  Mappings of classical computation onto statistical mechanics models have led
to remarkable successes in addressing some complex computational problems.
However, such mappings display thermodynamic phase transitions that may prevent
reaching solution even for easy problems known to be solvable in polynomial
time. Here we map universal reversible classical computations onto a planar
vertex model that exhibits no bulk classical thermodynamic phase transition,
independent of the computational circuit. Within our approach the solution of
the computation is encoded in the ground state of the vertex model and its
complexity is reflected in the dynamics of the relaxation of the system to its
ground state. We use thermal annealing with and without 'learning' to explore
typical computational problems. We also construct a mapping of the vertex model
into the Chimera architecture of the D-Wave machine, initiating an approach to
reversible classical computation based on state-of-the-art implementations of
quantum annealing.
