Observation of topological prethermal strong zero modes

Symmetry-protected topological phases cannot be described by any local order parameter and are beyond the conventional symmetry-breaking paradigm for understanding quantum matter. They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations. In clean, gapped systems without disorder, the stability of these edge modes is restricted to the ground state manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay. Here, we report the observation of a distinct type of topological edge modes, which are protected by emergent symmetries and persist across the system's entire spectrum, in an array of 100 programmable superconducting qubits. In particular, through digital quantum simulation of the dynamics of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between the topological edge modes and bulk thermal excitations can be suppressed by dimerizing the interactions across the two sublattices, dramatically prolonging the lifetime of these edge modes even at infinite temperature. These edge modes are protected not by disorder, but by an emergent U(1)×U(1) symmetry brought on by this dimerization. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence in the dimerized and off-resonant regime, despite the system being disorder-free and far from its ground state. Our results establish a viable digital simulation approach to experimentally study topological matter at finite-temperature and demonstrate a potential route to construct long-lived robust boundary qubits in disorder-free systems.