Add multi-control functionality

include/mqt-core/zx/FunctionalityConstruction.hpp

@@ -113,6 +113,18 @@ class FunctionalityConstruction {
                const std::optional<double>& unconvertedBeta = std::nullopt);
   static void addCcx(ZXDiagram& diag, Qubit ctrl0, Qubit ctrl1, Qubit target,
                      std::vector<Vertex>& qubits);
+  static void addCcz(ZXDiagram& diag, Qubit ctrl0, Qubit ctrl1, Qubit target,
+                     std::vector<Vertex>& qubits);
+  static void addCrz(ZXDiagram& diag, const PiExpression& phase,
+                     const Qubit control, const Qubit target,
+                     std::vector<Vertex>& qubits);
+  static void addMcrz(ZXDiagram& diag, const PiExpression& phase,
+                      std::vector<Qubit> controls, const Qubit target,
+                      std::vector<Vertex>& qubits);
+  static void addMcx(ZXDiagram& diag, std::vector<Qubit> controls,
+                     const Qubit target, std::vector<Vertex>& qubits);
+  static void addMcz(ZXDiagram& diag, std::vector<Qubit> controls,
+                     const Qubit target, std::vector<Vertex>& qubits);
   static op_it parseOp(ZXDiagram& diag, op_it it, op_it end,
                        std::vector<Vertex>& qubits, const qc::Permutation& p);
   static op_it parseCompoundOp(ZXDiagram& diag, op_it it, op_it end,

src/zx/FunctionalityConstruction.cpp

@@ -307,6 +307,123 @@
   addCnot(diag, ctrl0, ctrl1, qubits);
 }
 
+void FunctionalityConstruction::addCcz(ZXDiagram& diag, const Qubit ctrl0,
+                                       const Qubit ctrl1, const Qubit target,
+                                       std::vector<Vertex>& qubits) {
+
+  addCnot(diag, ctrl1, target, qubits);
+  addZSpider(diag, target, qubits, PiExpression(PiRational(-1, 4)));
+  addCnot(diag, ctrl0, target, qubits);
+  addZSpider(diag, target, qubits, PiExpression(PiRational(1, 4)));
+  addCnot(diag, ctrl1, target, qubits);
+  addZSpider(diag, ctrl1, qubits, PiExpression(PiRational(1, 4)));
+  addZSpider(diag, target, qubits, PiExpression(PiRational(-1, 4)));
+  addCnot(diag, ctrl0, target, qubits);
+  addZSpider(diag, target, qubits, PiExpression(PiRational(1, 4)));
+  addCnot(diag, ctrl0, ctrl1, qubits);
+  addZSpider(diag, ctrl0, qubits, PiExpression(PiRational(1, 4)));
+  addZSpider(diag, ctrl1, qubits, PiExpression(PiRational(-1, 4)));
+  addZSpider(diag, target, qubits, PiExpression(PiRational(0, 1)),
+             EdgeType::Hadamard);
+  addCnot(diag, ctrl0, ctrl1, qubits);
+  addZSpider(diag, target, qubits, PiExpression(), EdgeType::Hadamard);
+}
+
+void FunctionalityConstruction::addCrz(ZXDiagram& diag,
+                                       const PiExpression& phase,
+                                       const Qubit q0, const Qubit q1,
+                                       std::vector<Vertex>& qubits) {
+  // CRZ decomposition uses reversed CNOT direction
+  addCnot(diag, q1, q0, qubits);
+  addZSpider(diag, q0, qubits, -phase / 2);
+  addZSpider(diag, q1, qubits, phase / 2);
+  addCnot(diag, q1, q0, qubits);
+}
+
+void FunctionalityConstruction::addMcrz(ZXDiagram& diag,
+                                        const PiExpression& phase,
+                                        std::vector<Qubit> controls,
+                                        const Qubit target,
+                                        std::vector<Vertex>& qubits) {
+
+  const Qubit nextControl = controls.back();
+  controls.pop_back();
+
+  addCrz(diag, phase / 2, nextControl, target, qubits);
+  addMcx(diag, controls, target, qubits);
+  addCrz(diag, -phase / 2, nextControl, target, qubits);
+  addMcx(diag, controls, target, qubits);
+}
+
+void FunctionalityConstruction::addMcx(ZXDiagram& diag,
+                                       std::vector<Qubit> controls,
+                                       const Qubit target,
+                                       std::vector<Vertex>& qubits) {
+
+  switch (controls.size()) {
+  case 0:
+    addXSpider(diag, target, qubits, PiExpression(PiRational(1, 1)));
+    return;
+  case 1:
+    addCnot(diag, controls.front(), target, qubits);
+    return;
+  case 2:
+    addCcx(diag, controls.front(), controls.back(), target, qubits);
+    return;
+  default:
+    const auto half = static_cast<std::ptrdiff_t>((controls.size() + 1) / 2);
+    const std::vector<Qubit> first(controls.begin(), controls.begin() + half);
+    std::vector<Qubit> second(controls.begin() + half, controls.end());
+
+    if (qubits.size() > controls.size() + 1) {
+      std::vector<Qubit> blocked = controls;
+      blocked.emplace_back(target);
+      std::ranges::sort(blocked);
+      std::ranges::sort(qubits);
+
+      std::vector<Qubit> available;
+      available.reserve(qubits.size());
+      std::ranges::set_difference(qubits, blocked,
+                                  std::back_inserter(available));
+
+      second.emplace_back(available.front());
+
+      addMcx(diag, first, available.front(), qubits);
+      addMcx(diag, second, target, qubits);
+
+      addMcx(diag, first, available.front(), qubits);
+      addMcx(diag, second, target, qubits);
+    } else {
+      addRx(diag, PiExpression(PiRational(1, 4)), target, qubits);
+      addMcz(diag, second, target, qubits);
+      addRx(diag, PiExpression(-PiRational(1, 4)), target, qubits);
+      addMcx(diag, first, target, qubits);
+
+      addRx(diag, PiExpression(PiRational(1, 4)), target, qubits);
+      addMcz(diag, second, target, qubits);
+      addRx(diag, PiExpression(-PiRational(1, 4)), target, qubits);
+      addMcx(diag, first, target, qubits);
+      const Qubit lastControl = controls.back();
+      controls.pop_back();
+      addMcrz(diag, PiExpression(PiRational(1, 2)), controls, lastControl,
+              qubits);
+    }
+  }
+}
+
+void FunctionalityConstruction::addMcz(ZXDiagram& diag,
+                                       std::vector<Qubit> controls,
+                                       const Qubit target,
+                                       std::vector<Vertex>& qubits) {
+  const Qubit nextControl = controls.back();
+  controls.pop_back();
+
+  addCrz(diag, PiExpression(PiRational(1, 2)), nextControl, target, qubits);
+  addMcx(diag, controls, target, qubits);
+  addCrz(diag, PiExpression(-PiRational(1, 2)), nextControl, target, qubits);
+  addMcx(diag, controls, target, qubits);
+}
+
 FunctionalityConstruction::op_it
 FunctionalityConstruction::parseOp(ZXDiagram& diag, op_it it, op_it end,
                                    std::vector<Vertex>& qubits,
@@ -538,6 +655,9 @@
                    qubits[static_cast<std::size_t>(target)],
                    EdgeType::Hadamard);
       break;
+    case qc::OpType::RZ:
+      addCrz(diag, parseParam(op.get(), 0), ctrl, target, qubits);
+      break;
 
     case qc::OpType::I:
       break;
@@ -582,11 +702,32 @@
     case qc::OpType::X:
       addCcx(diag, ctrl0, ctrl1, target, qubits);
       break;
-
     case qc::OpType::Z:
-      addZSpider(diag, target, qubits, PiExpression(), EdgeType::Hadamard);
-      addCcx(diag, ctrl0, ctrl1, target, qubits);
-      addZSpider(diag, target, qubits, PiExpression(), EdgeType::Hadamard);
+      addCcz(diag, ctrl0, ctrl1, target, qubits);
+      break;
+    case qc::OpType::RZ:
+      addMcrz(diag, parseParam(op.get(), 0), {ctrl0, ctrl1}, target, qubits);
+      break;
+    default:
+      throw ZXException("Unsupported Multi-control operation: " +
+                        qc::toString(op->getType()));
+    }
+  } else if (op->getNtargets() == 1) {
+    const auto target = static_cast<Qubit>(p.at(op->getTargets().front()));
+    std::vector<Qubit> controls;
+    controls.reserve(op->getNcontrols());
+    for (const auto& ctrl : op->getControls()) {
+      controls.emplace_back(static_cast<Qubit>(p.at(ctrl.qubit)));
+    }
+    switch (op->getType()) {
+    case qc::OpType::X:
+      addMcx(diag, controls, target, qubits);
+      break;
+    case qc::OpType::Z:
+      addMcz(diag, controls, target, qubits);
+      break;
+    case qc::OpType::RZ:
+      addMcrz(diag, parseParam(op.get(), 0), controls, target, qubits);
       break;
     default:
       throw ZXException("Unsupported Multi-control operation: " +
@@ -701,15 +842,16 @@
     case qc::OpType::S:
     case qc::OpType::Tdg:
     case qc::OpType::Sdg:
+    case qc::OpType::RZ:
       return true;
-
     default:
       return false;
     }
-  } else if (op->getNcontrols() == 2) {
+  } else if (op->getNtargets() == 1) {
     switch (op->getType()) {
     case qc::OpType::X:
     case qc::OpType::Z:
+    case qc::OpType::RZ:
       return true;
     default:
       return false;