  We introduce and study the discrete-time version of the Quantum East model,
an interacting quantum spin chain inspired by simple kinetically constrained
models of classical glasses. Previous work has established that its
continuous-time counterpart displays a disorder-free localisation transition
signalled by the appearance of an exponentially large (in the volume) family of
non-thermal, localised eigenstates. Here we combine analytical and numerical
approaches to show that: i) The transition persists for discrete times, in
fact, it is present for any finite value of the time step apart from a zero
measure set; ii) It is directly detected by following the non-equilibrium
dynamics of the fully polarised state. Our findings imply that the transition
is currently observable in state-of-the-art platforms for digital quantum
simulation.
