Device-Algorithm Co-Design of Ferroelectric Compute-in-Memory In-Situ Annealer for Combinatorial Optimization Problems

Abstract: Combinatorial optimization problems (COPs) are crucial in many applications but are computationally demanding. Traditional Ising annealers address COPs by directly converting them into Ising models (known as direct-E transformation) and solving them through iterative annealing. However, these approaches require vector-matrix-vector (VMV) multiplications with a complexity of $O(n^2)$ for Ising energy computation and complex exponential annealing factor calculations during annealing process, thus significantly increasing hardware costs. In this work, we propose a ferroelectric compute-in-memory (CiM) in-situ annealer to overcome aforementioned challenges. The proposed device-algorithm co-design framework consists of (i) a novel transformation method (first to our known) that converts COPs into an innovative incremental-E form, which reduces the complexity of VMV multiplication from $O(n^2)$ to $O(n)$, and approximates exponential annealing factor with a much simplified fractional form; (ii) a double gate ferroelectric FET (DG FeFET)-based CiM crossbar that efficiently computes the in-situ incremental-E form by leveraging the unique structure of DG FeFETs; (iii) %When feasible solutions are detected, a CiM annealer that approaches the solutions of COPs via iterative incremental-E computations within a tunable back gate-based in-situ annealing flow. Evaluation results show that our proposed CiM annealer significantly reduces hardware overhead, reducing energy consumption by 1503/1716$\times$ and time cost by 8.08/8.15$\times$ in solving 3000-node Max-Cut problems compared to two state-of-the-art annealers. It also exhibits high solving efficiency, achieving a remarkable average success rate of 98\%, whereas other annealers show only 50\% given the same iteration counts.