✨ Dynamical QFT

[morrishuismans]

Note

This issue is part of unitaryHACK 2026; note that you have to be registered to complete this issue. Learn more about the PR review process here. 

A message from unitaryHACK about AI Slop: "While we allow LLMs as collaborative tools, fully AI-generated PRs are prohibited. Maintainers have the right to reject any contribution that appears to be automated or lacks human oversight."

Learn more about unitaryHACK rules and opportunities here and about the usage of AI, in particular, here!

Please also read the information on the general idea behind dynamic circuit benchmarks in the parent issue. You may take inspiration from the already implemented dynamic circuit benchmarks.

Problem Statement

The Quantum Fourier Transform is one of the most important subroutines in quantum circuits, particularly in Shor's factoring algorithm. The QFT algorithm, however, uses many 2-qubit gates (O(N^2)) and assumes all-to-all connectivity, which is not applicable to most hardware platforms. To this end, a dynamical circuit version of this algorithm has been developed to resolve some of these issues.

This dynamical circuit version of the QFT, immediately followed by measurement (QFT + M), uses O(n) mid-circuit measurements and classical feed-forward instead of O(n^2) 2-qubit gates and removes the assumption of all-to-all connectivity.

Relevant Literature
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.150602

Proposed Solution

Briefly describe the intended benchmark design in the comments below.
A maintainer will review the proposal, help refine it if needed, and approve the implementation once the design is clear.

[burgholzer]

@Vinny010 What you propose sounds reasonable. Feel free to open up a PR. Do not forget to read (and follow) the guidelines on the usage of AI that apply when contributing to this repository.

[arvizu-god]

Hi! Interested in contributing to this issue, but I have a few questions to narrow the contribution down.

1. The parent issue doesn't say that much to me about what you are expecting for this challenge. What benchmark do you expect? Off the top of my head, I thinking of comparing the QFT and D-QFT through some metrics such as: decomposition of transpiled gates in qiskit (how many gates and what kind of gate are used in each one), fidelity for each one, etc. Is there an online resource you can point me to? I mean, we can reproduce the comparisons that Baumer et.al present on their paper, but I dont think that what you are looking for.
2. What is the expected file for this challenge? A jupyter notebook? A package?

A little bit more detail would be very helpful!

[FedorShind]

Hi, I’d like to also pick this up

I plan to implement this as dynamic_qft, following the semiclassical QFT-followed-by-measurement construction from the linked paper. The circuit would process qubits from high to low, measure each qubit after its Hadamard, and replace the usual controlled-phase gates with classically controlled phase rotations on the remaining lower index qubits. The final QFT swaps would be handled through the classical measurement order.

Btw: also looked at the previous PR feedback, so I’d keep the naming consistent as "Dynamic QFT", use the usual c classical register name, add a docstring explaining the construction and reference, handle very small phase angles safely, and include tests plus a changelog entry.

Does this match what you want for this issue? Thanks in advance for answer