diff --git a/include/QuantumComputation.hpp b/include/QuantumComputation.hpp
index 2d8ceb683..b1879c60e 100644
--- a/include/QuantumComputation.hpp
+++ b/include/QuantumComputation.hpp
@@ -479,6 +479,7 @@ class QuantumComputation {
   DEFINE_TWO_TARGET_OPERATION(dcx)
   DEFINE_TWO_TARGET_OPERATION(ecr)
   DEFINE_TWO_TARGET_OPERATION(iswap)
+  DEFINE_TWO_TARGET_OPERATION(iswapdg)
   DEFINE_TWO_TARGET_OPERATION(peres)
   DEFINE_TWO_TARGET_OPERATION(peresdg)
 
diff --git a/include/dd/Operations.hpp b/include/dd/Operations.hpp
index b7ba6f104..8c9676b37 100644
--- a/include/dd/Operations.hpp
+++ b/include/dd/Operations.hpp
@@ -121,6 +121,9 @@ qc::MatrixDD getStandardOperationDD(const qc::StandardOperation* op,
     case qc::iSWAP:
       gm = inverse ? ISWAPDG_MAT : ISWAP_MAT;
       break;
+    case qc::iSWAPdg:
+      gm = inverse ? ISWAP_MAT : ISWAPDG_MAT;
+      break;
     case qc::DCX:
       gm = DCX_MAT;
       break;
@@ -165,6 +168,11 @@ qc::MatrixDD getStandardOperationDD(const qc::StandardOperation* op,
                                 startQubit);
     }
     return dd->makeiSWAPDD(nqubits, controls, target0, target1, startQubit);
+  case qc::iSWAPdg:
+    if (inverse) {
+      return dd->makeiSWAPDD(nqubits, controls, target0, target1, startQubit);
+    }
+    return dd->makeiSWAPinvDD(nqubits, controls, target0, target1, startQubit);
   case qc::Peres:
     if (inverse) {
       return dd->makePeresdagDD(nqubits, controls, target0, target1,
diff --git a/include/operations/OpType.hpp b/include/operations/OpType.hpp
index 8037858e2..a18f8fbc4 100644
--- a/include/operations/OpType.hpp
+++ b/include/operations/OpType.hpp
@@ -33,7 +33,8 @@ enum OpType : std::uint8_t {
   RY,
   RZ,
   SWAP,
-  iSWAP, // NOLINT (readability-identifier-naming)
+  iSWAP,   // NOLINT (readability-identifier-naming)
+  iSWAPdg, // NOLINT (readability-identifier-naming)
   Peres,
   Peresdg,
   DCX,
@@ -109,6 +110,8 @@ inline std::string toString(const OpType& opType) {
     return "swap";
   case iSWAP:
     return "iswap";
+  case iSWAPdg:
+    return "iswapdg";
   case Peres:
     return "peres";
   case Peresdg:
@@ -163,6 +166,8 @@ inline std::string shortName(const OpType& opType) {
     return "sw";
   case iSWAP:
     return "isw";
+  case iSWAPdg:
+    return "isd";
   case Peres:
     return "pr";
   case Peresdg:
@@ -188,6 +193,7 @@ inline bool isTwoQubitGate(const OpType& opType) {
   switch (opType) {
   case SWAP:
   case iSWAP:
+  case iSWAPdg:
   case Peres:
   case Peresdg:
   case DCX:
@@ -262,6 +268,7 @@ const inline static std::unordered_map<std::string, qc::OpType>
         {"swap", OpType::SWAP},
         {"cswap", OpType::SWAP},
         {"iswap", OpType::iSWAP},
+        {"iswapdg", OpType::iSWAPdg},
         {"peres", OpType::Peres},
         {"peresdg", OpType::Peresdg},
         {"dcx", OpType::DCX},
diff --git a/include/parsers/qasm_parser/Parser.hpp b/include/parsers/qasm_parser/Parser.hpp
index c3809dad2..f7d7a9297 100644
--- a/include/parsers/qasm_parser/Parser.hpp
+++ b/include/parsers/qasm_parser/Parser.hpp
@@ -151,6 +151,7 @@ class Parser {
       {"teleport", {0, 3, 0, qc::Teleportation}},
       {"swap", {0, 2, 0, qc::SWAP}},
       {"iswap", {0, 2, 0, qc::iSWAP}},
+      {"iswapdg", {0, 2, 0, qc::iSWAPdg}},
       {"cnot", {1, 1, 0, qc::X}},
       {"CX", {1, 1, 0, qc::X}},
       {"cx", {1, 1, 0, qc::X}},
diff --git a/src/mqt/core/_core/__init__.pyi b/src/mqt/core/_core/__init__.pyi
index 4218cb471..91bb455d0 100644
--- a/src/mqt/core/_core/__init__.pyi
+++ b/src/mqt/core/_core/__init__.pyi
@@ -217,6 +217,9 @@ class QuantumComputation(MutableSequence[Operation]):
     def iswap(self: Self, target1: int, target2: int) -> None: ...
     def ciswap(self: Self, control: Control | int, target1: int, target2: int) -> None: ...
     def mciswap(self: Self, controls: set[Control | int], target1: int, target2: int) -> None: ...
+    def iswapdg(self: Self, target1: int, target2: int) -> None: ...
+    def ciswapdg(self: Self, control: Control | int, target1: int, target2: int) -> None: ...
+    def mciswapdg(self: Self, controls: set[Control | int], target1: int, target2: int) -> None: ...
     def peres(self: Self, target1: int, target2: int) -> None: ...
     def cperes(self: Self, control: Control | int, target1: int, target2: int) -> None: ...
     def mcperes(self: Self, controls: set[Control | int], target1: int, target2: int) -> None: ...
diff --git a/src/mqt/core/_core/operations.pyi b/src/mqt/core/_core/operations.pyi
index 1b1a47043..ae2140b53 100644
--- a/src/mqt/core/_core/operations.pyi
+++ b/src/mqt/core/_core/operations.pyi
@@ -35,27 +35,28 @@ class Control:
 class OpType:
     __members__: ClassVar[dict[OpType, str]]  # readonly
     barrier: ClassVar[OpType]  # value = <OpType.barrier: 3>
-    classic_controlled: ClassVar[OpType]  # value = <OpType.classic_controlled: 38>
-    compound: ClassVar[OpType]  # value = <OpType.compound: 34>
-    dcx: ClassVar[OpType]  # value = <OpType.dcx: 26>
-    ecr: ClassVar[OpType]  # value = <OpType.ecr: 27>
+    classic_controlled: ClassVar[OpType]  # value = <OpType.classic_controlled: 39>
+    compound: ClassVar[OpType]  # value = <OpType.compound: 35>
+    dcx: ClassVar[OpType]  # value = <OpType.dcx: 27>
+    ecr: ClassVar[OpType]  # value = <OpType.ecr: 28>
     gphase: ClassVar[OpType]  # value = <OpType.gphase: 1>
     h: ClassVar[OpType]  # value = <OpType.h: 4>
     i: ClassVar[OpType]  # value = <OpType.i: 2>
     iswap: ClassVar[OpType]  # value = <OpType.iswap: 23>
-    measure: ClassVar[OpType]  # value = <OpType.measure: 35>
+    iswapdg: ClassVar[OpType]  # value = <OpType.iswapdg: 24>
+    measure: ClassVar[OpType]  # value = <OpType.measure: 36>
     none: ClassVar[OpType]  # value = <OpType.none: 0>
-    peres: ClassVar[OpType]  # value = <OpType.peres: 24>
-    peresdg: ClassVar[OpType]  # value = <OpType.peresdg: 25>
+    peres: ClassVar[OpType]  # value = <OpType.peres: 25>
+    peresdg: ClassVar[OpType]  # value = <OpType.peresdg: 26>
     p: ClassVar[OpType]  # value = <OpType.p: 16>
-    reset: ClassVar[OpType]  # value = <OpType.reset: 36>
+    reset: ClassVar[OpType]  # value = <OpType.reset: 37>
     rx: ClassVar[OpType]  # value = <OpType.rx: 19>
-    rxx: ClassVar[OpType]  # value = <OpType.rxx: 28>
+    rxx: ClassVar[OpType]  # value = <OpType.rxx: 29>
     ry: ClassVar[OpType]  # value = <OpType.ry: 20>
-    ryy: ClassVar[OpType]  # value = <OpType.ryy: 29>
+    ryy: ClassVar[OpType]  # value = <OpType.ryy: 30>
     rz: ClassVar[OpType]  # value = <OpType.rz: 21>
-    rzx: ClassVar[OpType]  # value = <OpType.rzx: 31>
-    rzz: ClassVar[OpType]  # value = <OpType.rzz: 30>
+    rzx: ClassVar[OpType]  # value = <OpType.rzx: 32>
+    rzz: ClassVar[OpType]  # value = <OpType.rzz: 31>
     s: ClassVar[OpType]  # value = <OpType.s: 8>
     sdg: ClassVar[OpType]  # value = <OpType.sdg: 9>
     swap: ClassVar[OpType]  # value = <OpType.swap: 22>
@@ -63,14 +64,14 @@ class OpType:
     sxdg: ClassVar[OpType]  # value = <OpType.sxdg: 18>
     t: ClassVar[OpType]  # value = <OpType.t: 10>
     tdg: ClassVar[OpType]  # value = <OpType.tdg: 11>
-    teleportation: ClassVar[OpType]  # value = <OpType.teleportation: 37>
+    teleportation: ClassVar[OpType]  # value = <OpType.teleportation: 38>
     u2: ClassVar[OpType]  # value = <OpType.u2: 15>
     u: ClassVar[OpType]  # value = <OpType.u: 14>
     v: ClassVar[OpType]  # value = <OpType.v: 12>
     vdg: ClassVar[OpType]  # value = <OpType.vdg: 13>
     x: ClassVar[OpType]  # value = <OpType.x: 5>
-    xx_minus_yy: ClassVar[OpType]  # value = <OpType.xx_minus_yy: 32>
-    xx_plus_yy: ClassVar[OpType]  # value = <OpType.xx_plus_yy: 33>
+    xx_minus_yy: ClassVar[OpType]  # value = <OpType.xx_minus_yy: 33>
+    xx_plus_yy: ClassVar[OpType]  # value = <OpType.xx_plus_yy: 34>
     y: ClassVar[OpType]  # value = <OpType.y: 6>
     z: ClassVar[OpType]  # value = <OpType.z: 7>
     @property
diff --git a/src/operations/StandardOperation.cpp b/src/operations/StandardOperation.cpp
index 340c568f0..17b5841e7 100644
--- a/src/operations/StandardOperation.cpp
+++ b/src/operations/StandardOperation.cpp
@@ -368,6 +368,9 @@ void StandardOperation::dumpOpenQASM(
   case iSWAP:
     op << "iswap";
     break;
+  case iSWAPdg:
+    op << "iswapdg";
+    break;
   case Peres:
     of << op.str() << "cx";
     for (const auto& c : controls) {
@@ -541,8 +544,12 @@ void StandardOperation::invert() {
   case Peresdg:
     type = Peres;
     break;
-  // Tracking issue for iSwap: https://github.com/cda-tum/mqt-core/issues/423
   case iSWAP:
+    type = iSWAPdg;
+    break;
+  case iSWAPdg:
+    type = iSWAP;
+    break;
   case None:
   case Compound:
   case Measure:
diff --git a/src/python/operations/register_optype.cpp b/src/python/operations/register_optype.cpp
index bb1799b0b..c36c18ad7 100644
--- a/src/python/operations/register_optype.cpp
+++ b/src/python/operations/register_optype.cpp
@@ -30,6 +30,7 @@ void registerOptype(py::module& m) {
       .value("rz", qc::OpType::RZ)
       .value("swap", qc::OpType::SWAP)
       .value("iswap", qc::OpType::iSWAP)
+      .value("iswapdg", qc::OpType::iSWAPdg)
       .value("peres", qc::OpType::Peres)
       .value("peresdg", qc::OpType::Peresdg)
       .value("dcx", qc::OpType::DCX)
diff --git a/test/dd/test_dd_functionality.cpp b/test/dd/test_dd_functionality.cpp
index ef2af2def..243cb5a18 100644
--- a/test/dd/test_dd_functionality.cpp
+++ b/test/dd/test_dd_functionality.cpp
@@ -57,8 +57,9 @@ INSTANTIATE_TEST_SUITE_P(
     testing::Values(qc::GPhase, qc::I, qc::H, qc::X, qc::Y, qc::Z, qc::S,
                     qc::Sdg, qc::T, qc::Tdg, qc::SX, qc::SXdg, qc::V, qc::Vdg,
                     qc::U, qc::U2, qc::P, qc::RX, qc::RY, qc::RZ, qc::Peres,
-                    qc::Peresdg, qc::SWAP, qc::iSWAP, qc::DCX, qc::ECR, qc::RXX,
-                    qc::RYY, qc::RZZ, qc::RZX, qc::XXminusYY, qc::XXplusYY),
+                    qc::Peresdg, qc::SWAP, qc::iSWAP, qc::iSWAPdg, qc::DCX,
+                    qc::ECR, qc::RXX, qc::RYY, qc::RZZ, qc::RZX, qc::XXminusYY,
+                    qc::XXplusYY),
     [](const testing::TestParamInfo<DDFunctionality::ParamType>& inf) {
       const auto gate = inf.param;
       return toString(gate);
@@ -91,6 +92,7 @@ TEST_P(DDFunctionality, standardOpBuildInverseBuild) {
 
   case qc::SWAP:
   case qc::iSWAP:
+  case qc::iSWAPdg:
   case qc::DCX:
   case qc::ECR:
     op = qc::StandardOperation(nqubits, Controls{}, 0, 1, gate);
@@ -126,6 +128,11 @@ TEST_F(DDFunctionality, buildCircuit) {
 
   qc.x(0);
   qc.swap(0, 1);
+  qc.cswap(2, 0, 1);
+  qc.mcswap({2, 3}, 0, 1);
+  qc.iswap(0, 1);
+  qc.ciswap(2, 0, 1);
+  qc.mciswap({2, 3}, 0, 1);
   qc.h(0);
   qc.s(3);
   qc.sdg(2);
@@ -178,6 +185,11 @@ TEST_F(DDFunctionality, buildCircuit) {
   qc.s(2);
   qc.sdg(3);
   qc.h(0);
+  qc.mciswapdg({2, 3}, 0, 1);
+  qc.ciswapdg(2, 0, 1);
+  qc.iswapdg(0, 1);
+  qc.mcswap({2, 3}, 0, 1);
+  qc.cswap(2, 0, 1);
   qc.swap(0, 1);
   qc.x(0);
 
diff --git a/test/unittests/test_io.cpp b/test/unittests/test_io.cpp
index 9f7ce9acb..c2b611a0d 100644
--- a/test/unittests/test_io.cpp
+++ b/test/unittests/test_io.cpp
@@ -380,6 +380,16 @@ TEST_F(IO, iSWAPDumpIsValid) {
   std::cout << *qc << "\n";
 }
 
+TEST_F(IO, iSWAPdagDumpIsValid) {
+  qc->addQubitRegister(2);
+  qc->iswapdg(0, 1);
+  std::cout << *qc << "\n";
+  std::stringstream ss{};
+  qc->dumpOpenQASM(ss);
+  EXPECT_NO_THROW(qc->import(ss, qc::Format::OpenQASM););
+  std::cout << *qc << "\n";
+}
+
 TEST_F(IO, PeresDumpIsValid) {
   qc->addQubitRegister(2);
   qc->peres(0, 1);
diff --git a/test/unittests/test_qfr_functionality.cpp b/test/unittests/test_qfr_functionality.cpp
index b285a0919..347b2ba42 100644
--- a/test/unittests/test_qfr_functionality.cpp
+++ b/test/unittests/test_qfr_functionality.cpp
@@ -772,6 +772,9 @@ TEST_F(QFRFunctionality, gateShortCutsAndCloning) {
   qc.iswap(0, 1);
   qc.ciswap(2, 0, 1);
   qc.mciswap({2, 3_nc}, 0, 1);
+  qc.iswapdg(0, 1);
+  qc.ciswapdg(2, 0, 1);
+  qc.mciswapdg({2, 3_nc}, 0, 1);
   qc.peres(0, 1);
   qc.cperes(2, 0, 1);
   qc.mcperes({2, 3_nc}, 0, 1);
@@ -2161,7 +2164,7 @@ TEST_F(QFRFunctionality, invertStandardOpInvertClone) {
 TEST_F(QFRFunctionality, invertStandardOpSpecial) {
   const auto opTypes = {
       std::pair{S, Sdg},   std::pair{T, Tdg},         std::pair{V, Vdg},
-      std::pair{SX, SXdg}, std::pair{Peres, Peresdg},
+      std::pair{SX, SXdg}, std::pair{Peres, Peresdg}, std::pair{iSWAP, iSWAPdg},
   };
 
   for (const auto& [opType, opTypeInv] : opTypes) {