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Title: Existence of a self-correcting quantum memory in three dimensions
Plain: A four-dimensional version of a known quantum code keeps its stored qubit safe from heat for a time that grows exponentially with size, and two-dimensional versions of this code family cannot. Whether some three-dimensional system can do it was open for over twenty years.
Precise: Does there exist a family of geometrically local Hamiltonians on qubits in $R^{3}$, with bounded interaction strength and qubit density, whose ground space encodes at least one qubit with a memory time, under a weakly coupled thermal bath (Davies dynamics), that grows as $\operatorname{exp}(c L^{b})$, $b > 0$, at some fixed temperature $T > 0$?
Settled by: A proof of exponential memory time for an explicit 3D local Hamiltonian, checked independently.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: A May 2026 preprint (Balasubramanian, Davydova and Lin, arXiv:2605.10943) constructs a non-translation-invariant 3D Pauli stabilizer Hamiltonian with provably exponential memory time below a critical temperature; independent verification is pending.
Posed since: (empty)