  We introduce a model of non-unitary quantum dynamics that exhibits infinitely
long-lived discrete spatiotemporal order robust against any unitary or
dissipative perturbation. Ergodicity is evaded by combining a sequence of
projective measurements with a local feedback rule that is inspired by Toom's
`North-East-Center' classical cellular automaton. The measurements in question
only partially collapse the wavefunction of the system, allowing some quantum
coherence to persist. We demonstrate our claims using numerical simulations of
a Clifford circuit in two spatial dimensions which allows access to large
system sizes, and also present results for more generic dynamics on modest
system sizes. We also devise explicit experimental protocols realising this
dynamics using one- and two-qubit gates that are available on present-day
quantum computing platforms.
