  We introduce a novel method of quantum emulation of a classical reversible
cellular automaton. By applying this method to a chaotic cellular automaton,
the obtained quantum many-body system thermalizes while all the energy
eigenstates and eigenvalues are solvable. These explicit solutions allow us to
verify the validity of some scenarios of thermalization to this system. We find
that two leading scenarios, the eigenstate thermalization hypothesis scenario
and the large effective dimension scenario, do not explain thermalization in
this model.
