  We investigate the evolution of complexity and entanglement following a
quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger
model. We demonstrate that complexity can detect quantum phase transitions and
shows signatures of revivals; this observation provides a practical advantage
in information processing. We also show that the complexity saturates much
faster than the entanglement entropy in this system, and we provide a physical
argument for this. Finally, we demonstrate that complexity is a less sensitive
probe of topological order, compared with measures of entanglement.
