diff --git a/ccsrc/include/simulator/vector/vector_state.tpp b/ccsrc/include/simulator/vector/vector_state.tpp
index 1003fcda98ab72a480f36714dcdca432cfe01f07..1e938ed19f79b517491d0527267eb63aab281ce0 100644
--- a/ccsrc/include/simulator/vector/vector_state.tpp
+++ b/ccsrc/include/simulator/vector/vector_state.tpp
@@ -1346,6 +1346,7 @@ auto VectorState<qs_policy_t_>::GetExpectationWithGradParameterShiftOneMulti(
             if (gate->GradRequired()) {
                 auto p_gate = static_cast<Parameterizable*>(gate.get());
                 std::shared_ptr<BasicGate> tmp_gate;
+                bool is_multi_pr = false;
                 switch (gate->id_) {
                     case (GateID::RX): {
                         tmp_gate = CONVERT_GATE(RXGate, p_gate);
@@ -1397,10 +1398,12 @@ auto VectorState<qs_policy_t_>::GetExpectationWithGradParameterShiftOneMulti(
                     }
                     case (GateID::U3): {
                         tmp_gate = CONVERT_GATE(U3, p_gate);
+                        is_multi_pr = true;
                         break;
                     }
                     case (GateID::FSim): {
                         tmp_gate = CONVERT_GATE(FSim, p_gate);
+                        is_multi_pr = true;
                         break;
                     }
                     case (GateID::CUSTOM): {
@@ -1444,16 +1447,10 @@ auto VectorState<qs_policy_t_>::GetExpectationWithGradParameterShiftOneMulti(
                         VT<py_qs_data_t> intrin_grad_list(tmp_p_gate->prs_.size());
                         for (int k = 0; k < tmp_p_gate->prs_.size(); k++) {
                             tmp_p_gate->prs_[k] += -pr_shift;
-                            if (gate->id_ == GateID::U3 || gate->id_ == GateID::FSim) {
-                                parameter::tn::Tensor coeff;
-                                parameter::tn::Tensor tmp;
-                                std::string key;
-                                for (auto& [key_, v] : tmp_p_gate->prs_[k].data_) {
-                                    key = key_;
-                                    coeff = v;
-                                    tmp = pr.GetItem(key_);
-                                }
-                                tmp += -pr_shift / coeff;
+                            if (is_multi_pr) {
+                                std::string key = tmp_p_gate->prs_[k].data_.begin()->first;
+                                parameter::tn::Tensor tmp = pr.GetItem(key);
+                                tmp += -pr_shift / tmp_p_gate->prs_[k].data_.begin()->second;
                                 tmp_pr.SetItem(key, tmp);
                             }
                             sim_l = *this;
@@ -1464,16 +1461,10 @@ auto VectorState<qs_policy_t_>::GetExpectationWithGradParameterShiftOneMulti(
                             sim_rs[j - start].ApplyHamiltonian(*hams[j]);
                             auto expect0 = qs_policy_t::Vdot(sim_l.qs, sim_rs[j - start].qs, dim);
                             tmp_p_gate->prs_[k] += 2 * pr_shift;
-                            if (gate->id_ == GateID::U3 || gate->id_ == GateID::FSim) {
-                                parameter::tn::Tensor coeff;
-                                parameter::tn::Tensor tmp;
-                                std::string key;
-                                for (auto& [key_, v] : tmp_p_gate->prs_[k].data_) {
-                                    key = key_;
-                                    coeff = v;
-                                    tmp = pr.GetItem(key_);
-                                }
-                                tmp += pr_shift / coeff;
+                            if (is_multi_pr) {
+                                std::string key = tmp_p_gate->prs_[k].data_.begin()->first;
+                                parameter::tn::Tensor tmp = pr.GetItem(key);
+                                tmp += pr_shift / tmp_p_gate->prs_[k].data_.begin()->second;
                                 tmp_pr.SetItem(key, tmp);
                             }
                             sim_l = *this;
@@ -1484,16 +1475,9 @@ auto VectorState<qs_policy_t_>::GetExpectationWithGradParameterShiftOneMulti(
                             sim_rs[j - start].ApplyHamiltonian(*hams[j]);
                             auto expect1 = qs_policy_t::Vdot(sim_l.qs, sim_rs[j - start].qs, dim);
                             tmp_p_gate->prs_[k] += -pr_shift;
-                            if (gate->id_ == GateID::U3 || gate->id_ == GateID::FSim) {
-                                parameter::tn::Tensor coeff;
-                                parameter::tn::Tensor tmp;
-                                std::string key;
-                                for (auto& [key_, v] : tmp_p_gate->prs_[k].data_) {
-                                    key = key_;
-                                    coeff = v;
-                                    tmp = pr.GetItem(key_);
-                                }
-                                tmp_pr.SetItem(key, tmp);
+                            if (is_multi_pr) {
+                                std::string key = tmp_p_gate->prs_[k].data_.begin()->first;
+                                tmp_pr.SetItem(key, pr.GetItem(key));
                             }
                             intrin_grad_list[k] = {coeff * std::real(expect1 - expect0), 0};
                         }
diff --git a/docs/api_python/core/circuit/mindquantum.core.circuit.Circuit.rst b/docs/api_python/core/circuit/mindquantum.core.circuit.Circuit.rst
index 0af61083c5bbc05cd9ff47aa3281dd7e9374244c..347f5548023f260230e457cf8e9d750616841dcf 100644
--- a/docs/api_python/core/circuit/mindquantum.core.circuit.Circuit.rst
+++ b/docs/api_python/core/circuit/mindquantum.core.circuit.Circuit.rst
@@ -59,6 +59,10 @@ mindquantum.core.circuit.Circuit
 
         删除所有未使用的量子比特，并将量子比特映射到 `range(n_qubits)` 。
 
+    .. py:method:: copy()
+
+        返回该量子线路的浅拷贝。
+
     .. py:method:: encoder_params_name
         :property:
 
diff --git a/mindquantum/core/circuit/circuit.py b/mindquantum/core/circuit/circuit.py
index 25945d04c7c38b1f5331ff81fe0d0ba0f58154b1..35f2db3084646a6f5a68f903bb12235228437b4c 100644
--- a/mindquantum/core/circuit/circuit.py
+++ b/mindquantum/core/circuit/circuit.py
@@ -363,6 +363,10 @@ class Circuit(list):  # pylint: disable=too-many-instance-attributes,too-many-pu
                 self.append(gate)
         self.has_cpp_obj = False
 
+    def copy(self):
+        """Returns a shallow copy of the circuit."""
+        return copy.copy(self)
+
     def __add__(self, gates):
         """Addition operator."""
         out = Circuit()
diff --git a/mindquantum/core/gates/channel.py b/mindquantum/core/gates/channel.py
index e8f7e516c93ecbbb10a8709580f48cee7e0a277b..c53d213ea3b3483bfffeb3b8a678b2d41aff0da9 100644
--- a/mindquantum/core/gates/channel.py
+++ b/mindquantum/core/gates/channel.py
@@ -174,6 +174,8 @@ class PauliChannel(NoiseGate, SelfHermitianGate):
             raise TypeError(f"Unsupported type for py, get {type(py)}.")
         if not isinstance(pz, (int, float)):
             raise TypeError(f"Unsupported type for pz, get {type(pz)}.")
+        if np.any(np.array([px, py, pz]) < 0.0):
+            raise ValueError("Probability cannot be negative value.")
         if 0 <= px + py + pz <= 1:
             self.px = float(px)
             self.py = float(py)