# Resource-efficient equivariant quantum convolutional neural networks

arXiv: https://arxiv.org/abs/2410.01252 · HTML: https://mlsanity.com/paper/2410.01252/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 80 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Quantum Convolutional Neural Networks for High Energy Physics Data Analysis](https://mlsanity.com/paper/2012.12177/) (2020)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [Variational quantum simulation: a case study for understanding warm starts](https://mlsanity.com/paper/2404.10044/) (2024)
- [A Unified Theory of Quantum Neural Network Loss Landscapes](https://mlsanity.com/paper/2408.11901/) (2024)
- [Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems](https://mlsanity.com/paper/2010.00157/) (2020)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024)
- [Quantum Curriculum Learning](https://mlsanity.com/paper/2407.02419/) (2024)

## Built on by (most cited first, 4 of 4)

- [Quantum-Audit: Evaluating the Reasoning Limits of LLMs on Quantum Computing](https://mlsanity.com/paper/2602.10092/) (2026)
- [Iterative Quantum Feature Maps](https://mlsanity.com/paper/2506.19461/) (2025)
- [PERM EQ x GRAPH EQ: Equivariant Neural Networks for Quantum Molecular Learning](https://mlsanity.com/paper/2512.05475/) (2025)
- [Pixel-Translation-Equivariant Quantum Convolutional Neural Networks via Fourier Multiplexers](https://mlsanity.com/paper/2604.06094/) (2026)

## Abstract (arXiv)

Equivariant quantum neural networks (QNNs) are promising variational models that exploit symmetries to improve machine learning capabilities. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum devices remains challenging due to limited computational resources. This study proposes a resource-efficient model of equivariant quantum convolutional neural networks (QCNNs) called equivariant split-parallelizing QCNN (sp-QCNN). Using a group-theoretical approach, we encode general symmetries into our model beyond the translational symmetry addressed by previous sp-QCNNs. We achieve this by splitting the circuit at the pooling layer while preserving symmetry. This splitting structure effectively parallelizes QCNNs to improve measurement efficiency in estimating the expectation value of an observable and its gradient by order of the number of qubits. Our model also exhibits high trainability and generalization performance, including the absence of barren plateaus. Numerical experiments demonstrate that the equivariant sp-QCNN can be trained and generalized with fewer measurement resources than a conventional equivariant QCNN in a noisy quantum data classification task. Our results contribute to the advancement of practical quantum machine learning algorithms.