✨ Iterative Quantum Phase Estimation (IQPE)

[carlareciofdz]

Note

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Problem Statement

Iterative Quantum Phase Estimation (IQPE)

Iterative Quantum Phase Estimation (IQPE) is a variant of the standard Quantum Phase Estimation algorithm that replaces the quantum Fourier transform with repeated mid-circuit measuremets and classical feed-forward. Hence, it reduces the required number of qubits.

Instead of using multiple ancilla qubits, IQPE reuses a single ancilla qubit for several iterations. After each iteration, the ancilla is measured, and this outcome is used to classically control subsequent rotation gates.

Relevant literature
https://journals.aps.org/pra/pdf/10.1103/PhysRevA.76.030306
First proposed: https://arxiv.org/abs/quant-ph/9511026

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.

[kpassito]

I would propose implementing IQPE as a dynamic-circuit benchmark built around a one-qubit phase-estimation target where the expected phase is known analytically.

Design sketch:

• Use one reusable measurement ancilla plus one eigenstate/preparation qubit, so the benchmark clearly exercises mid-circuit measurement and classical feed-forward instead of a QFT register.
• Parameterize by num_bits / iteration count and a simple phase angle, with defaults that keep the circuit small and deterministic for tests.
• In each iteration, apply the controlled power of a phase unitary, measure/reset the ancilla, and apply the classically conditioned feedback rotation derived from previously measured bits.
• Add the benchmark alongside the existing Qiskit benchmark definitions, include docs explaining IQPE vs standard QPE and its dynamic-circuit constraints, and add tests that check construction succeeds, contains mid-circuit measurements/control-flow, and scales with num_bits.

I can take this direction unless you would prefer a different target unitary or parameter surface.

[burgholzer]

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

[JohannesWittmann9]

hey @burgholzer @flowerthrower ! :)
I did a little hackathon last night, would be great to get some feedback on my opened PR.
The implementation is consitent with other benchmarks and tries to incorporate what you noted in this conversation so far.
LG

[JohannesWittmann9]

hello :) @burgholzer
I have now implemented the feedback.
Additionally, did some local testing again to check for any unexpected errors, especially for higher qubit/iteration numbers.

Everything works, I think this is done! 🚀

One note, I think the failing test is not something based on my code, is it? Maybe an infrastructure error, a re-run will fix it?