Compute engine circuitry configured to represent a spin network mapping of a graph representing a combinatorial optimization problem includes a plurality of ring oscillator cells, each of which includes a ring oscillator having an oscillator output, at least one coupling block, and a read block. Each coupling block connects the ring oscillator of the cell to the ring oscillator of one of a plurality of neighboring cells to form a coupled ring oscillator. The read block generates a state output for each coupled ring oscillator that indicates whether the coupled ring oscillator is in one of a same-phase state, in which the connected ring oscillators oscillate in phase with each other, and an opposite-phase state, in which the connected ring oscillators oscillate in an opposite phase from each other. A controller is configured to output a total energy of the mapping based on the state outputs.
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