Symmetry enhanced boundary qubits at infinite temperature

The $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry protected topological (SPT) phase hosts a robust boundary qubit at zero temperature. At finite energy density, the SPT phase is destroyed and bulk observables equilibrate in finite time. Nevertheless, we predict parametric regimes in which the boundary qubit survives to arbitrarily high temperature, with an exponentially longer coherence time than that of the thermal bulk degrees of freedom. In a dual picture, the persistence of the qubit stems from the inability of the bulk to absorb the virtual $\mathbb{Z}_2 \times \mathbb{Z}_2$ domain walls emitted by the edge during the relaxation process. We confirm the long coherence time by exact diagonalization and connect it to the presence of a pair of conjugate almost strong zero modes. Our results provide a route to experimentally construct long-lived coherent boundary qubits at infinite temperature in disorder-free systems.