# Quantum Topological Data Encoding

arXiv: https://arxiv.org/abs/2607.13847 · HTML: https://mlsanity.com/paper/2607.13847/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 63 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Quantum-enhanced machine learning](https://mlsanity.com/paper/1610.08251/) (2016)
- [High Dimensional Quantum Machine Learning With Small Quantum Computers](https://mlsanity.com/paper/2203.13739/) (2022)
- [Quantum machine learning with subspace states](https://mlsanity.com/paper/2202.00054/) (2022)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Towards quantum advantage via topological data analysis](https://mlsanity.com/paper/2005.02607/) (2020)
- [Quantum Topological Data Analysis with Linear Depth and Exponential Speedup](https://mlsanity.com/paper/2108.02811/) (2021)
- [Topological data analysis on noisy quantum computers](https://mlsanity.com/paper/2209.09371/) (2022)
- [Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension](https://mlsanity.com/paper/2403.19099/) (2024)
- [Provable quantum speedups for computing persistence in topological data analysis](https://mlsanity.com/paper/2410.21258/) (2024)
- [Benchmarking data encoding methods in Quantum Machine Learning](https://mlsanity.com/paper/2505.14295/) (2025)
- [Non-variational supervised quantum kernel methods: a review](https://mlsanity.com/paper/2604.07896/) (2026)
- [Persistent homology analysis of multiqubit entanglement](https://mlsanity.com/paper/1907.06914/) (2019)
- [Higher-order topological kernels via quantum computation](https://mlsanity.com/paper/2307.07383/) (2023)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)

## Abstract (arXiv)

Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce quantum topological data encoding (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.