✨ Dynamic Bernstein-Vazirani

[TomasVF]

Problem Statement

The Bernstein-Vazirani algorithm is one of the first quantum algorithms. In its standard implementation, the algorithm requires $n$ input qubits and one ancilla qubit.

The dynamic circuit version of Bernstein-Vazirani uses mid-circuit measurements and qubit reuse to reduce the hardware requirements from the $n+1$ qubits to only 2 (one data qubit and one ancilla).

Relevant literature:
https://arxiv.org/abs/2308.00194

Proposed Solution

Bernstein-Vazirani was one of the first algorithms designed to demonstrate a clear quantum advantage. Because of its simple structure and having a deterministic output, the dynamic version serves as an ideal ideal circuit to validate the performance of mid-circuit measurements and qubit reuse.

[flowerthrower]

Thank you @TomasVF for your suggestions and initial work on this. As you have correctly pointed out, the dynamic BV is already part of the Python-only implementation. In fact the circuit seems structually differnt enough to be its own benchmark on the web app. @simon1hofmann, perhaps you could evaluate wether it makes sense to also expose the dynamic BV on the web app.