Evolution-time–optimal certification without locality assumptions

Determine whether certification of equality versus ε-far (in normalized Frobenius norm) for arbitrary n‑qubit Hamiltonians H and H0—using only forward time‑evolution access to e^{-iHt} (and a known specification H0 or access to e^{-iH0 t})—can be achieved with total evolution time O(1/ε) (Heisenberg scaling) without any locality assumptions and without inverse or controlled‑time evolution.

Background

The paper proves an O(1/ε) total evolution time algorithm for certifying constant‑local (k‑local) Hamiltonians via access to their dynamics, achieving Heisenberg scaling without inverse or controlled evolution. This is the first optimal certification result in the time‑evolution access model under locality.

For general (non‑local) Hamiltonians, prior optimal certification protocols rely on inverse or controlled‑time evolution. The authors explicitly ask whether Heisenberg‑optimal certification is possible when locality is removed, clarifying whether locality is essential or merely technical in enabling optimal protocols.