✨ Add Hadamard Lifting

CHANGELOG.md

@@ -14,6 +14,7 @@ This project adheres to [Semantic Versioning], with the exception that minor rel
 - ✨ Add Sampler and Estimator Primitives to the QDMI-Qiskit Interface ([#1507]) ([**@marcelwa**])
 - ✨ Add conversions between Jeff and QCO ([#1479], [#1548], [#1565]) ([**@denialhaag**])
 - ✨ Add a `place-and-route` pass for mapping circuits to architectures with restricted topologies ([#1537], [#1547], [#1568], [#1581], [#1583], [#1588]) ([**@MatthiasReumann**])
+- ✨ Add a `hadamard-lifting` pass for lifting Hadamard gates above Pauli gates ([#1605]) ([**@lirem101**])
 - ✨ 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], [#1542], [#1548], [#1550], [#1554], [#1567], [#1569], [#1570], [#1572], [#1573], [#1580], [#1602], [#1623])
   ([**@burgholzer**], [**@denialhaag**], [**@taminob**], [**@DRovara**], [**@li-mingbao**], [**@Ectras**], [**@MatthiasReumann**], [**@simon1hofmann**])
@@ -336,6 +337,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 <!-- PR links -->
 
 [#1623]: https://github.com/munich-quantum-toolkit/core/pull/1623
+[#1605]: https://github.com/munich-quantum-toolkit/core/pull/1605
 [#1602]: https://github.com/munich-quantum-toolkit/core/pull/1602
 [#1596]: https://github.com/munich-quantum-toolkit/core/pull/1596
 [#1593]: https://github.com/munich-quantum-toolkit/core/pull/1593

mlir/include/mlir/Compiler/CompilerPipeline.h

@@ -40,6 +40,9 @@ struct QuantumCompilerConfig {
 
   /// Print IR after each stage
   bool printIRAfterAllStages = false;
+
+  /// Enable Hadamard lifting
+  bool hadamardLifting = false;
 };
 
 /**

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

@@ -72,4 +72,64 @@ def MappingPass : Pass<"place-and-route", "mlir::ModuleOp"> {
                               "The number of inserted SWAPs">];
 }
 
+//===----------------------------------------------------------------------===//
+// Optimization Passes
+//===----------------------------------------------------------------------===//
+
+def HadamardLifting : Pass<"hadamard-lifting", "mlir::ModuleOp"> {
+  let dependentDialects = ["mlir::qco::QCODialect"];
+  let summary = "This pass attempts to move Hadamard gates as far away from "
+                "measurements as possible by flipping them "
+                "with Pauli gates. Additionally, it can change target and "
+                "control qubits from Pauli-Z gates to make "
+                "Hadamard lifting applicable. It also lifts Hadamard gates "
+                "over CNOT gates if that moves a measurement "
+                "directly after a control.";
+  let description = [{
+    This pass lifts Hadamard gates away from the measurements in order to apply measurement lifting more effectively. It
+    uses the following commutation rules:
+         ┌───┐ ┌───┐      ┌───┐ ┌───┐
+        ─┤ X ├─┤ H ├─ => ─┤ H ├─┤ Z ├─
+         └───┘ └───┘      └───┘ └───┘
+         ┌───┐ ┌───┐      ┌───┐ ┌───┐
+        ─┤ Z ├─┤ H ├─ => ─┤ H ├─┤ X ├─
+         └───┘ └───┘      └───┘ └───┘
+         ┌───┐ ┌───┐      ┌───┐ ┌───┐
+        ─┤ Y ├─┤ H ├─ => ─┤ H ├─┤ Y ├─
+         └───┘ └───┘      └───┘ └───┘
+    Hadamard lifting is only applied to lift Hadamard gates further in front in the circuit, not the other way around.
+
+    If the Hadamard and Pauli gates are controlled, they are only lifted if both gates are controlled by exactly the
+    same qubits and the Pauli gate is not a Pauli Y gate. In that case, the swap of the Pauli Y gate and the Hadamard
+    gate introduces a phase (YH = -HY) which leads to a non-global phase for controlled gates.
+
+    In the case of the controlled Pauli Z gate, controls and targets are interchangeable. Therefore, transformation
+    routines as follows are possible and applied:
+        ┌───┐
+        ┤ Z ├──■──    ──■────■──    ──■────■──
+        └─┬─┘┌─┴─┐ => ┌─┴─┐┌─┴─┐ => ┌─┴─┐┌─┴─┐
+        ──■──┤ H ├    ┤ Z ├┤ H ├    ┤ H ├┤ X ├
+             └───┘    └───┘└───┘    └───┘└───┘
+    The commutation of controlled gates is only done if there are no gates applied between the two controlled gates to
+    any of the qubits used on the controlled gates.
+
+    In order to reduce multi-qubit gates, a third transformation routine is applied. Using the commutation rule
+                 ┌───┐┌───┐┌───┐
+        ──■──    ┤ H ├┤ X ├┤ H ├
+        ┌─┴─┐ => │───│└─┬─┘│───│
+        ┤ X ├    ┤ H ├──■──┤ H ├
+        └───┘    └───┘     └───┘
+    the following transformation is applied to circuits where a Hadamard gate follows a target gate of a controlled
+    Pauli X gate, which is followed by a measurement:
+                              ┌───┐┌───┐┌───┐
+        ──■─────────────      ┤ H ├┤ X ├┤ H ├──
+        ┌─┴─┐┌───┐┌──────┐ => │───│└─┬─┘│───┘──┐
+        ┤ X ├┤ H ├┤ Meas │    ┤ H ├──■──┤ Meas │
+        └───┘└───┘└──────┘    └───┘     └──────┘
+
+     Afterward the measurement lifting routine could transform the CNOT into a classically controlled Pauli X.
+
+  }];
+}
+
 #endif // MLIR_DIALECT_QCO_TRANSFORMS_PASSES_TD

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 +137,12 @@ 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_.hadamardLifting) {
+          pm.addPass(qco::createHadamardLifting());
+        }
+        populateQCOCleanupPipeline(pm);
+      }))) {
     return failure();
   }
   if (record != nullptr && config_.recordIntermediates) {