# Quantum-inspired annealers as Boltzmann generators for machine learning and statistical physics

arXiv: https://arxiv.org/abs/1912.08480 · HTML: https://mlsanity.com/paper/1912.08480/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning](https://mlsanity.com/paper/2112.11534/) (2021)
- [Hybrid quantum-classical machine learning for generative chemistry and drug design](https://mlsanity.com/paper/2108.11644/) (2021)
- [Training Energy-Based Models with Non-MCMC Samplers and Efficient Temperature Estimation](https://mlsanity.com/paper/2512.02323/) (2025)
- [Optimizing Energy-based Neural Network Training with Coherent Ising Machine](https://mlsanity.com/paper/2606.09117/) (2026)

## Abstract (arXiv)

Quantum simulators and processors are rapidly improving nowadays, but they are still not able to solve complex and multidimensional tasks of practical value. However, certain numerical algorithms inspired by the physics of real quantum devices prove to be efficient in application to specific problems, related, for example, to combinatorial optimization. Here we implement a numerical annealer based on simulating the coherent Ising machine as a tool to sample from a high-dimensional Boltzmann probability distribution with the energy functional defined by the classical Ising Hamiltonian. Samples provided by such a generator are then utilized for the partition function estimation of this distribution and for the training of a general Boltzmann machine. Our study opens up a door to practical application of numerical quantum-inspired annealers.