✨ Add Dynamic QFT (#946)

## Description

Adds the dynamic_qft benchmark, a dynamic-circuit version of QFT using
mid-circuit measurements and classically controlled phase gates. The
implementation matches the regular QFT benchmark’s decomposed register
order, measurement mapping, source/target qubit associations, and phase
angles.

Fixes #798

Assisted by: GPT 5.5 via Codex

## Checklist:

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- [x] The pull request only contains commits that are focused and
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- [x] I have added appropriate tests that cover the new/changed
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- [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
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Author: flowerthrower

CHANGELOG.md

@@ -11,6 +11,7 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 
 ### Added
 
+- ✨ Add Dynamic Quantum Fourier Transform benchmark ([#946]) ([**@flowerthrower**])
 - ✨ Add Iterative Quantum Phase Estimation (IQPE) benchmark ([#925]) ([**@johanneswittmann9**])
 
 ### Fixed
@@ -130,6 +131,7 @@ _📚 Refer to the [GitHub Release Notes] for previous changelogs._
 
 <!-- PR links -->
 
+[#946]: https://github.com/munich-quantum-toolkit/bench/pull/946
 [#925]: https://github.com/munich-quantum-toolkit/bench/pull/925
 [#914]: https://github.com/munich-quantum-toolkit/bench/pull/914
 [#895]: https://github.com/munich-quantum-toolkit/bench/pull/895

src/mqt/bench/benchmarks/dynamic_qft.py

@@ -0,0 +1,46 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# Copyright (c) 2025 - 2026 Munich Quantum Software Company GmbH
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Dynamic QFT benchmark definition."""
+
+from __future__ import annotations
+
+import numpy as np
+from qiskit.circuit import ClassicalRegister, QuantumCircuit, QuantumRegister
+
+from ._registry import register_benchmark
+
+
+@register_benchmark("dynamic_qft", description="Dynamic Quantum Fourier Transformation (QFT)")
+def create_circuit(num_qubits: int) -> QuantumCircuit:
+    """Returns a quantum circuit implementing the Dynamic Quantum Fourier Transform algorithm.
+
+    More details on the “Semiclassical Fourier Transform for Quantum Computation” can be found in https://arxiv.org/abs/quant-ph/9511007
+
+    Arguments:
+        num_qubits: number of qubits of the returned quantum circuit
+
+    Returns:
+        QuantumCircuit: a quantum circuit implementing the Dynamic Quantum Fourier Transform algorithm
+    """
+    q = QuantumRegister(num_qubits, "q")
+    meas = ClassicalRegister(num_qubits, "meas")
+    qc = QuantumCircuit(q, meas, name="dynamic_qft")
+
+    # Mirror index order of regular "qft" benchmark
+    for qubit in reversed(range(num_qubits)):
+        for source in reversed(range(qubit + 1, num_qubits)):
+            source_bit = num_qubits - source - 1
+            with qc.if_test((meas[source_bit], 1)):
+                qc.p(np.pi * (2.0 ** (qubit - source)), q[qubit])
+
+        bit = num_qubits - qubit - 1
+        qc.h(q[qubit])
+        qc.measure(q[qubit], meas[bit])
+
+    return qc

tests/test_bench.py

@@ -308,6 +308,33 @@ def test_dynamic_ghz_circuit_structure(num_qubits: int) -> None:
     assert ops.get("if_else", 0) == expected_if_test
 
 
+@pytest.mark.parametrize("num_qubits", [1, 2, 3, 7, 10])
+def test_dynamic_qft_circuit_structure(num_qubits: int) -> None:
+    """Verify the structure of the dynamic QFT circuit for various qubit counts."""
+    qc = create_circuit("dynamic_qft", num_qubits)
+
+    # Check quantum and classical registers
+    assert [(qreg.name, qreg.size) for qreg in qc.qregs] == [("q", num_qubits)]
+    assert [(creg.name, creg.size) for creg in qc.cregs] == [("meas", num_qubits)]
+
+    ops: OrderedDict[str, int] = qc.count_ops()
+
+    # Check gate counts
+    expected_phase_gates = num_qubits * (num_qubits - 1) // 2
+    assert ops.get("h", 0) == num_qubits
+    assert ops.get("measure", 0) == num_qubits
+    assert ops.get("if_else", 0) == expected_phase_gates
+    assert (
+        sum(
+            inst.operation.name == "p"
+            for instruction in qc.data
+            if isinstance(instruction.operation, IfElseOp)
+            for inst in instruction.operation.blocks[0].data
+        )
+        == expected_phase_gates
+    )
+
+
 @pytest.mark.parametrize("num_qubits", [17, 34, 51, 68])
 def test_shors_nine_qubit_code_circuit_structure(num_qubits: int) -> None:
     """Test that Shor's 9-qubit code circuits have the expected structure.