# High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware

arXiv: https://arxiv.org/abs/2109.01690 · HTML: https://mlsanity.com/paper/2109.01690/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 67 references that are in the map.
- First posted on arXiv 3 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models](https://mlsanity.com/paper/1605.07252/) (2016)
- [Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models](https://mlsanity.com/paper/1609.02542/) (2016)
- [Optimal structure and parameter learning of Ising models](https://mlsanity.com/paper/1612.05024/) (2016)
- [A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers](https://mlsanity.com/paper/1912.02119/) (2019)
- [Programmable Quantum Annealers as Noisy Gibbs Samplers](https://mlsanity.com/paper/2012.08827/) (2020)
- [Single-Qubit Fidelity Assessment of Quantum Annealing Hardware](https://mlsanity.com/paper/2104.03335/) (2021)

## Built on by (most cited first, 9 of 9)

- [Thermodynamic Computing System for AI Applications](https://mlsanity.com/paper/2312.04836/) (2023)
- [Thermodynamic AI and the fluctuation frontier](https://mlsanity.com/paper/2302.06584/) (2023)
- [On the challenges of using D-Wave computers to sample Boltzmann Random Variables](https://mlsanity.com/paper/2111.15295/) (2021)
- [On Quantum Circuits for Discrete Graphical Models](https://mlsanity.com/paper/2206.00398/) (2022)
- [Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing](https://mlsanity.com/paper/2310.12153/) (2023)
- [Density Operator Expectation Maximization](https://mlsanity.com/paper/2507.22786/) (2025)
- [Multi-Mode Quantum Annealing for Generative Representation Learning with Boltzmann Priors](https://mlsanity.com/paper/2604.00919/) (2026)
- [A quantum annealing approach to graph node embedding](https://mlsanity.com/paper/2503.06332/) (2025)
- [Quantum Adiabatic Generation of Human-Like Passwords](https://mlsanity.com/paper/2506.08917/) (2025)

## Abstract (arXiv)

Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a procedure for executing these models on QA hardware to maximize Gibbs sampling performance. Experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature. Furthermore, we show that this effective temperature can be adjusted by modulating the annealing time and energy scale. The procedure proposed in this work provides an approach to using QA hardware for Ising model sampling presenting potential new opportunities for applications in machine learning and physics simulation.