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.
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