  Nanomagnetic logic, which makes use of arrays of dipolar-coupled single
domain nanomagnets for computation, holds promise as a low power alternative to
traditional computation with CMOS. Beyond the use of nanomagnets for Boolean
logic, nanomagnets can also be exploited for non-deterministic computational
schemes such as edge detection in images and for solving the traveling salesman
problem. Here, we demonstrate the potential of arrangements of thermally-active
nanomagnets based on artificial spin ice for both deterministic and
probabilistic computation. This is achieved by engineering structures that
follow particular thermal relaxation pathway consisting of a sequence of
reorientations of magnet moments from an initial field-set state to a final low
energy output state. Additionally, we demonstrate that it is possible to tune
the probability of attaining a particular final low-energy state, and therefore
the likelihood of a given output, by modifying the intermagnet distance.
Finally, we experimentally demonstrate a scheme to connect several
computational building blocks for complex computation.
