Revision 1

Accepted · first revision · record

Title: A classically hard equilibrium observable an analog simulator can reach
Plain: Hot quantum systems turn out to be easy for classical computers. The question is whether any cooled simulator can reach a regime that is both hard for classical methods and accessible to the hardware.
Precise: Identify a family of local Hamiltonians and a temperature $T$ for which estimating a local observable in the Gibbs state is classically hard (under standard complexity assumptions), while an analog simulator with realistic cooling can prepare that Gibbs state to accuracy $\epsilon$. Answer: an explicit family with a hardness proof and a preparation scheme.
Settled by: A complexity-theoretic hardness proof for a specific Hamiltonian family plus a cooling scheme with proven or measured accuracy.
Kind: well-posed
Answer type: identification
References: (empty)
Literature status: open
Status note: 2024 results showed Gibbs states above a constant temperature are efficiently preparable classically (Bakshi, Liu, Moitra, Tang), so any advantage must be at low T.
Posed since: (empty)