# Iterative Quantum Feature Maps

arXiv: https://arxiv.org/abs/2506.19461 · HTML: https://mlsanity.com/paper/2506.19461/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 69 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 30 of 30)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [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)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Rank-N-Contrast: Learning Continuous Representations for Regression](https://mlsanity.com/paper/2210.01189/) (2022)
- [Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces](https://mlsanity.com/paper/2009.00298/) (2020)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [On quantum backpropagation, information reuse, and cheating measurement collapse](https://mlsanity.com/paper/2305.13362/) (2023)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [Harnessing disordered quantum dynamics for machine learning](https://mlsanity.com/paper/1602.08159/) (2016)
- [Higher-Order Quantum Reservoir Computing](https://mlsanity.com/paper/2006.08999/) (2020)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Learning Temporal Quantum Tomography](https://mlsanity.com/paper/2103.13973/) (2021)
- [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024)
- [NoProp: Training Neural Networks without Full Back-propagation or Full Forward-propagation](https://mlsanity.com/paper/2503.24322/) (2025)
- [Resource-efficient equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2410.01252/) (2024)
- [Efficient quantum-enhanced classical simulation for patches of quantum landscapes](https://mlsanity.com/paper/2411.19896/) (2024)
- [HQCC: A Hybrid Quantum-Classical Classifier with Adaptive Structure](https://mlsanity.com/paper/2504.02167/) (2025)

## Built on by (most cited first, 3 of 3)

- [Learnable quantum spectral filters for hybrid graph neural networks](https://mlsanity.com/paper/2507.05640/) (2025)
- [Dimension reduction with structure-aware quantum circuits for hybrid machine learning](https://mlsanity.com/paper/2508.00048/) (2025)
- [Recurrent Quantum Feature Maps for Reservoir Computing](https://mlsanity.com/paper/2604.03469/) (2026)

## Abstract (arXiv)

Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for specific families of classification problems. However, deploying deep QFMs on real quantum hardware remains challenging due to circuit noise and hardware constraints. Additionally, variational quantum algorithms often suffer from computational bottlenecks, particularly in accurate gradient estimation, which significantly increases quantum resource demands during training. We propose Iterative Quantum Feature Maps (IQFMs), a hybrid quantum-classical framework that constructs a deep architecture by iteratively connecting shallow QFMs with classically computed augmentation weights. By incorporating contrastive learning and a layer-wise training mechanism, the IQFMs framework effectively reduces quantum runtime and mitigates noise-induced degradation. In tasks involving noisy quantum data, numerical experiments show that the IQFMs framework outperforms quantum convolutional neural networks, without requiring the optimization of variational quantum parameters. Even for a typical classical image classification benchmark, a carefully designed IQFMs framework achieves performance comparable to that of classical neural networks. This framework presents a promising path to address current limitations and harness the full potential of quantum-enhanced machine learning.