diff --git a/include/checker/dd/TaskManager.hpp b/include/checker/dd/TaskManager.hpp
index 170a5270..83118115 100644
--- a/include/checker/dd/TaskManager.hpp
+++ b/include/checker/dd/TaskManager.hpp
@@ -13,8 +13,10 @@
 #include "ir/operations/OpType.hpp"
 #include "ir/operations/Operation.hpp"
 
+#include <cassert>
 #include <cstddef>
 #include <memory>
+#include <utility>
 
 namespace ec {
 enum class Direction : bool { Left = true, Right = false };
@@ -53,10 +55,10 @@ template <class DDType, class Config = dd::DDPackageConfig> class TaskManager {
   }
 
   [[nodiscard]] qc::MatrixDD getDD() {
-    return dd::getDD((*iterator).get(), *package, permutation);
+    return dd::getDD(iterator->get(), *package, permutation);
   }
   [[nodiscard]] qc::MatrixDD getInverseDD() {
-    return dd::getInverseDD((*iterator).get(), *package, permutation);
+    return dd::getInverseDD(iterator->get(), *package, permutation);
   }
 
   [[nodiscard]] const qc::QuantumComputation* getCircuit() const noexcept {
@@ -85,17 +87,22 @@ template <class DDType, class Config = dd::DDPackageConfig> class TaskManager {
     ++iterator;
   }
 
-  void applySwapOperations(DDType& state) {
-    while (!finished() && (*iterator)->getType() == qc::SWAP) {
-      applyGate(state);
+  void applySwapOperations() {
+    while (!finished() && (*iterator)->getType() == qc::SWAP &&
+           !(*iterator)->isControlled()) {
+      const auto& targets = (*iterator)->getTargets();
+      assert(targets.size() == 2);
+      const auto t1 = targets[0];
+      const auto t2 = targets[1];
+      std::swap(permutation.at(t1), permutation.at(t2));
+      ++iterator;
     }
   }
-  void applySwapOperations() { applySwapOperations(internalState); }
 
   void advance(DDType& state, const std::size_t steps) {
     for (std::size_t i = 0U; i < steps && !finished(); ++i) {
       applyGate(state);
-      applySwapOperations(state);
+      applySwapOperations();
     }
   }
   void advance(DDType& state) { advance(state, 1U); }
diff --git a/src/checker/dd/DDAlternatingChecker.cpp b/src/checker/dd/DDAlternatingChecker.cpp
index 6ee0c313..32a700c1 100644
--- a/src/checker/dd/DDAlternatingChecker.cpp
+++ b/src/checker/dd/DDAlternatingChecker.cpp
@@ -52,8 +52,8 @@ void DDAlternatingChecker::initialize() {
 void DDAlternatingChecker::execute() {
   while (!taskManager1.finished() && !taskManager2.finished() && !isDone()) {
     // skip over any SWAP operations
-    taskManager1.applySwapOperations(functionality);
-    taskManager2.applySwapOperations(functionality);
+    taskManager1.applySwapOperations();
+    taskManager2.applySwapOperations();
 
     if (!taskManager1.finished() && !taskManager2.finished() && !isDone()) {
       // whenever the current functionality resembles the identity, identical
diff --git a/src/checker/dd/DDSimulationChecker.cpp b/src/checker/dd/DDSimulationChecker.cpp
index b2957768..2cf9af15 100644
--- a/src/checker/dd/DDSimulationChecker.cpp
+++ b/src/checker/dd/DDSimulationChecker.cpp
@@ -38,6 +38,7 @@ EquivalenceCriterion DDSimulationChecker::checkEquivalence() {
   // adjust reference counts to facilitate reuse of the simulation checker
   taskManager1.decRef();
   taskManager2.decRef();
+  dd->decRef(initialState);
 
   return equivalence;
 }
diff --git a/src/checker/dd/simulation/StateGenerator.cpp b/src/checker/dd/simulation/StateGenerator.cpp
index 0a326f1b..3ddc80eb 100644
--- a/src/checker/dd/simulation/StateGenerator.cpp
+++ b/src/checker/dd/simulation/StateGenerator.cpp
@@ -143,15 +143,15 @@ qc::VectorDD StateGenerator::generateRandomStabilizerState(
   // circuit
   auto stabilizer = simulate(&rcs, dd.makeZeroState(randomQubits), dd);
 
-  // decrease the ref count right after so that it stays correct later on
-  dd.decRef(stabilizer);
-
   // add |0> edges for all the ancillary qubits
   auto initial = stabilizer;
   for (std::size_t p = randomQubits; p < totalQubits; ++p) {
     initial = dd.makeDDNode(static_cast<dd::Qubit>(p),
                             std::array{initial, qc::VectorDD::zero()});
   }
+  // properly set the reference count for the state
+  dd.incRef(initial);
+  dd.decRef(stabilizer);
 
   // return the resulting decision diagram
   return initial;