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Nanomagnetic logic is promising for low-power computing, and for integration of data processing and memory in the same architecture. In this work the thermal relaxation paths associated with logic operations in artificial spin ice are considered, which involve switching of individual nanomagnets toward a low-energy state. Both monotonic and intermittent paths have been identified, which lend themselves to deterministic and probabilistic computing respectively. Furthermore, the balance of competing relaxation paths can be shifted, which is essential for implementing probabilistic computation---for example, in artificial neural networks where the outcome can be tuned via a feedback loop.
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