Energy-efficient superparamagnetic Ising machine and its application to traveling salesman problems

The growth of artificial intelligence and IoT has created a significant computational load for solving non-deterministic polynomial-time (NP)-hard problems, which are difficult to solve using conventional computers. The Ising computer, based on the Ising model and annealing process, has been highly sought for finding approximate solutions to NP-hard problems by observing the convergence of dynamic spin states. However, it faces several challenges, including high power consumption due to artificial spins and randomness emulated by complex circuits, as well as low scalability caused by the rapidly growing connectivity when considering large-scale problems. Here, we present an experimental Ising annealing computer based on superparamagnetic tunnel junctions (SMTJs) with all-to-all connections, which successfully solves a 70-city travelling salesman problem (4761-node Ising problem). By taking advantage of the intrinsic randomness of SMTJs, implementing a proper global annealing scheme, and using an efficient algorithm, our SMTJ-based Ising annealer shows superior performance in terms of power consumption and energy efficiency compared to other Ising schemes. Additionally, our approach provides a promising way to solve complex problems with limited hardware resources. Moreover, we propose a crossbar array architecture for scalable integration using conventional magnetic random access memories. Our results demonstrate that the SMTJ-based Ising annealing computer with high energy efficiency, speed, and scalability is a strong candidate for future unconventional computing schemes.