# QKSAN: A Quantum Kernel Self-Attention Network

arXiv: https://arxiv.org/abs/2308.13422 · HTML: https://mlsanity.com/paper/2308.13422/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 65 references that are in the map.
- First posted on arXiv 25 Aug 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Bottleneck Transformers for Visual Recognition](https://mlsanity.com/paper/2101.11605/) (2021)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Generalizing Face Forgery Detection with High-frequency Features](https://mlsanity.com/paper/2103.12376/) (2021)
- [Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kernel](https://mlsanity.com/paper/1908.11775/) (2019)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces](https://mlsanity.com/paper/2009.00298/) (2020)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [QSAN: A Near-term Achievable Quantum Self-Attention Network](https://mlsanity.com/paper/2207.07563/) (2022)
- [Benchmarking Adversarial Patch Against Aerial Detection](https://mlsanity.com/paper/2210.16765/) (2022)
- [Towards Open-World Recommendation: An Inductive Model-based Collaborative Filtering Approach](https://mlsanity.com/paper/2007.04833/) (2020)
- [Quantum Computing: Lecture Notes](https://mlsanity.com/paper/1907.09415/) (2019)
- [Learning Self-Modulating Attention in Continuous Time Space with Applications to Sequential Recommendation](https://mlsanity.com/paper/2204.06517/) (2022)
- [Learning Dual Dynamic Representations on Time-Sliced User-Item Interaction Graphs for Sequential Recommendation](https://mlsanity.com/paper/2109.11790/) (2021)
- [Quantum circuits with classical channels and the principle of deferred measurements](https://mlsanity.com/paper/2107.08324/) (2021)
- [MHSCNet: A Multimodal Hierarchical Shot-aware Convolutional Network for Video Summarization](https://mlsanity.com/paper/2204.08352/) (2022)

## Built on by (most cited first, 23 of 23)

- [Quantum Mixed-State Self-Attention Network](https://mlsanity.com/paper/2403.02871/) (2024)
- [Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transform](https://mlsanity.com/paper/2505.11892/) (2025)
- [HQViT: Hybrid Quantum Vision Transformer for Image Classification](https://mlsanity.com/paper/2504.02730/) (2025)
- [Only Large Weights (And Not Skip Connections) Can Prevent the Perils of Rank Collapse](https://mlsanity.com/paper/2505.16284/) (2025)
- [GQHAN: A Grover-inspired Quantum Hard Attention Network](https://mlsanity.com/paper/2401.14089/) (2024)
- [Personalized Quantum Federated Learning for Privacy Image Classification](https://mlsanity.com/paper/2410.02547/) (2024)
- [Quantum-Enhanced Natural Language Generation: A Multi-Model Framework with Hybrid Quantum-Classical Architectures](https://mlsanity.com/paper/2508.21332/) (2025)
- [Quantum Adjoint Convolutional Layers for Effective Data Representation](https://mlsanity.com/paper/2404.17378/) (2024)
- [QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning](https://mlsanity.com/paper/2504.11083/) (2025)
- [Quantum Graph Attention Network: A Novel Quantum Multi-Head Attention Mechanism for Graph Learning](https://mlsanity.com/paper/2508.17630/) (2025)
- [Quantum Graph Attention Networks: Trainable Quantum Encoders for Inductive Graph Learning](https://mlsanity.com/paper/2509.11390/) (2025)
- [Integrating Quantum-Classical Attention in Patch Transformers for Enhanced Time Series Forecasting](https://mlsanity.com/paper/2504.00068/) (2025)
- [HQCC: A Hybrid Quantum-Classical Classifier with Adaptive Structure](https://mlsanity.com/paper/2504.02167/) (2025)
- [Hybrid Quantum Neural Networks for Efficient Protein-Ligand Binding Affinity Prediction](https://mlsanity.com/paper/2509.11046/) (2025)
- [Multi-Scale Feature Fusion Quantum Depthwise Convolutional Neural Networks for Text Classification](https://mlsanity.com/paper/2405.13515/) (2024)
- [Quantum-machine-assisted Drug Discovery](https://mlsanity.com/paper/2408.13479/) (2024)
- [Quantum Complex-Valued Self-Attention Model](https://mlsanity.com/paper/2503.19002/) (2025)
- [Quantum Attention by Overlap Interference: Predicting Classical and Many-Body Quantum Sequences](https://mlsanity.com/paper/2602.06699/) (2026)
- [Q-Tag: Watermarking Quantum Circuit Generative Models](https://mlsanity.com/paper/2602.23085/) (2026)
- [QAROO: AI-Driven Online Task Offloading for Energy-Efficient and Sustainable MEC Networks](https://mlsanity.com/paper/2604.25740/) (2026)
- [Resilient Concurrent Causal Discovery for Topological Event Sequences](https://mlsanity.com/paper/2608.21815/) (2026)
- [QTrans: A Quantum Transformer for Sentiment Classification](https://mlsanity.com/paper/2609.12011/) (2026)
- [QiT: Quantum-Inspired Transformer for Visual Recognition Task](https://mlsanity.com/paper/2609.17789/) (2026)

## Abstract (arXiv)

Self-Attention Mechanism (SAM) excels at distilling important information from the interior of data to improve the computational efficiency of models. Nevertheless, many Quantum Machine Learning (QML) models lack the ability to distinguish the intrinsic connections of information like SAM, which limits their effectiveness on massive high-dimensional quantum data. To tackle the above issue, a Quantum Kernel Self-Attention Mechanism (QKSAM) is introduced to combine the data representation merit of Quantum Kernel Methods (QKM) with the efficient information extraction capability of SAM. Further, a Quantum Kernel Self-Attention Network (QKSAN) framework is proposed based on QKSAM, which ingeniously incorporates the Deferred Measurement Principle (DMP) and conditional measurement techniques to release half of quantum resources by mid-circuit measurement, thereby bolstering both feasibility and adaptability. Simultaneously, the Quantum Kernel Self-Attention Score (QKSAS) with an exponentially large characterization space is spawned to accommodate more information and determine the measurement conditions. Eventually, four QKSAN sub-models are deployed on PennyLane and IBM Qiskit platforms to perform binary classification on MNIST and Fashion MNIST, where the QKSAS tests and correlation assessments between noise immunity and learning ability are executed on the best-performing sub-model. The paramount experimental finding is that a potential learning advantage is revealed in partial QKSAN subclasses that acquire an impressive more than 98.05% high accuracy with very few parameters that are much less in aggregate than classical machine learning models. Predictably, QKSAN lays the foundation for future quantum computers to perform machine learning on massive amounts of data while driving advances in areas such as quantum computer vision.