Bernstein-Vazirani (4-bit hidden string) referencing arXiv:2607.06033

Primitive: Bernstein-Vazirani. This card runs the textbook Bernstein-Vazirani (BV) algorithm, the primitive referenced by the arXiv paper linked above. The paper studies a variant - the initialization-free (IF) BV algorithm - in which an arbitrary ancilla state is allowed on the oracle register. As its abstract states, it builds on Naseri et al. [Phys. Rev. A 106, 062429 (2022); arXiv:2205.13610], derives an explicit formula for the performance (the optimal average success probability over all measurements) of the probabilistic IF-BV algorithm, and examines which quantum resources are essential to that performance. We do not reproduce or evaluate any of those analytical results.

What we ran. We prepared the standard single-query BV circuit for a 4-bit hidden string s = 1011. Four query qubits are placed in uniform superposition; a phase-kickback ancilla (prepared in the |-> state) receives a CNOT from each query qubit i for which s_i = 1 (here qubits 0, 2, and 3), implementing the oracle f(x) = s.x. A final layer of Hadamards on the query register maps the accumulated phase pattern back to the computational basis, so an ideal device recovers s in a single query.

Scope. This is a deterministic state-vector simulator run on Provenova (4096 shots, seed 1729), not a reproduction of the paper's results and not an implementation of the initialization-free variant the authors analyze. It is included only as an attributed, faithful small reproduction of the classical textbook primitive that the paper references. Nothing here implies endorsement by the authors.