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 $\mathbb{R}^3$.

翻译：我们构建了一个三维泡利稳定子哈密顿量，其在非零温度下与热库耦合时，基态空间可将一个量子比特指数级长时间编码。该构造通过对种子哈密顿量递归应用一系列变换，在保持$\mathbb{R}^3$中几何局域性的同时，延长了编码量子比特的存储寿命。