Super‑polynomial lower bound on stabilizer rank of |H>^{⊗n}

Prove that the stabilizer rank of the n‑qubit magic state |H⟩^{⊗n} grows super‑polynomially with n.

Background

In qubit settings, stabilizer rank quantifies the classical simulation cost of circuits augmented with magic states. Current best lower bounds are only quadratic up to logarithmic factors, and no super‑polynomial lower bounds are known. Establishing a super‑polynomial lower bound for |H⟩^{⊗n} is highlighted as a key open challenge with implications for separating classical and quantum computational capabilities.