diff --git a/mlir/include/mlir/Dialect/Common/IR/CommonTraits.h b/mlir/include/mlir/Dialect/Common/IR/CommonTraits.h
index 23ec89ceb..9009fb5db 100644
--- a/mlir/include/mlir/Dialect/Common/IR/CommonTraits.h
+++ b/mlir/include/mlir/Dialect/Common/IR/CommonTraits.h
@@ -10,13 +10,41 @@
 
 #pragma once
 
+#include <array>
+#include <cmath>
 #include <cstddef>
+#include <functional>
 #include <mlir/IR/OpDefinition.h>
 #include <mlir/IR/Operation.h>
 #include <mlir/Support/LLVM.h>
+#include <stdexcept>
 
 namespace mqt::ir::common {
-template <size_t N> class TargetArityTrait {
+
+template <std::size_t NumQubits> struct DefinitionMatrix {
+  static constexpr std::size_t MatrixSize = 1 << NumQubits;
+
+  template <typename T>
+  using MatrixType = std::array<T, MatrixSize * MatrixSize>;
+
+  MatrixType<double (*)(mlir::ValueRange)> matrix;
+
+  static constexpr std::size_t index(std::size_t x, std::size_t y) {
+    return (y * MatrixSize) + x;
+  }
+
+  constexpr MatrixType<double> getMatrix(mlir::ValueRange params) {
+    // TODO? lazy-initialized cache
+    MatrixType<double> result;
+    static_assert(result.size() == matrix.size());
+    for (std::size_t i = 0; i < result.size(); ++i) {
+      result[i] = matrix[i](params);
+    }
+    return result;
+  }
+};
+
+template <size_t N, DefinitionMatrix<N> Matrix> class TargetArityTrait {
 public:
   template <typename ConcreteOp>
   class Impl : public mlir::OpTrait::TraitBase<ConcreteOp, Impl> {
@@ -29,6 +57,17 @@ template <size_t N> class TargetArityTrait {
       }
       return mlir::success();
     }
+
+    [[nodiscard]] static auto getDefinitionMatrix() { return Matrix; }
+    [[nodiscard]] static auto getDefinitionMatrix(mlir::Operation* op) {
+      auto concreteOp = mlir::cast<ConcreteOp>(op);
+      return Matrix.getMatrix(concreteOp.getParams());
+    }
+    [[nodiscard]] static double getDefinitionMatrixElement(mlir::Operation* op,
+                                                           std::size_t x,
+                                                           std::size_t y) {
+      return getDefinitionMatrix(op).at(DefinitionMatrix<N>::index(x, y));
+    }
   };
 };
 
diff --git a/mlir/include/mlir/Dialect/Common/IR/CommonTraits.td b/mlir/include/mlir/Dialect/Common/IR/CommonTraits.td
index 55849f726..550ec9a60 100644
--- a/mlir/include/mlir/Dialect/Common/IR/CommonTraits.td
+++ b/mlir/include/mlir/Dialect/Common/IR/CommonTraits.td
@@ -14,8 +14,39 @@ include "mlir/IR/EnumAttr.td"
 include "mlir/IR/DialectBase.td"
 include "mlir/Interfaces/SideEffectInterfaces.td"
 
-class TargetArity<int N>
-    : ParamNativeOpTrait<"TargetArityTrait", !cast<string>(N)> {
+class DecimalFraction<int BeforeSeparator, int AfterSeparator> {
+  int Before = BeforeSeparator;
+  int After = AfterSeparator;
+}
+class Int<int I> : DecimalFraction<I, 0>;
+
+class DefinitionElementType<int Id> {
+  int id = Id;
+}
+def Value : DefinitionElementType<0>;
+def ParameterIndex : DefinitionElementType<1>;
+
+class FunctionType<int Id> {
+  int id = Id;
+}
+
+def Identity : FunctionType<0>;
+def Sin : FunctionType<1>;
+def Cos : FunctionType<2>;
+
+class DefinitionElement<DecimalFraction V, DefinitionElementType T, FunctionType F = Identity> {
+  DecimalFraction v = V;
+  DefinitionElementType t = T;
+  FunctionType f = F;
+}
+
+class Value<DecimalFraction V> : DefinitionElement<V, Value, Identity>;
+
+class TargetArity<int N, list<DefinitionElement> MatrixDefinition = []>
+    : ParamNativeOpTrait<
+        "TargetArityTrait",
+        !cast<string>(N) # ", {{" # !foldl("", MatrixDefinition, acc, var, "[]([[maybe_unused]] mlir::ValueRange params) { return " # !cond(!eq(var.f, Identity) : "std::identity{}(") # !cond(!eq(var.t, Value) : var.v.Before # "." # var.v.After) # "); }") # "}}"
+    > {
     let cppNamespace = "::mqt::ir::common";
 }
 
diff --git a/mlir/include/mlir/Dialect/Common/IR/StdOps.td.inc b/mlir/include/mlir/Dialect/Common/IR/StdOps.td.inc
index 675c4b992..ebf57c77a 100644
--- a/mlir/include/mlir/Dialect/Common/IR/StdOps.td.inc
+++ b/mlir/include/mlir/Dialect/Common/IR/StdOps.td.inc
@@ -22,7 +22,7 @@ def GPhaseOp : UnitaryOp<"gphase", [NoTarget, OneParameter]> {
     }];
 }
 
-def IOp : UnitaryOp<"i", [OneTarget, NoParameter]> {
+def IOp : UnitaryOp<"i", [TargetArity<1, [Value<Int<1>>, Value<Int<0>>, Value<Int<0>>, Value<Int<1>>]>, NoParameter]> {
     let summary = "I operation";
 
     let description = [{
diff --git a/mlir/include/mlir/Dialect/MQTOpt/IR/MQTOptInterfaces.td b/mlir/include/mlir/Dialect/MQTOpt/IR/MQTOptInterfaces.td
index 7562057fe..f856d0a1b 100644
--- a/mlir/include/mlir/Dialect/MQTOpt/IR/MQTOptInterfaces.td
+++ b/mlir/include/mlir/Dialect/MQTOpt/IR/MQTOptInterfaces.td
@@ -167,6 +167,35 @@ def UnitaryInterface : OpInterface<"UnitaryInterface"> {
             /*methodBody=*/  [{}],
             /*defaultImpl=*/ [{
                return  $_op->getName().getStringRef().split('.').second;
+            }]>,
+        InterfaceMethod<
+            /*desc=*/        "Check if operation operates on a single qubit.",
+            /*returnType=*/  "bool",
+            /*methodName=*/  "isSingleQubitOperation",
+            /*args=*/        (ins),
+            /*methodBody=*/  [{}],
+            /*defaultImpl=*/ [{
+                auto&& inQubits = $_op.getInQubits();
+                auto&& outQubits = $_op.getOutQubits();
+                return inQubits.size() == 1 && outQubits.size() == 1 && !$_op.isControlled();
+            }]>,
+            InterfaceMethod<
+            /*desc=*/        "Check if operation operates on exactly two qubits.",
+            /*returnType=*/  "bool",
+            /*methodName=*/  "isTwoQubitOperation",
+            /*args=*/        (ins),
+            /*methodBody=*/  [{}],
+            /*defaultImpl=*/ [{
+                auto&& inQubits = $_op.getInQubits();
+                auto&& inPosCtrlQubits = $_op.getPosCtrlInQubits();
+                auto&& inNegCtrlQubits = $_op.getNegCtrlInQubits();
+                auto&& outQubits = $_op.getOutQubits();
+                auto&& outPosCtrlQubits = $_op.getPosCtrlInQubits();
+                auto&& outNegCtrlQubits = $_op.getNegCtrlInQubits();
+
+                auto inQubitSize = inQubits.size() + inPosCtrlQubits.size() + inNegCtrlQubits.size();
+                auto outQubitSize = outQubits.size() + outPosCtrlQubits.size() + outNegCtrlQubits.size();
+                return inQubitSize == 2 && outQubitSize == 2;
             }]>
     ];