  Novel dynamical phases that violate ergodicity have been a subject of
extensive research in recent years. A periodically driven system is naively
expected to lose all memory of its initial state due to thermalization, yet
this can be avoided in the presence of many-body localization. A discrete time
crystal represents a driven system whose local observables spontaneously break
time translation symmetry and retain memory of the initial state indefinitely.
Here we report the observation of a discrete time crystal on a chain consisting
of 57 superconducting qubits on a state--of--the--art quantum computer. We
probe random initial states and compare the cases of vanishing and finite
disorder to distinguish many-body localization from pre-thermal dynamics. We
further report results on the dynamical phase transition between the discrete
time crystal and a thermal regime, which is observed via critical fluctuations
in the system's sub-harmonic frequency response and a significant speed-up of
spin depolarisation.
