# Robust data encodings for quantum classifiers

arXiv: https://arxiv.org/abs/2003.01695 · HTML: https://mlsanity.com/paper/2003.01695/

## Key facts

- Cited by 91 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 30 of 91)

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- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
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- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
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- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
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- [QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design](https://mlsanity.com/paper/2410.07961/) (2024)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Incremental Data-Uploading for Full-Quantum Classification](https://mlsanity.com/paper/2205.03057/) (2022)
- [Avoiding Barren Plateaus with Classical Deep Neural Networks](https://mlsanity.com/paper/2205.13418/) (2022)
- [Quantum Neural Network Compression](https://mlsanity.com/paper/2207.01578/) (2022)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)

## Abstract (arXiv)

Data representation is crucial for the success of machine learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and effectively deal with noise arise. In this work, we study data encodings for binary quantum classification and investigate their properties both with and without noise. For the common classifier we consider, we show that encodings determine the classes of learnable decision boundaries as well as the set of points which retain the same classification in the presence of noise. After defining the notion of a robust data encoding, we prove several results on robustness for different channels, discuss the existence of robust encodings, and prove an upper bound on the number of robust points in terms of fidelities between noisy and noiseless states. Numerical results for several example implementations are provided to reinforce our findings.