Submit progress

on Learning Hamiltonians using only long time evolutions

The statement

Let $H=\sum_{a=1}^m\lambda_a E_a$ be an $n$ -qubit geometrically local Hamiltonian, where $E_a$ are known constant-support Pauli products and $-1\leq\lambda_a\leq1$ . Learn its coefficients to additive error $\varepsilon$ , given access only to $\rho\mapsto e^{-iHt}\rho e^{iHt}$ for $t>100$ . Is time-efficient learning possible, and can it achieve total evolution time $O(\log(n)/\varepsilon)$ ?

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.