# Quantum Vision Transformers

arXiv: https://arxiv.org/abs/2209.08167 · HTML: https://mlsanity.com/paper/2209.08167/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 57 references that are in the map.
- First posted on arXiv 16 Sep 2022.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs](https://mlsanity.com/paper/1612.05231/) (2016)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Regularizing Deep Neural Networks by Noise: Its Interpretation and Optimization](https://mlsanity.com/paper/1710.05179/) (2017)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [projUNN: efficient method for training deep networks with unitary matrices](https://mlsanity.com/paper/2203.05483/) (2022)
- [Attention-based Quantum Tomography](https://mlsanity.com/paper/2006.12469/) (2020)
- [Semiconductor Defect Detection by Hybrid Classical-Quantum Deep Learning](https://mlsanity.com/paper/2208.03514/) (2022)
- [Quantum machine learning with subspace states](https://mlsanity.com/paper/2202.00054/) (2022)
- [Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving](https://mlsanity.com/paper/1911.07306/) (2019)
- [Short Quantum Circuits in Reinforcement Learning Policies for the Vehicle Routing Problem](https://mlsanity.com/paper/2109.07498/) (2021)

## Built on by (most cited first, 30 of 48)

- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [Beyond Classical Attention: Quantum Attention for Scalable Computation](https://mlsanity.com/paper/2307.08045/) (2023)
- [Improved Financial Forecasting via Quantum Machine Learning](https://mlsanity.com/paper/2306.12965/) (2023)
- [Quantum Adaptive Self-Attention for Quantum Transformer Models](https://mlsanity.com/paper/2504.05336/) (2025)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)
- [Investigating the Quality of DermaMNIST and Fitzpatrick17k Dermatological Image Datasets](https://mlsanity.com/paper/2401.14497/) (2024)
- [Quantum Vision Transformers for Quark-Gluon Classification](https://mlsanity.com/paper/2405.10284/) (2024)
- [HQViT: Hybrid Quantum Vision Transformer for Image Classification](https://mlsanity.com/paper/2504.02730/) (2025)
- [A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks](https://mlsanity.com/paper/2311.18672/) (2023)
- [Benchmarking MedMNIST dataset on real quantum hardware](https://mlsanity.com/paper/2502.13056/) (2025)
- [Quantum Doubly Stochastic Transformers](https://mlsanity.com/paper/2504.16275/) (2025)
- [QuIC: Quantum-Inspired Compound Adapters for Parameter Efficient Fine-Tuning](https://mlsanity.com/paper/2502.06916/) (2025)
- [Quantum Artificial Intelligence: A Brief Survey](https://mlsanity.com/paper/2408.10726/) (2024)
- [Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries](https://mlsanity.com/paper/2409.15645/) (2024)
- [Quantum-Enhanced Attention Mechanism in NLP: A Hybrid Classical-Quantum Approach](https://mlsanity.com/paper/2501.15630/) (2025)
- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [Quantum autoencoders for image classification](https://mlsanity.com/paper/2502.15254/) (2025)
- [Bayesian Quantum Orthogonal Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2504.18103/) (2025)
- [TabularQGAN: A quantum generative model for tabular data synthesis](https://mlsanity.com/paper/2505.22533/) (2025)
- [Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning](https://mlsanity.com/paper/2507.08746/) (2025)
- [Quantum Adaptive Self-Attention for Financial Rebalancing: An Empirical Study on Automated Market Makers in Decentralized Finance](https://mlsanity.com/paper/2509.16955/) (2025)
- [A supplemental investigation of non-linearity in quantum generative models with respect to simulatability and optimization](https://mlsanity.com/paper/2302.00788/) (2023)
- [VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning](https://mlsanity.com/paper/2506.10275/) (2025)
- [Accelerating Inference for Multilayer Neural Networks with Quantum Computers](https://mlsanity.com/paper/2510.07195/) (2025)
- [Quantum Implicit Neural Representations for Novel View Synthesis](https://mlsanity.com/paper/2601.05250/) (2026)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Model selection in hybrid quantum neural networks with applications to quantum transformer architectures](https://mlsanity.com/paper/2603.21749/) (2026)
- [Do Quantum Transformers Help? A Systematic VQC Architecture Comparison on Tabular Benchmarks](https://mlsanity.com/paper/2604.23931/) (2026)
- [Scalable On-Hardware Training of Quantum Neural Networks and Application to Clinical Data Imputation](https://mlsanity.com/paper/2606.03517/) (2026)
- [QMViT: A Mushroom is worth 16x16 Words](https://mlsanity.com/paper/2407.04708/) (2024)

## Abstract (arXiv)

In this work, quantum transformers are designed and analysed in detail by extending the state-of-the-art classical transformer neural network architectures known to be very performant in natural language processing and image analysis. Building upon the previous work, which uses parametrised quantum circuits for data loading and orthogonal neural layers, we introduce three types of quantum transformers for training and inference, including a quantum transformer based on compound matrices, which guarantees a theoretical advantage of the quantum attention mechanism compared to their classical counterpart both in terms of asymptotic run time and the number of model parameters. These quantum architectures can be built using shallow quantum circuits and produce qualitatively different classification models. The three proposed quantum attention layers vary on the spectrum between closely following the classical transformers and exhibiting more quantum characteristics. As building blocks of the quantum transformer, we propose a novel method for loading a matrix as quantum states as well as two new trainable quantum orthogonal layers adaptable to different levels of connectivity and quality of quantum computers. We performed extensive simulations of the quantum transformers on standard medical image datasets that showed competitively, and at times better performance compared to the classical benchmarks, including the best-in-class classical vision transformers. The quantum transformers we trained on these small-scale datasets require fewer parameters compared to standard classical benchmarks. Finally, we implemented our quantum transformers on superconducting quantum computers and obtained encouraging results for up to six qubit experiments.