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The conjecture says that even an estimate with a fixed fractional error stays that hard.","posed_since":"","precise":"Let $H = \\sum_{i=1}^m H_i$ be a $k$-local Hamiltonian on $n$ qubits with $\\mid\\mid H_i\\mid\\mid \\le 1$ and each qubit in $O(1)$ terms. Is it QMA-hard to approximate its ground energy to additive error $\\epsilon m$ for some constant $\\epsilon > 0$? An answer is a proof of QMA-hardness, or a proof that the problem lies in NP (or a smaller class).","problem_ref":"a3b98bfc838655c2c7a1abb8e6c9bddedeaddc2f66784b8c1121de63659e139d","references":"","settled_by":"A QMA-hardness reduction for constant relative precision, or a classical-witness algorithm for it.","status_note":"The weaker NLTS conjecture was proved in 2022 (Anshu, Breuckmann and Nirkhe, arXiv:2206.13228); the full conjecture is open.","title":"The quantum PCP conjecture for local 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