diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7ed8c0f998..4e2da940e4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -15,7 +15,7 @@ This project adheres to [Semantic Versioning], with the exception that minor rel
 - ✨ Add conversions between Jeff and QCO ([#1479], [#1548]) ([**@denialhaag**])
 - ✨ Add a `place-and-route` pass for mapping circuits to architectures with restricted topologies ([#1537], [#1547]) ([**@MatthiasReumann**])
 - ✨ Add initial infrastructure for new QC and QCO MLIR dialects
-  ([#1264], [#1330], [#1402], [#1428], [#1430], [#1436], [#1443], [#1446], [#1464], [#1465], [#1470], [#1471], [#1472], [#1474], [#1475], [#1506], [#1510], [#1513], [#1521], [#1548], [#1550], [#1554])
+  ([#1264], [#1330], [#1402], [#1428], [#1430], [#1436], [#1443], [#1446], [#1464], [#1465], [#1470], [#1471], [#1472], [#1474], [#1475], [#1506], [#1510], [#1513], [#1521], [#1548], [#1550], [#1554], [#1567])
   ([**@burgholzer**], [**@denialhaag**], [**@taminob**], [**@DRovara**], [**@li-mingbao**], [**@Ectras**], [**@MatthiasReumann**], [**@simon1hofmann**])
 
 ### Changed
@@ -331,6 +331,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 
 <!-- PR links -->
 
+[#1567]: https://github.com/munich-quantum-toolkit/core/pull/1567
 [#1554]: https://github.com/munich-quantum-toolkit/core/pull/1554
 [#1550]: https://github.com/munich-quantum-toolkit/core/pull/1550
 [#1549]: https://github.com/munich-quantum-toolkit/core/pull/1549
diff --git a/mlir/include/mlir/Compiler/CompilerPipeline.h b/mlir/include/mlir/Compiler/CompilerPipeline.h
index ee7fbc9adf..ec7473a8cf 100644
--- a/mlir/include/mlir/Compiler/CompilerPipeline.h
+++ b/mlir/include/mlir/Compiler/CompilerPipeline.h
@@ -115,8 +115,8 @@ class QuantumCompilerPipeline {
    * @brief Add canonicalization and cleanup passes
    *
    * @details
-   * Always adds the standard MLIR canonicalization pass followed by dead
-   * value removal.
+   * Always adds the standard MLIR canonicalization pass followed by common
+   * sub-expression elimination and dead value removal.
    */
   static void addCleanupPasses(PassManager& pm);
 
diff --git a/mlir/lib/Compiler/CompilerPipeline.cpp b/mlir/lib/Compiler/CompilerPipeline.cpp
index 18040d7720..119e343755 100644
--- a/mlir/lib/Compiler/CompilerPipeline.cpp
+++ b/mlir/lib/Compiler/CompilerPipeline.cpp
@@ -46,8 +46,10 @@ static void prettyPrintStage(ModuleOp module, const llvm::StringRef stageName,
 }
 
 void QuantumCompilerPipeline::addCleanupPasses(PassManager& pm) {
-  // Always run canonicalization and dead value removal
+  // Always run canonicalization, common sub-expression elimination, and dead
+  // value removal
   pm.addPass(createCanonicalizerPass());
+  pm.addPass(createCSEPass());
   pm.addPass(createRemoveDeadValuesPass());
 }
 
diff --git a/mlir/lib/Support/Passes.cpp b/mlir/lib/Support/Passes.cpp
index 242d48b8bf..5e998761bc 100644
--- a/mlir/lib/Support/Passes.cpp
+++ b/mlir/lib/Support/Passes.cpp
@@ -20,6 +20,7 @@ using namespace mlir;
 void runCanonicalizationPasses(ModuleOp module) {
   PassManager pm(module.getContext());
   pm.addPass(createCanonicalizerPass());
+  pm.addPass(createCSEPass());
   pm.addPass(createRemoveDeadValuesPass());
   if (pm.run(module).failed()) {
     llvm::errs() << "Failed to run canonicalization passes.\n";
diff --git a/mlir/unittests/Compiler/test_compiler_pipeline.cpp b/mlir/unittests/Compiler/test_compiler_pipeline.cpp
index 1b72a08521..f6958ed3e4 100644
--- a/mlir/unittests/Compiler/test_compiler_pipeline.cpp
+++ b/mlir/unittests/Compiler/test_compiler_pipeline.cpp
@@ -185,6 +185,11 @@ INSTANTIATE_TEST_SUITE_P(
             "StaticQubits", nullptr, MQT_NAMED_BUILDER(mlir::qc::staticQubits),
             MQT_NAMED_BUILDER(mlir::qc::staticQubits),
             MQT_NAMED_BUILDER(mlir::qir::staticQubits), false},
+        CompilerPipelineTestCase{
+            "StaticQubitsWithDuplicates", nullptr,
+            MQT_NAMED_BUILDER(mlir::qc::staticQubitsWithDuplicates),
+            MQT_NAMED_BUILDER(mlir::qc::staticQubits),
+            MQT_NAMED_BUILDER(mlir::qir::staticQubits), false},
         CompilerPipelineTestCase{"AllocQubit",
                                  MQT_NAMED_BUILDER(qc::allocQubit), nullptr,
                                  MQT_NAMED_BUILDER(mlir::qc::allocQubit),
diff --git a/mlir/unittests/Conversion/QCToQIR/test_qc_to_qir.cpp b/mlir/unittests/Conversion/QCToQIR/test_qc_to_qir.cpp
index f8825c0dc1..132265f228 100644
--- a/mlir/unittests/Conversion/QCToQIR/test_qc_to_qir.cpp
+++ b/mlir/unittests/Conversion/QCToQIR/test_qc_to_qir.cpp
@@ -618,7 +618,10 @@ INSTANTIATE_TEST_SUITE_P(
                         MQT_NAMED_BUILDER(qc::allocLargeRegister),
                         MQT_NAMED_BUILDER(qir::emptyQIR)},
         QCToQIRTestCase{"StaticQubits", MQT_NAMED_BUILDER(qc::staticQubits),
-                        MQT_NAMED_BUILDER(qir::emptyQIR)},
+                        MQT_NAMED_BUILDER(qir::staticQubits)},
+        QCToQIRTestCase{"StaticQubitsWithDuplicates",
+                        MQT_NAMED_BUILDER(qc::staticQubitsWithDuplicates),
+                        MQT_NAMED_BUILDER(qir::staticQubits)},
         QCToQIRTestCase{"AllocDeallocPair",
                         MQT_NAMED_BUILDER(qc::allocDeallocPair),
                         MQT_NAMED_BUILDER(qir::emptyQIR)}));
diff --git a/mlir/unittests/Dialect/QC/IR/test_qc_ir.cpp b/mlir/unittests/Dialect/QC/IR/test_qc_ir.cpp
index fe8c0abd7a..e1f90f7c30 100644
--- a/mlir/unittests/Dialect/QC/IR/test_qc_ir.cpp
+++ b/mlir/unittests/Dialect/QC/IR/test_qc_ir.cpp
@@ -893,7 +893,10 @@ INSTANTIATE_TEST_SUITE_P(
         QCTestCase{"AllocLargeRegister", MQT_NAMED_BUILDER(allocLargeRegister),
                    MQT_NAMED_BUILDER(emptyQC)},
         QCTestCase{"StaticQubits", MQT_NAMED_BUILDER(staticQubits),
-                   MQT_NAMED_BUILDER(emptyQC)},
+                   MQT_NAMED_BUILDER(staticQubits)},
+        QCTestCase{"StaticQubitsWithDuplicates",
+                   MQT_NAMED_BUILDER(staticQubitsWithDuplicates),
+                   MQT_NAMED_BUILDER(staticQubits)},
         QCTestCase{"AllocDeallocPair", MQT_NAMED_BUILDER(allocDeallocPair),
                    MQT_NAMED_BUILDER(emptyQC)}));
 /// @}
diff --git a/mlir/unittests/Dialect/QCO/IR/test_qco_ir.cpp b/mlir/unittests/Dialect/QCO/IR/test_qco_ir.cpp
index 3220aa753c..0df3151229 100644
--- a/mlir/unittests/Dialect/QCO/IR/test_qco_ir.cpp
+++ b/mlir/unittests/Dialect/QCO/IR/test_qco_ir.cpp
@@ -1051,7 +1051,7 @@ INSTANTIATE_TEST_SUITE_P(
         QCOTestCase{"AllocLargeRegister", MQT_NAMED_BUILDER(allocLargeRegister),
                     MQT_NAMED_BUILDER(emptyQCO)},
         QCOTestCase{"StaticQubits", MQT_NAMED_BUILDER(staticQubits),
-                    MQT_NAMED_BUILDER(emptyQCO)},
+                    MQT_NAMED_BUILDER(staticQubits)},
         QCOTestCase{"AllocDeallocPair", MQT_NAMED_BUILDER(allocDeallocPair),
                     MQT_NAMED_BUILDER(emptyQCO)}));
 /// @}
diff --git a/mlir/unittests/Dialect/QIR/IR/test_qir_ir.cpp b/mlir/unittests/Dialect/QIR/IR/test_qir_ir.cpp
index f9fdf94ddb..9c26a29fa0 100644
--- a/mlir/unittests/Dialect/QIR/IR/test_qir_ir.cpp
+++ b/mlir/unittests/Dialect/QIR/IR/test_qir_ir.cpp
@@ -529,5 +529,8 @@ INSTANTIATE_TEST_SUITE_P(
                                 MQT_NAMED_BUILDER(allocLargeRegister),
                                 MQT_NAMED_BUILDER(allocLargeRegister)},
                     QIRTestCase{"StaticQubits", MQT_NAMED_BUILDER(staticQubits),
+                                MQT_NAMED_BUILDER(staticQubits)},
+                    QIRTestCase{"StaticQubitsWithDuplicates",
+                                MQT_NAMED_BUILDER(staticQubitsWithDuplicates),
                                 MQT_NAMED_BUILDER(staticQubits)}));
 /// @}
diff --git a/mlir/unittests/programs/qc_programs.cpp b/mlir/unittests/programs/qc_programs.cpp
index 2134b1f368..2734918aeb 100644
--- a/mlir/unittests/programs/qc_programs.cpp
+++ b/mlir/unittests/programs/qc_programs.cpp
@@ -30,8 +30,23 @@ void allocMultipleQubitRegisters(QCProgramBuilder& b) {
 void allocLargeRegister(QCProgramBuilder& b) { b.allocQubitRegister(100); }
 
 void staticQubits(QCProgramBuilder& b) {
-  b.staticQubit(0);
-  b.staticQubit(1);
+  const auto q0 = b.staticQubit(0);
+  const auto q1 = b.staticQubit(1);
+
+  b.h(q0);
+  b.h(q1);
+  b.ctrl(q0, [&] { b.x(q1); });
+}
+
+void staticQubitsWithDuplicates(QCProgramBuilder& b) {
+  const auto q0a = b.staticQubit(0);
+  const auto q1a = b.staticQubit(1);
+  const auto q0b = b.staticQubit(0);
+  const auto q1b = b.staticQubit(1);
+
+  b.h(q0a);
+  b.h(q1a);
+  b.ctrl(q0b, [&] { b.x(q1b); });
 }
 
 void allocDeallocPair(QCProgramBuilder& b) {
diff --git a/mlir/unittests/programs/qc_programs.h b/mlir/unittests/programs/qc_programs.h
index 21225c5b44..da074cb208 100644
--- a/mlir/unittests/programs/qc_programs.h
+++ b/mlir/unittests/programs/qc_programs.h
@@ -30,9 +30,14 @@ void allocMultipleQubitRegisters(QCProgramBuilder& b);
 /// Allocates a large qubit register.
 void allocLargeRegister(QCProgramBuilder& b);
 
-/// Allocates two inline qubits.
+/// Allocates two inline qubits and applies H on both and a controlled-X between
+/// them.
 void staticQubits(QCProgramBuilder& b);
 
+/// Allocates duplicate static qubits and applies H on both and a controlled-X
+/// between them.
+void staticQubitsWithDuplicates(QCProgramBuilder& b);
+
 /// Allocates and explicitly deallocates a single qubit.
 void allocDeallocPair(QCProgramBuilder& b);
 
diff --git a/mlir/unittests/programs/qco_programs.cpp b/mlir/unittests/programs/qco_programs.cpp
index 5c6a42bf1e..4175f30c1a 100644
--- a/mlir/unittests/programs/qco_programs.cpp
+++ b/mlir/unittests/programs/qco_programs.cpp
@@ -34,8 +34,14 @@ void allocMultipleQubitRegisters(QCOProgramBuilder& b) {
 void allocLargeRegister(QCOProgramBuilder& b) { b.allocQubitRegister(100); }
 
 void staticQubits(QCOProgramBuilder& b) {
-  b.staticQubit(0);
-  b.staticQubit(1);
+  auto q0 = b.staticQubit(0);
+  auto q1 = b.staticQubit(1);
+
+  q0 = b.h(q0);
+  q1 = b.h(q1);
+  b.ctrl({q0}, {q1}, [&](mlir::ValueRange targets) {
+    return llvm::SmallVector<mlir::Value>{b.x(targets[0])};
+  });
 }
 
 void allocDeallocPair(QCOProgramBuilder& b) {
diff --git a/mlir/unittests/programs/qco_programs.h b/mlir/unittests/programs/qco_programs.h
index c0374325b2..c227297fd7 100644
--- a/mlir/unittests/programs/qco_programs.h
+++ b/mlir/unittests/programs/qco_programs.h
@@ -30,7 +30,8 @@ void allocMultipleQubitRegisters(QCOProgramBuilder& b);
 /// Allocates a large qubit register.
 void allocLargeRegister(QCOProgramBuilder& b);
 
-/// Allocates two inline qubits.
+/// Allocates two inline qubits and applies H on both and a controlled-X between
+/// them.
 void staticQubits(QCOProgramBuilder& b);
 
 /// Allocates and explicitly deallocates a single qubit.
diff --git a/mlir/unittests/programs/qir_programs.cpp b/mlir/unittests/programs/qir_programs.cpp
index 883cf59af8..dea9cf9864 100644
--- a/mlir/unittests/programs/qir_programs.cpp
+++ b/mlir/unittests/programs/qir_programs.cpp
@@ -28,8 +28,21 @@ void allocMultipleQubitRegisters(QIRProgramBuilder& b) {
 void allocLargeRegister(QIRProgramBuilder& b) { b.allocQubitRegister(100); }
 
 void staticQubits(QIRProgramBuilder& b) {
-  b.staticQubit(0);
-  b.staticQubit(1);
+  auto q0 = b.staticQubit(0);
+  auto q1 = b.staticQubit(1);
+  b.h(q0);
+  b.h(q1);
+  b.cx(q0, q1);
+}
+
+void staticQubitsWithDuplicates(QIRProgramBuilder& b) {
+  auto q0a = b.staticQubit(0);
+  auto q1a = b.staticQubit(1);
+  auto q0b = b.staticQubit(0);
+  auto q1b = b.staticQubit(1);
+  b.h(q0a);
+  b.h(q1a);
+  b.cx(q0b, q1b);
 }
 
 void singleMeasurementToSingleBit(QIRProgramBuilder& b) {
diff --git a/mlir/unittests/programs/qir_programs.h b/mlir/unittests/programs/qir_programs.h
index f379f19785..767e962464 100644
--- a/mlir/unittests/programs/qir_programs.h
+++ b/mlir/unittests/programs/qir_programs.h
@@ -30,9 +30,14 @@ void allocMultipleQubitRegisters(QIRProgramBuilder& b);
 /// Allocates a large qubit register.
 void allocLargeRegister(QIRProgramBuilder& b);
 
-/// Allocates two inline qubits.
+/// Allocates two inline qubits and applies H on both and a controlled-X between
+/// them.
 void staticQubits(QIRProgramBuilder& b);
 
+/// Allocates duplicate static qubits and applies H on both and a controlled-X
+/// between them.
+void staticQubitsWithDuplicates(QIRProgramBuilder& b);
+
 // --- MeasureOp ------------------------------------------------------------ //
 
 /// Measures a single qubit into a single classical bit.