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Tripartite Kerr Soliton Ising Machine for Combinatorial Optimization
Nitesh Chauhan1, Yan Jin1, Jizhao Zang1
1University of Colorado, National Institute of Standards and Technology, Time and Frequency Division, Boulder, Colorado, USA and Department of Physics, Boulder, Colorado, USA.
Abstract:
We introduce and explore a Kerr soliton Ising machine with all-to-all connectivity and up to tripartite (cubic) interactions, unlocking efficient approaches for combinatorial optimization. The machine is an ensemble of solitons in a Kerr resonator, where a programmable optoelectronic feedback circuit generates amplitude mixing terms involving up to three arbitrary soliton spins in the system Hamiltonian. This capability offers a key advantage for solving canonical NP-complete problems like Boolean satisfiability (SAT) with three literal clauses, substantially reducing the spin overhead compared to quadratic-only Ising mappings. To explore our cubic Ising machine, we solve randomly generated 3-SAT instances of 250 variables and 1000 clauses, approaching the intrinsic satisfiability threshold. Our results highlight Kerr solitons as a flexible and energy-efficient analog computing substrate, with the potential to address challenges in combinatorial optimization, artificial intelligence, and machine learning.
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