Tripartite Kerr Soliton Ising Machine for Combinatorial Optimization

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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.
Funding Information
  • Defense Advanced Research Projects Agency (FA8750-23-C-0539)
  • Air Force Office of Scientific Research (FA9550-20-1-0004)
  • Air Force Office of Scientific Research (19RT1019)
  • National Institute of Standards and Technology

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