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The search of hardware-compatible strategies for solving NP-hardcombinatorial optimization problems (COPs) is an important challenge of today scomputing research because of their wide range of applications in real worldoptimization problems. Here, we introduce an unconventional scalable approachto face maximum satisfiability problems (Max-SAT) which combines probabilisticcomputing with p-bits, parallel tempering, and the concept of invertible logicgates. We theoretically show the spintronic implementation of this approachbased on a coupled set of Landau-Lifshitz-Gilbert equations, showing apotential path for energy efficient and very fast (p-bits exhibiting ns timescale switching) architecture for the solution of COPs. The algorithm isbenchmarked with hard Max-SAT instances from the 2016 Max-SAT competition(e.g., HG-4SAT-V150-C1350-1.cnf which can be described with 2851 p-bits),including weighted Max-SAT and Max-Cut problems.

Spintronics-compatible approach to solving maximum satisfiability problems with probabilistic computing, invertible logic and parallel tempering