Ising Machines Based on Probabilistic Computing with P-Bits

Probabilistic computing with p-bits is a computing paradigm which has been proposed as a potential tool for dealing with different tasks such as inference. The identification of a strategy and the design of a hardware realization of probabilistic computers is very active nowadays.<br/>In addition, it is very promising for the calculation of the ground state of an Ising Hamiltonian, i.e. to implement an Ising machine, and hence can have an impact in the solution of combinatorial optimization problems which can be mapped into the Ising model. Currently, the research on Ising machines is growing in the light of the fact they have a hardware-friendly implementation, it is necessary a binary state variable (Ising spin) together with a multiply and accumulate operation. It can be realized with semiconductor technology, optics, and spintronics. In particular, most of the efforts have been focused on the use of parametrically-driven oscillators to generate the binarization of the oscillator phase necessary to define the Ising spin. Those implementations have been mainly benchmarked with max-cut optimization combinatorial problems. Recently, it has been proposed the implementation of invertible logic gates, within the framework of probabilistic computing, with the aim to solve the classes of combinatorial optimization problems which can be described by logic circuits. The procedure, proposed for the first time for memcomputing, is based on the creation of the logic circuits representing the specific problem to solve, the replacement of the standard logic gates with the invertible logic gates, and the clamping of the outputs in order to let the circuit working in reverse.<br/>In the talk, I will review our recent results on Ising machines (IMs) and their potential hardware implementation with spintronic technology focusing on oscillator-based IMs and IMs built with p-bits (probabilistic computing) [1].<br/>This computing paradigm is very promising to solve combinatorial optimization problems (COPs), which are a class of mathematical problems that have important applications in a variety of industrial and scientific fields, which span from logistics to geoscience, from water distribution network design to job scheduling. Many of these, such as maximum cut (Max-Cut), maximum Boolean satisfiability (max-SAT) or the travelling salesman problem, are NP-complete or NP-hard, meaning in their worst-case instances they have no polynomial-time solution.<br/>We show how the probabilistic computing can be used to solve max-sat instances (the other problems can be mapped on them) beating state-of-the art solvers having a time-to-solution to 95% at least one order of magnitude smaller [2].<br/>[1] A. Grimaldi, L. Sánchez-Tejerina, N. Anjum Aadit, S. Chiappini, M. Carpentieri, K. Camsari, and G. Finocchio, Phys. Rev. Appl. <b>17</b>, 024052 (2022).<br/>[2] N. A. Aadit, A. Grimaldi, M. Carpentieri, L. Theogarajan, J. M. Martinis, G. Finocchio, and K. Y. Camsari, Nat. Electron. <b>5</b>, 460 (2022).