Dynamical topological phase realized in a trapped-ion quantum simulator

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases and critical phenomena that exhibit topologically-robust methods to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. However, to date, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry protected topological phase (EDSPT), in a quasiperiodically-driven array of ten $^{171}\text{Yb}^+$ hyperfine qubits in Honeywell's System Model H1 trapped-ion quantum processor. This phase exhibits edge qubits that are dynamically protected from control errors, cross-talk, and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit-array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information.