Shankar Balasubramanian, Margarita Davydova, Ting-Chun Lin

We construct a 3D Pauli stabilizer Hamiltonian whose ground state space can encode a qubit for exponential time when coupled to a bath at non-zero temperature. Our construction recursively applies a sequence of transformations to a seed Hamiltonian that increases the memory lifetime of the encoded qubit while maintaining geometric locality in $\mathbb{R}^3$.