Simulated, not reproduced: textbook Bernstein-Vazirani with a 9-bit hidden string

This card runs the textbook Bernstein-Vazirani circuit on the Provenova simulator. It is inspired by arXiv:2608.04780, which is the reason we picked this primitive and nothing more. The paper is not reproduced here, and its authors have not reviewed or endorsed this card.

Restating only what that paper's abstract says: it describes dynamic quantum circuits as circuits using mid-circuit measurement, qubit reset and reuse, and classical feed-forward control. The authors demonstrate advantages of such circuits on a single hybrid superconducting qubit-cavity processor, in which a high-dimensional cavity qudit is the computational register and a dispersively coupled transmon ancilla is repeatedly measured, reset and reused to enable dynamic control. On that device they report a 10-bit Bernstein-Vazirani algorithm with an average success probability of 82%, an 8-bit quantum phase-estimation protocol with estimation errors below 10^-3, and the first dynamic-circuit implementation of Shor's algorithm on a superconducting platform, factoring 15 over all coprime bases with squared statistical overlap values above 99.8%. Those are the paper's own hardware figures. Nothing on this card measures, checks or supports any of them.

What we actually ran: a static, fully unitary, 10-qubit circuit — nine data qubits plus one phase-kickback ancilla — as a deterministic, seeded simulator run. The ancilla starts in the minus state, Hadamards cover the data register, the oracle is one CNOT into the ancilla from each data qubit whose hidden-string bit is 1, and a second Hadamard layer follows. In the ideal statevector that leaves the hidden string 101101001 on qubits 0 through 8, written qubit 0 first. The string is our choice; the abstract states none. We use 9 bits rather than the paper's 10 because the textbook n+1-qubit construction at 10 bits exceeds this platform's 10-qubit limit.

Two caveats for reading the histogram. The ancilla is never uncomputed, so in the ideal statevector its bit is unbiased and the weight splits evenly over two 10-bit outcomes that agree on qubits 0 through 8. And this is a simulated backend carrying a calibration-driven error model — no hardware is involved, and none of the paper's hardware is involved — so the sampled shots need not land only on that ideal support. Do not read this result next to the paper's 82%.