✨ Add support for multi-controlled gates to ZX package (backport #1380) (#1651)

## Description

Add CRZ, MCX, MCZ, MCRZ functionality to ZX package.
Add convenience addCCZ function as it avoids one additional Hardamard
edge (optimizes it away).

Fixes #1357

## Checklist:


- [X] The pull request only contains commits that are focused and
relevant to this change.
- [X] I have added appropriate tests that cover the new/changed
functionality.
- [X] ~~I have updated the documentation to reflect these changes.~~
- [x] I have added entries to the changelog for any noteworthy
additions, changes, fixes, or removals.
- [x] ~~I have added migration instructions to the upgrade guide (if
needed).~~
- [x] The changes follow the project's style guidelines and introduce no
new warnings.
- [x] The changes are fully tested and pass the CI checks.
- [X] I have reviewed my own code changes.



(cherry picked from commit 2497aee)

---------

Co-authored-by: Keefe Huang <30915130+keefehuang@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Daniel Haag <121057143+denialhaag@users.noreply.github.com>

Author: 4 people

CHANGELOG.md

@@ -11,6 +11,7 @@ This project adheres to [Semantic Versioning], with the exception that minor rel
 
 ### Added
 
+- ✨ Add support for multi-controlled gates to ZX package ([#1380]) ([**@keefehuang**])
 - ✨ Add Sampler and Estimator Primitives to the QDMI-Qiskit Interface ([#1507]) ([**@marcelwa**])
 
 ### Changed
@@ -342,6 +343,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 [#1383]: https://github.com/munich-quantum-toolkit/core/pull/1383
 [#1382]: https://github.com/munich-quantum-toolkit/core/pull/1382
 [#1381]: https://github.com/munich-quantum-toolkit/core/pull/1381
+[#1380]: https://github.com/munich-quantum-toolkit/core/pull/1380
 [#1378]: https://github.com/munich-quantum-toolkit/core/pull/1378
 [#1375]: https://github.com/munich-quantum-toolkit/core/pull/1375
 [#1371]: https://github.com/munich-quantum-toolkit/core/pull/1371
@@ -485,6 +487,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 [**@lsschmid**]: https://github.com/lsschmid
 [**@marcelwa**]: https://github.com/marcelwa
 [**@lirem101**]: https://github.com/lirem101
+[**@keefehuang**]: https://github.com/keefehuang
 
 <!-- General links -->
 

include/mqt-core/zx/FunctionalityConstruction.hpp

@@ -85,8 +85,14 @@ class FunctionalityConstruction {
                       EdgeType type = EdgeType::Simple);
   static void addCphase(ZXDiagram& diag, const PiExpression& phase, Qubit ctrl,
                         Qubit target, std::vector<Vertex>& qubits);
-  static void addSwap(ZXDiagram& diag, Qubit target, Qubit target2,
+  static void addMcphase(ZXDiagram& diag, const PiExpression& phase,
+                         const std::vector<Qubit>& controls, Qubit target,
+                         std::vector<Vertex>& qubits);
+  static void addSwap(ZXDiagram& diag, Qubit target1, Qubit target2,
                       std::vector<Vertex>& qubits);
+  static void addMcswap(ZXDiagram& diag, const std::vector<Qubit>& controls,
+                        Qubit target1, Qubit target2,
+                        std::vector<Vertex>& qubits);
   static void
   addRzz(ZXDiagram& diag, const PiExpression& phase, Qubit target,
          Qubit target2, std::vector<Vertex>& qubits,
@@ -99,6 +105,11 @@ class FunctionalityConstruction {
   addRzx(ZXDiagram& diag, const PiExpression& phase, Qubit target,
          Qubit target2, std::vector<Vertex>& qubits,
          const std::optional<double>& unconvertedPhase = std::nullopt);
+  static void
+  addMcrzz(ZXDiagram& diag, const PiExpression& phase,
+           const std::vector<Qubit>& controls, Qubit target, Qubit target2,
+           std::vector<Vertex>& qubits,
+           const std::optional<double>& unconvertedPhase = std::nullopt);
   static void addDcx(ZXDiagram& diag, Qubit qubit1, Qubit qubit2,
                      std::vector<Vertex>& qubits);
   static void
@@ -113,6 +124,22 @@ 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 addCrx(ZXDiagram& diag, const PiExpression& phase, Qubit control,
+                     Qubit target, std::vector<Vertex>& qubits);
+  static void addMcrx(ZXDiagram& diag, const PiExpression& phase,
+                      const std::vector<Qubit>& controls, Qubit target,
+                      std::vector<Vertex>& qubits);
+  static void addCrz(ZXDiagram& diag, const PiExpression& phase, Qubit control,
+                     Qubit target, std::vector<Vertex>& qubits);
+  static void addMcrz(ZXDiagram& diag, const PiExpression& phase,
+                      std::vector<Qubit> controls, Qubit target,
+                      std::vector<Vertex>& qubits);
+  static void addMcx(ZXDiagram& diag, std::vector<Qubit> controls, Qubit target,
+                     std::vector<Vertex>& qubits);
+  static void addMcz(ZXDiagram& diag, const std::vector<Qubit>& controls,
+                     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,