# Diffusion-Inspired Quantum Noise Mitigation in Parameterized Quantum Circuits

arXiv: https://arxiv.org/abs/2406.00843 · HTML: https://mlsanity.com/paper/2406.00843/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 54 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [An Image Patch is a Wave: Phase-Aware Vision MLP](https://mlsanity.com/paper/2111.12294/) (2021)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization](https://mlsanity.com/paper/2110.11331/) (2021)
- [A Co-Design Framework of Neural Networks and Quantum Circuits Towards Quantum Advantage](https://mlsanity.com/paper/2006.14815/) (2020)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [QuEst: Graph Transformer for Quantum Circuit Reliability Estimation](https://mlsanity.com/paper/2210.16724/) (2022)
- [Quantum Vision Clustering](https://mlsanity.com/paper/2309.09907/) (2023)
- [QClusformer: A Quantum Transformer-based Framework for Unsupervised Visual Clustering](https://mlsanity.com/paper/2405.19722/) (2024)
- [Quantum Visual Feature Encoding Revisited](https://mlsanity.com/paper/2405.19725/) (2024)

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

- [Hierarchical Quantum Control Gates for Functional MRI Understanding](https://mlsanity.com/paper/2408.03596/) (2024)
- [Quantum-Brain: Quantum-Inspired Neural Network Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2411.13378/) (2024)
- [QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks](https://mlsanity.com/paper/2507.05190/) (2025)
- [COBRA: A Continual Learning Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2411.17475/) (2024)
- [CLIFF: Continual Learning for Incremental Flake Features in 2D Material Identification](https://mlsanity.com/paper/2508.17261/) (2025)
- [Towards Quantum Machine Learning for Malicious Code Analysis](https://mlsanity.com/paper/2508.19381/) (2025)
- [OpenQlaw: An Agentic AI Assistant for Analysis of 2D Quantum Materials](https://mlsanity.com/paper/2603.17043/) (2026)
- [BRAIN: Bias-Mitigation Continual Learning Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2508.18187/) (2025)
- [QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modeling](https://mlsanity.com/paper/2605.13833/) (2026)
- [QuPAINT: Physics-Aware Multimodal Reasoning for Quantum Material Characterization](https://mlsanity.com/paper/2609.12202/) (2026)

## Abstract (arXiv)

Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the parameters in the quantum circuits are trained to minimize the target function. Although there have been comprehensive studies to improve the performance of the PQCs on practical tasks, the errors caused by the quantum noise downgrade the performance when running on real quantum computers. In particular, when the quantum state is transformed through multiple quantum circuit layers, the effect of the quantum noise happens cumulatively and becomes closer to the maximally mixed state or complete noise. This paper studies the relationship between the quantum noise and the diffusion model. Then, we propose a novel diffusion-inspired learning approach to mitigate the quantum noise in the PQCs and reduce the error for specific tasks. Through our experiments, we illustrate the efficiency of the learning strategy and achieve state-of-the-art performance on classification tasks in the quantum noise scenarios.