# All-to-all reconfigurability with sparse and higher-order Ising machines

arXiv: https://arxiv.org/abs/2312.08748 · HTML: https://mlsanity.com/paper/2312.08748/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2023.

## Built on by (most cited first, 10 of 10)

- [IsingFormer: Augmenting Parallel Tempering With Learned Proposals](https://mlsanity.com/paper/2509.23043/) (2025)
- [Programmable k-local Ising interactions and shallow optical Kolmogorov--Arnold networks through repeated data encounters](https://mlsanity.com/paper/2508.17440/) (2025)
- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [A Statistical Analysis for Per-Instance Evaluation of Stochastic Optimizers: Avoiding Unreliable Conclusions](https://mlsanity.com/paper/2503.16589/) (2025)
- [Generalized Probabilistic Approximate Optimization Algorithm](https://mlsanity.com/paper/2507.07420/) (2025)
- [Higher-Order Kuramoto Oscillator Network for Dense Associative Memory](https://mlsanity.com/paper/2507.21984/) (2025)
- [Nonlocal Monte Carlo via Reinforcement Learning](https://mlsanity.com/paper/2508.10520/) (2025)
- [Probabilistic Computers for Neural Quantum States](https://mlsanity.com/paper/2512.24558/) (2025)
- [Efficient Optimization Accelerator Framework for Multistate Ising Problems](https://mlsanity.com/paper/2505.20250/) (2025)
- [Probabilistic Algorithms for Ising Machines from Optimization to Generative AI](https://mlsanity.com/paper/2610.03972/) (2026)

## Abstract (arXiv)

Domain-specific hardware to solve computationally hard optimization problems has generated tremendous excitement. Here, we evaluate probabilistic bit (p-bit) based Ising Machines (IM) on the 3-regular 3-Exclusive OR Satisfiability (3R3X), as a representative hard optimization problem. We first introduce a multiplexed architecture that emulates all-to-all network functionality while maintaining highly parallelized chromatic Gibbs sampling. We implement this architecture in single Field-Programmable Gate Arrays (FPGA) and show that running the adaptive parallel tempering algorithm demonstrates competitive algorithmic and prefactor advantages over alternative IMs by D-Wave, Toshiba, and Fujitsu. We also implement higher-order interactions that lead to better prefactors without changing algorithmic scaling for the XORSAT problem. Even though FPGA implementations of p-bits are still not quite as fast as the best possible greedy algorithms accelerated on Graphics Processing Units (GPU), scaled magnetic versions of p-bit IMs could lead to orders of magnitude improvements over the state of the art for generic optimization.