# Quantum Adjoint Convolutional Layers for Effective Data Representation

arXiv: https://arxiv.org/abs/2404.17378 · HTML: https://mlsanity.com/paper/2404.17378/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 62 references that are in the map.
- First posted on arXiv 26 Apr 2024.

## Builds on (most cited first, 23 of 23)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Convolutional Neural Networks for High Energy Physics Data Analysis](https://mlsanity.com/paper/2012.12177/) (2020)
- [Evaluation of post-hoc interpretability methods in time-series classification](https://mlsanity.com/paper/2202.05656/) (2022)
- [QSAN: A Near-term Achievable Quantum Self-Attention Network](https://mlsanity.com/paper/2207.07563/) (2022)
- [QKSAN: A Quantum Kernel Self-Attention Network](https://mlsanity.com/paper/2308.13422/) (2023)
- [Deep Reinforcement Learning with Quantum-inspired Experience Replay](https://mlsanity.com/paper/2101.02034/) (2021)
- [Quantum Language Model with Entanglement Embedding for Question Answering](https://mlsanity.com/paper/2008.09943/) (2020)
- [Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning](https://mlsanity.com/paper/2301.09138/) (2023)
- [On the Interpretability of Quantum Neural Networks](https://mlsanity.com/paper/2308.11098/) (2023)
- [A Quantum-inspired Similarity Measure for the Analysis of Complete Weighted Graphs](https://mlsanity.com/paper/1904.13239/) (2019)
- [Tomography of Quantum States from Structured Measurements via quantum-aware transformer](https://mlsanity.com/paper/2305.05433/) (2023)
- [QuantumEyes: Towards Better Interpretability of Quantum Circuits](https://mlsanity.com/paper/2311.07980/) (2023)
- [GQHAN: A Grover-inspired Quantum Hard Attention Network](https://mlsanity.com/paper/2401.14089/) (2024)
- [Recurrence-Aware Long-Term Cognitive Network for Explainable Pattern Classification](https://mlsanity.com/paper/2107.03423/) (2021)
- [Feasible Architecture for Quantum Fully Convolutional Networks](https://mlsanity.com/paper/2110.01771/) (2021)
- [A Quantum-like Model for Predicting Human Decisions in the Entangled Social Systems](https://mlsanity.com/paper/2111.13902/) (2021)

## Built on by (most cited first, 2 of 2)

- [QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning](https://mlsanity.com/paper/2504.11083/) (2025)
- [HQCC: A Hybrid Quantum-Classical Classifier with Adaptive Structure](https://mlsanity.com/paper/2504.02167/) (2025)

## Abstract (arXiv)

Quantum Convolutional Layer (QCL) is considered as one of the core of Quantum Convolutional Neural Networks (QCNNs) due to its efficient data feature extraction capability. However, the current principle of QCL is not as mathematically understandable as Classical Convolutional Layer (CCL) due to its black-box structure. Moreover, classical data mapping in many QCLs is inefficient. To this end, firstly, the Quantum Adjoint Convolution Operation (QACO) consisting of a quantum amplitude encoding and its inverse is theoretically shown to be equivalent to the quantum normalization of the convolution operation based on the Frobenius inner product while achieving an efficient characterization of the data. Subsequently, QACO is extended into a Quantum Adjoint Convolutional Layer (QACL) by Quantum Phase Estimation (QPE) to compute all Frobenius inner products in parallel. At last, comparative simulation experiments are carried out on PennyLane and TensorFlow platforms, mainly for the two cases of kernel fixed and unfixed in QACL. The results demonstrate that QACL with the insight of special quantum properties for the same images, provides higher training accuracy in MNIST and Fashion MNIST classification experiments, but sacrifices the learning performance to some extent. Predictably, our research lays the foundation for the development of efficient and interpretable quantum convolutional networks and also advances the field of quantum machine vision.