# Probabilistic Algorithms for Ising Machines from Optimization to Generative AI

arXiv: https://arxiv.org/abs/2610.03972 · HTML: https://mlsanity.com/paper/2610.03972/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 137 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 30 of 34)

- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization](https://mlsanity.com/paper/2406.01661/) (2024)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics](https://mlsanity.com/paper/2502.08696/) (2025)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Massively Parallel Probabilistic Computing with Sparse Ising Machines](https://mlsanity.com/paper/2110.02481/) (2021)
- [Accelerated Parallel Tempering via Neural Transports](https://mlsanity.com/paper/2502.10328/) (2025)
- [Efficient Optimization with Higher-Order Ising Machines](https://mlsanity.com/paper/2212.03426/) (2022)
- [CMOS + stochastic nanomagnets: heterogeneous computers for probabilistic inference and learning](https://mlsanity.com/paper/2304.05949/) (2023)
- [All-to-all reconfigurability with sparse and higher-order Ising machines](https://mlsanity.com/paper/2312.08748/) (2023)
- [Automatic Graph Partitioning for Very Large-scale Deep Learning](https://mlsanity.com/paper/2103.16063/) (2021)
- [The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model](https://mlsanity.com/paper/2110.14206/) (2021)
- [Nonequilibrium Monte Carlo for unfreezing variables in hard combinatorial optimization](https://mlsanity.com/paper/2111.13628/) (2021)
- [Message Passing Variational Autoregressive Network for Solving Intractable Ising Models](https://mlsanity.com/paper/2404.06225/) (2024)
- [How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits](https://mlsanity.com/paper/2411.10406/) (2024)
- [CMOS-compatible Ising and Potts Annealing Using Single Photon Avalanche Diodes](https://mlsanity.com/paper/2211.12607/) (2022)
- [Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization](https://mlsanity.com/paper/2510.19544/) (2025)
- [Scalable Connectivity for Ising Machines: Dense to Sparse](https://mlsanity.com/paper/2503.01177/) (2025)
- [IsingFormer: Augmenting Parallel Tempering With Learned Proposals](https://mlsanity.com/paper/2509.23043/) (2025)
- [A Generative Neural Annealer for Black-Box Combinatorial Optimization](https://mlsanity.com/paper/2505.09742/) (2025)
- [Parallel Tempering-Inspired Distributed Binary Optimization with In-Memory Computing](https://mlsanity.com/paper/2409.09152/) (2024)
- [Self-Adaptive Ising Machines for Constrained Optimization](https://mlsanity.com/paper/2501.04971/) (2025)
- [Two-dimensional Parallel Tempering for Constrained Optimization](https://mlsanity.com/paper/2506.14781/) (2025)
- [Generalized Probabilistic Approximate Optimization Algorithm](https://mlsanity.com/paper/2507.07420/) (2025)
- [Probabilistic Computers for Neural Quantum States](https://mlsanity.com/paper/2512.24558/) (2025)
- [Probabilistic Computers for MIMO Detection: From Sparsification to 2D Parallel Tempering](https://mlsanity.com/paper/2601.09037/) (2026)

## Abstract (arXiv)

Ising machines have emerged as promising hardware accelerators for intractable optimization and sampling problems, yet their practical impact increasingly hinges on the co-design of algorithms and hardware, where algorithmic demands shape new architectures and new hardware capabilities inspire entirely new algorithms. In this Review, we survey probabilistic algorithms designed for portability across diverse Ising platforms, advocating a top-down perspective that prioritizes principled methods with provable guarantees. We cover foundational methods such as simulated annealing and parallel tempering, including two-dimensional extensions that natively encode hard constraints, and examine approaches that expand the scale of solvable problems from cluster mean-field methods to variational samplers. We highlight the Probabilistic Approximate Optimization Algorithm (PAOA), a classical analog of QAOA that emerged directly from probabilistic hardware development, and explore how generative AI and Ising machines might reinforce each other: learned models propose global moves to accelerate optimization, while probabilistic techniques improve inference in large language models. Much as quantum computing has seen algorithms co-evolve with hardware, probabilistic and Ising computing stand at a similar inflection point. We outline a co-design framework for accelerating the capabilities and adoption of next-generation Ising machines.