✨ Add rotation-gate merging using quaternions

CHANGELOG.md

@@ -11,6 +11,7 @@ This project adheres to [Semantic Versioning], with the exception that minor rel
 
 ### Added
 
+- ✨ Add a `merge-single-qubit-rotation-gates` pass for merging consecutive rotation gates using quaternions ([#1407]) ([**@J4MMlE**])
 - ✨ Add support for multi-controlled gates to ZX package ([#1380]) ([**@keefehuang**])
 - ✨ Add Sampler and Estimator Primitives to the QDMI-Qiskit Interface ([#1507]) ([**@marcelwa**])
 - ✨ Add conversions between `jeff` and QCO ([#1479], [#1548], [#1565], [#1637]) ([**@denialhaag**])
@@ -396,6 +397,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 [#1413]: https://github.com/munich-quantum-toolkit/core/pull/1413
 [#1412]: https://github.com/munich-quantum-toolkit/core/pull/1412
 [#1411]: https://github.com/munich-quantum-toolkit/core/pull/1411
+[#1407]: https://github.com/munich-quantum-toolkit/core/pull/1407
 [#1406]: https://github.com/munich-quantum-toolkit/core/pull/1406
 [#1403]: https://github.com/munich-quantum-toolkit/core/pull/1403
 [#1402]: https://github.com/munich-quantum-toolkit/core/pull/1402
@@ -554,6 +556,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 [**@Ectras**]: https://github.com/Ectras
 [**@simon1hofmann**]: https://github.com/simon1hofmann
 [**@keefehuang**]: https://github.com/keefehuang
+[**@J4MMlE**]: https://github.com/J4MMlE
 
 <!-- General links -->
 

mlir/include/mlir/Compiler/CompilerPipeline.h

@@ -40,6 +40,9 @@ struct QuantumCompilerConfig {
 
   /// Print IR after each stage
   bool printIRAfterAllStages = false;
+
+  /// Disable quaternion-based single-qubit rotation gate merging
+  bool disableMergeSingleQubitRotationGates = false;
 };
 
 /**

mlir/include/mlir/Dialect/QCO/Transforms/Passes.td

@@ -11,6 +11,35 @@
 
 include "mlir/Pass/PassBase.td"
 
+def MergeSingleQubitRotationGates
+    : Pass<"merge-single-qubit-rotation-gates", "mlir::ModuleOp"> {
+  let dependentDialects = ["mlir::qco::QCODialect",
+                           "::mlir::arith::ArithDialect",
+                           "::mlir::math::MathDialect"];
+  let summary = "Merge rotation gates using quaternion-based fusion";
+  let description = [{
+    Merges consecutive single-qubit rotation gates acting on the same qubit into a single equivalent U gate, reducing circuit depth and gate count.
+
+    Supported gate types: `rx`, `ry`, `rz`, `p`, `r`, `u2`, `u`.
+
+    The pass greedily collects the longest possible chain of consecutive mergeable gates.
+    Each gate is converted to a unit quaternion:
+
+    - `rx`, `ry`, `rz`, `p`: single-axis rotations via half-angle formulas.
+    - `r(theta, phi)`: rotation by `theta` around axis `(cos(phi), sin(phi), 0)`.
+    - `u2(phi, lambda) = u(pi / 2, phi, lambda)`.
+    - `u(theta, phi, lambda)`: ZYZ decomposition `rz(phi) * ry(theta) * rz(lambda)`, each factor converted to a quaternion and merged via the Hamilton product.
+
+    The gates are then folded one by one via the Hamilton product into a single quaternion, which is decomposed back into ZYZ Euler angles and emitted as a single `UOp`, representing the same rotation as the chain of single gates.
+    The global phase of each gate is tracked alongside and combined together.
+
+    The emitted `UOp` is defined by $U = \exp [i (\phi + \lambda) / 2] R_z (\phi) R_y (\theta) R_z (\lambda)$.
+    Each merge emits a `GPhaseOp` carrying the accumulated input phase of the chain.
+    Because the synthesized `UOp` introduces an additional intrinsic phase of $(\phi + \lambda) / 2$, the `GPhaseOp` must compensate for it.
+    This applies even to chains composed entirely of $\mathrm{SU} (2)$ gates (`rx`, `ry`, `rz`, `r`) because the synthesis into a `UOp` still produces the intrinsic phase term.
+  }];
+}
+
 //===----------------------------------------------------------------------===//
 // Transpilation Passes
 //===----------------------------------------------------------------------===//

mlir/lib/Compiler/CMakeLists.txt

@@ -20,6 +20,7 @@ add_mlir_library(
   MLIRQCToQCO
   MLIRQCOToQC
   MLIRQCToQIR
+  MLIRQCOTransforms
   MQT::MLIRSupport)
 
 mqt_mlir_target_use_project_options(MQTCompilerPipeline)

mlir/lib/Compiler/CompilerPipeline.cpp

@@ -13,6 +13,7 @@
 #include "mlir/Conversion/QCOToQC/QCOToQC.h"
 #include "mlir/Conversion/QCToQCO/QCToQCO.h"
 #include "mlir/Conversion/QCToQIR/QCToQIR.h"
+#include "mlir/Dialect/QCO/Transforms/Passes.h"
 #include "mlir/Support/Passes.h"
 #include "mlir/Support/PrettyPrinting.h"
 
@@ -136,9 +137,11 @@ QuantumCompilerPipeline::runPipeline(ModuleOp module,
     }
   }
   // Stage 5: Optimization passes
-  // TODO: Add optimization passes
-  if (failed(
-          runStage([&](PassManager& pm) { populateQCOCleanupPipeline(pm); }))) {
+  if (failed(runStage([&](PassManager& pm) {
+        if (!config_.disableMergeSingleQubitRotationGates) {
+          pm.addPass(qco::createMergeSingleQubitRotationGates());
+        }
+      }))) {
     return failure();
   }
   if (record != nullptr && config_.recordIntermediates) {

mlir/lib/Dialect/QCO/Transforms/CMakeLists.txt

@@ -15,6 +15,8 @@ add_mlir_library(
   PRIVATE
   MLIRQCODialect
   MLIRQCOUtils
+  MLIRArithDialect
+  MLIRMathDialect
   DEPENDS
   MLIRQCOTransformsIncGen)