# Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data arXiv: https://arxiv.org/abs/2306.07331 ยท HTML: https://mlsanity.com/paper/2306.07331/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Builds on 28 of its 76 references that are in the map. - First posted on arXiv 12 Jun 2023. ## Builds on (most cited first, 28 of 28) - [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) - [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018) - [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018) - [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020) - [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020) - [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019) - [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016) - [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020) - [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023) - [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021) - [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) - [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018) - [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021) - [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) - [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) - [On quantum backpropagation, information reuse, and cheating measurement collapse](https://mlsanity.com/paper/2305.13362/) (2023) - [Quantum Deep Learning](https://mlsanity.com/paper/1412.3489/) (2014) - [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021) - [Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era](https://mlsanity.com/paper/2102.05321/) (2021) - [How Parallel Circuit Execution Can Be Useful for NISQ Computing?](https://mlsanity.com/paper/2112.00387/) (2021) ## Built on by (most cited first, 10 of 10) - [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024) - [Resource-efficient equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2410.01252/) (2024) - [Enhancing variational quantum algorithms by balancing training on classical and quantum hardware](https://mlsanity.com/paper/2503.16361/) (2025) - [Iterative Quantum Feature Maps](https://mlsanity.com/paper/2506.19461/) (2025) - [Quantum Curriculum Learning](https://mlsanity.com/paper/2407.02419/) (2024) - [Inductive Graph Representation Learning with Quantum Graph Neural Networks](https://mlsanity.com/paper/2503.24111/) (2025) - [Provably scalable learning from quantum many-body data via locality](https://mlsanity.com/paper/2509.13705/) (2025) - [Permutation-equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2404.18198/) (2024) - [Quantum Kernel Machine Learning for Autonomous Materials Science](https://mlsanity.com/paper/2601.11775/) (2026) - [A Novel Parallel QCNN Architecture with Efficient Classical Simulability](https://mlsanity.com/paper/2607.08928/) (2026) ## Abstract (arXiv) The quantum convolutional neural network (QCNN) is a promising quantum machine learning (QML) model that is expected to achieve quantum advantages in classically intractable problems. However, the QCNN requires a large number of measurements for data learning, limiting its practical applications in large-scale problems. To alleviate this requirement, we propose a novel architecture called split-parallelizing QCNN (sp-QCNN), which exploits the prior knowledge of quantum data to design an efficient model. This architecture draws inspiration from geometric quantum machine learning and targets translationally symmetric quantum data commonly encountered in physics and quantum computing science. By splitting the quantum circuit based on translational symmetry, the sp-QCNN can substantially parallelize the conventional QCNN without increasing the number of qubits and improve the measurement efficiency by an order of the number of qubits. To demonstrate its effectiveness, we apply the sp-QCNN to a quantum phase recognition task and show that it can achieve comparable classification accuracy to the conventional QCNN while considerably reducing the measurement resources required. Due to its high measurement efficiency, the sp-QCNN can mitigate statistical errors in estimating the gradient of the loss function, thereby accelerating the learning process. These results open up new possibilities for incorporating the prior data knowledge into the efficient design of QML models, leading to practical quantum advantages.