_paras(self) -> Dict:
         return self._named_pos
 
     def to_qasm(self):
-        # TODO: this is similar to QuantumCircuit.to_qasm
-        raise NotImplemented
+        if len(self.gate_structure) > 0:
+            return super().to_qasm()
+        else:
+            # TODO: decompose matrix in a Just-In-Time style
+            raise NotImplemented
+
+    @property
+    def circuit(self):
+        from quafu import QuantumCircuit
+        qc = QuantumCircuit(self.qubit_num)
+        for gate in self.insides:
+            qc.add_gate(gate)
+        return qc
 
     def __instantiate_gates__(self) -> None:
         """
diff --git a/quafu/elements/quantum_gate.py b/quafu/elements/quantum_gate.py
index a2482ca..1cb541d 100644
--- a/quafu/elements/quantum_gate.py
+++ b/quafu/elements/quantum_gate.py
@@ -14,7 +14,7 @@
 
 
 import copy
-from abc import ABC, abstractmethod
+from abc import ABC
 from typing import Callable, Dict, Iterable, List, Optional, Union
 
 import numpy as np
@@ -61,12 +61,7 @@ class QuantumGate(Instruction, ABC):
     """Base class for standard and combined quantum gates, namely unitary operation
     upon quantum states.
 
-    Attributes:
-        pos: Position of this gate in the circuit.
-        paras: Parameters of this gate.
-
     Properties:
-        symbol: Text symbolic representation of this gate.
         matrix: Matrix representation of this gate.
 
     Functions:
@@ -74,13 +69,14 @@ class QuantumGate(Instruction, ABC):
         to_qasm: Convert this gate to QASM format.
         update_paras: Update the parameters of this gate.
 
+    see docstring of Instruction for other members.
     """
 
     gate_classes = {}
 
     def __init__(
             self,
-            pos: PosType,
+            pos: Union[PosType, List[PosType]],
             paras: Optional[Union[ParameterType, List[ParameterType]]] = None,
             matrix: Optional[Union[ndarray, Callable]] = None,
     ):
@@ -160,14 +156,17 @@ def symbol(self, symbol: str):
         self._symbol = symbol
 
     @property
-    @abstractmethod
-    def matrix(self):
-        if self._matrix is not None:
+    def matrix(self) -> ndarray:
+        """Return numpy.ndarray matrix representation, real-time updated with parameters, if any."""
+        if isinstance(self._matrix, ndarray):
             return self._matrix
+        elif isinstance(self._matrix, Callable):
+            paras = [float(p) for p in self.paras]  # TODO: check that if float() is well supported
+            return self._matrix(paras)
         else:
             raise NotImplementedError(
                 "Matrix is not implemented for %s" % self.__class__.__name__
-                + ", this should never happen."
+                + ". This should never happen, please report it on our github page."
             )
 
     def to_qasm(self) -> str:
@@ -370,8 +369,8 @@ class ControlledGate(MultiQubitGate):
     def __init__(
             self,
             targ_name: str,
-            ctrls: PosType,
-            targs: PosType,
+            ctrls: Union[PosType, List[PosType]],
+            targs: Union[PosType, List[PosType]],
             paras: Optional[Union[ParameterType, List[ParameterType]]] = None,
             tar_matrix: MatrixType = None,
     ):
@@ -408,11 +407,6 @@ def symbol(self):
     def symbol(self, symbol):
         self._symbol = symbol
 
-    @property
-    def matrix(self):
-        # TODO: update matrix when paras of controlled-gate changed
-        return self._matrix
-
     @property
     def ct_nums(self):
         targ_num = len(self.targs)
@@ -423,7 +417,7 @@ def ct_nums(self):
     @property
     def targ_matrix(self):
         if isinstance(self._targ_matrix, Callable):
-            return self._targ_matrix(self.paras)
+            return self._targ_matrix(*self.paras)
         else:
             return self._targ_matrix