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Ising-ReRAM: A Low Power Ising Machine ReRAM Crossbar for NP Problems

Everest Bloomer, Irem Didin, Ching-Yi Lin, Sahil Shah

Abstract

Computational workloads are growing exponentially, driving power consumption to unsustainable levels. Efficiently distributing large-scale networks is an NP-Complete problem equivalent to Boolean satisfiability (SAT), making it one of the core challenges in modern computation. To address this, physics and device inspired methods such as Ising systems have been explored for solving SAT more efficiently. In this work, we implement an Ising model equivalence of the 3-SAT problem using a ReRAM crossbar fabricated in the Skywater 130 nm CMOS process. Our ReRAM-based algorithm achieves $91.0\%$ accuracy in matrix representation across iterative reprogramming cycles. Additionally, we establish a foundational energy profile by measuring the energy costs of small sub-matrix structures within the problem space, demonstrating under linear growth trajectory for combining sub-matrices into larger problems. These results demonstrate a promising platform for developing scalable architectures to accelerate NP-Complete problem solving.

Ising-ReRAM: A Low Power Ising Machine ReRAM Crossbar for NP Problems

Abstract

Computational workloads are growing exponentially, driving power consumption to unsustainable levels. Efficiently distributing large-scale networks is an NP-Complete problem equivalent to Boolean satisfiability (SAT), making it one of the core challenges in modern computation. To address this, physics and device inspired methods such as Ising systems have been explored for solving SAT more efficiently. In this work, we implement an Ising model equivalence of the 3-SAT problem using a ReRAM crossbar fabricated in the Skywater 130 nm CMOS process. Our ReRAM-based algorithm achieves accuracy in matrix representation across iterative reprogramming cycles. Additionally, we establish a foundational energy profile by measuring the energy costs of small sub-matrix structures within the problem space, demonstrating under linear growth trajectory for combining sub-matrices into larger problems. These results demonstrate a promising platform for developing scalable architectures to accelerate NP-Complete problem solving.
Paper Structure (11 sections, 4 figures, 2 tables)

This paper contains 11 sections, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Algorithm
  4. Physical ReRAM Fabrication and Characterization
  5. Simulated Supported Units
  6. Benchmarks and Results
  7. Key Graph Kernels: Benchmark
  8. Key Graph Kernels: Results
  9. Full CNF Solving: Benchmark
  10. Full CNF Solving: Results
  11. Conclusion

Figures (4)

  • Figure 1: Flowchart overall process, python and hardware. The numbers correspond to the the algorithm flow discussed in Subsection \ref{['SubSec:Algo']}
  • Figure 2: Illustration of 3-SAT to an Ising Graph.
  • Figure 3: Key subgraph structures, and the average profiled energy states for the Skywater ReRAM. Red circles highlight the chosen HRS and LRS elected to be State 0 and State 1, respectively. Blue bars represent the error windows accepted.
  • Figure 4: An example of the transformation of the Conductance in the ReRAM array between loop iterations.