✨ Add Python interface improvements and Qiskit export support (#859)

## Description

This pull request introduces several changes to enhance Python
interoperability and integration with Qiskit. Key updates include:
- Adding a method to natively export `QuantumComputations` objects to
Qiskit `QuantumCircuit`.
- Exposing registers from `QuantumComputation` in the Python interface.
- Addressing issues with calling `name` and `end` on Python registers.
- Fixing the implementation of `__iter__` and providing `items` for
`Permutation`.
- Enhancing `CompoundOperation` to implement the
`MutableSequence[Operation]` interface.

These changes provide better usability and extend functionality when
using the library in Python environments.

Fixes #35

## Checklist:

- [x] The pull request only contains commits that are related to it.
- [x] I have added appropriate tests and documentation.
- [x] I have made sure that all CI jobs on GitHub pass.
- [x] The pull request introduces no new warnings and follows the
project's style guidelines

include/mqt-core/ir/operations/CompoundOperation.hpp

@@ -189,7 +189,16 @@ class CompoundOperation final : public Operation {
     return ops.insert(iter, std::forward<decltype(op)>(op));
   }
 
+  // Element access (pass-through)
   [[nodiscard]] const auto& at(const std::size_t i) const { return ops.at(i); }
+  [[nodiscard]] auto& operator[](const std::size_t i) { return ops[i]; }
+  [[nodiscard]] const auto& operator[](const std::size_t i) const {
+    return ops[i];
+  }
+  [[nodiscard]] auto& front() { return ops.front(); }
+  [[nodiscard]] const auto& front() const { return ops.front(); }
+  [[nodiscard]] auto& back() { return ops.back(); }
+  [[nodiscard]] const auto& back() const { return ops.back(); }
 };
 } // namespace qc
 

pyproject.toml

@@ -138,6 +138,7 @@ filterwarnings = [
   # Qiskit 1.3 deprecations
   'ignore:.*``qiskit.dagcircuit.dagcircuit.DAGCircuit.*`` is deprecated as of qiskit 1.3.0.*:DeprecationWarning:',
   'ignore:.*``qiskit.circuit.library.standard_gates.x.*`` is pending deprecation as of qiskit 1.3.*:PendingDeprecationWarning:',
+  'ignore:.*``qiskit.circuit.instruction.Instruction.condition`` is deprecated as of qiskit 1.3.0.*:DeprecationWarning:',
 ]
 log_cli_level = "info"
 testpaths = ["test/python"]

src/mqt/core/ir/__init__.pyi

@@ -7,7 +7,7 @@
 
 """MQT Core IR  - The MQT Core Intermediate Representation (IR) module."""
 
-from collections.abc import Iterable, Iterator, Mapping, MutableMapping, MutableSequence, Sequence
+from collections.abc import ItemsView, Iterable, Iterator, Mapping, MutableMapping, MutableSequence, Sequence
 from os import PathLike
 from typing import overload
 
@@ -59,6 +59,9 @@ class Permutation(MutableMapping[int, int]):
     def __iter__(self) -> Iterator[int]:
         """Return an iterator over the indices of the permutation."""
 
+    def items(self) -> ItemsView[int, int]:
+        """Return an iterable over the items of the permutation."""
+
     def __len__(self) -> int:
         """Return the number of indices in the permutation."""
 
@@ -353,6 +356,18 @@ class QuantumComputation(MutableSequence[Operation]):
             The unified quantum register.
         """
 
+    @property
+    def qregs(self) -> dict[str, QuantumRegister]:
+        """The quantum registers in the quantum computation."""
+
+    @property
+    def cregs(self) -> dict[str, ClassicalRegister]:
+        """The classical registers in the quantum computation."""
+
+    @property
+    def ancregs(self) -> dict[str, QuantumRegister]:
+        """The ancillary registers in the quantum computation."""
+
     # --------------------------------------------------------------------------
     #                  Initial Layout and Output Permutation
     # --------------------------------------------------------------------------

src/mqt/core/ir/operations.pyi

@@ -6,7 +6,7 @@
 # Licensed under the MIT License
 
 from abc import ABC, abstractmethod
-from collections.abc import Mapping, Sequence
+from collections.abc import Iterable, Mapping, MutableSequence, Sequence
 from typing import ClassVar, overload
 
 from .registers import ClassicalRegister
@@ -665,7 +665,7 @@ class NonUnitaryOperation(Operation):
     def invert(self) -> None:
         """Non-unitary operations are, per definition, not invertible."""
 
-class CompoundOperation(Operation):
+class CompoundOperation(Operation, MutableSequence[Operation]):
     """Compound quantum operation.
 
     This class is used to aggregate and group multiple operations into a single
@@ -712,12 +712,57 @@ class CompoundOperation(Operation):
             This gives direct access to the operations in the compound operation.
         """
 
+    @overload
+    def __setitem__(self, idx: int, op: Operation) -> None:
+        """Set the operation at the given index.
+
+        Args:
+            idx: The index of the operation to set.
+            op: The operation to set at the given index.
+        """
+
+    @overload
+    def __setitem__(self, idx: slice, ops: Iterable[Operation]) -> None:
+        """Set the operations in the given slice.
+
+        Args:
+            idx: The slice of operations to set.
+            ops: The operations to set in the given slice.
+        """
+
+    @overload
+    def __delitem__(self, idx: int) -> None:
+        """Delete the operation at the given index.
+
+        Args:
+            idx: The index of the operation to delete.
+        """
+
+    @overload
+    def __delitem__(self, idx: slice) -> None:
+        """Delete the operations in the given slice.
+
+        Args:
+            idx: The slice of operations to delete.
+        """
+
+    def insert(self, idx: int, op: Operation) -> None:
+        """Insert an operation at the given index.
+
+        Args:
+            idx: The index to insert the operation at.
+            op: The operation to insert.
+        """
+
     def append(self, op: Operation) -> None:
         """Append an operation to the compound operation."""
 
     def empty(self) -> bool:
         """Check if the compound operation is empty."""
 
+    def clear(self) -> None:
+        """Clear all operations in the compound operation."""
+
     def add_control(self, control: Control) -> None:
         """Add a control to the operation.
 

src/mqt/core/plugins/qiskit/__init__.py

@@ -0,0 +1,18 @@
+# Copyright (c) 2025 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""MQT Qiskit Plugin."""
+
+from __future__ import annotations
+
+from .mqt_to_qiskit import mqt_to_qiskit
+from .qiskit_to_mqt import qiskit_to_mqt
+
+__all__ = [
+    "mqt_to_qiskit",
+    "qiskit_to_mqt",
+]