diff --git a/include/checker/dd/DDAlternatingChecker.hpp b/include/checker/dd/DDAlternatingChecker.hpp
index 8d71cbed..74652292 100644
--- a/include/checker/dd/DDAlternatingChecker.hpp
+++ b/include/checker/dd/DDAlternatingChecker.hpp
@@ -48,11 +48,6 @@ class DDAlternatingChecker final
 private:
   qc::MatrixDD functionality{};
 
-  void initializeTask(
-      [[maybe_unused]] TaskManager<qc::MatrixDD, AlternatingDDPackageConfig>&
-          taskManager) override{
-      // task initialization is conducted separately for this checker
-  };
   void                 initialize() override;
   void                 execute() override;
   void                 finish() override;
diff --git a/include/checker/dd/DDConstructionChecker.hpp b/include/checker/dd/DDConstructionChecker.hpp
index a5df34fd..10437fb9 100644
--- a/include/checker/dd/DDConstructionChecker.hpp
+++ b/include/checker/dd/DDConstructionChecker.hpp
@@ -30,6 +30,7 @@ class DDConstructionChecker final
 private:
   void initializeTask(TaskManager<qc::MatrixDD, ConstructionDDPackageConfig>&
                           taskManager) override {
+    DDEquivalenceChecker::initializeTask(taskManager);
     const auto initial = dd->makeIdent(nqubits);
     taskManager.setInternalState(initial);
     taskManager.incRef();
diff --git a/include/checker/dd/DDEquivalenceChecker.hpp b/include/checker/dd/DDEquivalenceChecker.hpp
index 59545af6..11579893 100644
--- a/include/checker/dd/DDEquivalenceChecker.hpp
+++ b/include/checker/dd/DDEquivalenceChecker.hpp
@@ -52,7 +52,7 @@ class DDEquivalenceChecker : public EquivalenceChecker {
   // in some form
   EquivalenceCriterion equals(const DDType& e, const DDType& f);
 
-  virtual void initializeTask(TaskManager<DDType, Config>& taskManager) = 0;
+  virtual void initializeTask(TaskManager<DDType, Config>& taskManager);
   virtual void initialize();
   virtual void execute();
   virtual void finish();
diff --git a/include/checker/dd/TaskManager.hpp b/include/checker/dd/TaskManager.hpp
index 2f64edc4..631a61e2 100644
--- a/include/checker/dd/TaskManager.hpp
+++ b/include/checker/dd/TaskManager.hpp
@@ -23,6 +23,11 @@ template <class DDType, class Config = dd::DDPackageConfig> class TaskManager {
   TaskManager(const qc::QuantumComputation& circ, DDPackage& dd) noexcept
       : TaskManager(circ, dd, Direction::Left) {}
 
+  void reset() noexcept {
+    iterator    = qc->begin();
+    permutation = qc->initialLayout;
+  }
+
   [[nodiscard]] bool finished() const noexcept { return iterator == end; }
 
   const std::unique_ptr<qc::Operation>& operator()() const { return *iterator; }
diff --git a/src/checker/dd/DDEquivalenceChecker.cpp b/src/checker/dd/DDEquivalenceChecker.cpp
index 4f26ffe0..1efdfda9 100644
--- a/src/checker/dd/DDEquivalenceChecker.cpp
+++ b/src/checker/dd/DDEquivalenceChecker.cpp
@@ -143,6 +143,12 @@ EquivalenceCriterion DDEquivalenceChecker<DDType, Config>::run() {
   return equivalence;
 }
 
+template <class DDType, class Config>
+void DDEquivalenceChecker<DDType, Config>::initializeTask(
+    TaskManager<DDType, Config>& taskManager) {
+  taskManager.reset();
+}
+
 template <class DDType, class Config>
 void DDEquivalenceChecker<DDType, Config>::initialize() {
   initializeTask(taskManager1);
diff --git a/src/checker/dd/DDSimulationChecker.cpp b/src/checker/dd/DDSimulationChecker.cpp
index daaefd95..7a7f97d2 100644
--- a/src/checker/dd/DDSimulationChecker.cpp
+++ b/src/checker/dd/DDSimulationChecker.cpp
@@ -16,6 +16,7 @@ DDSimulationChecker::DDSimulationChecker(const qc::QuantumComputation& circ1,
 
 void DDSimulationChecker::initializeTask(
     TaskManager<qc::VectorDD, SimulationDDPackageConfig>& taskManager) {
+  DDEquivalenceChecker::initializeTask(taskManager);
   taskManager.setInternalState(initialState);
   taskManager.incRef();
 }
diff --git a/test/test_equality.cpp b/test/test_equality.cpp
index 7cf2b3e4..158f8afe 100644
--- a/test/test_equality.cpp
+++ b/test/test_equality.cpp
@@ -48,6 +48,32 @@ TEST_F(EqualityTest, GlobalPhase) {
             ec::EquivalenceCriterion::EquivalentUpToGlobalPhase);
 }
 
+/**
+ * @brief The following is a regression test for
+ * https://github.com/cda-tum/mqt-qcec/issues/347
+ */
+TEST_F(EqualityTest, GlobalPhaseSimulation) {
+  qc1.x(0);
+  qc2.x(0);
+
+  // add a global phase of -1
+  qc2.z(0);
+  qc2.x(0);
+  qc2.z(0);
+  qc2.x(0);
+
+  config.execution.runAlternatingChecker  = false;
+  config.execution.runConstructionChecker = false;
+  config.execution.runZXChecker           = false;
+  config.execution.runSimulationChecker   = true;
+  config.execution.parallel               = false;
+  ec::EquivalenceCheckingManager ecm(qc1, qc2, config);
+  ecm.run();
+  const auto json       = ecm.json();
+  const auto simChecker = json["checkers"].front();
+  EXPECT_EQ(simChecker["equivalence"], "equivalent_up_to_phase");
+}
+
 TEST_F(EqualityTest, CloseButNotEqualAlternating) {
   qc1.x(0);