# Spectral Phase Encoding for Quantum Kernel Methods

arXiv: https://arxiv.org/abs/2602.19644 · HTML: https://mlsanity.com/paper/2602.19644/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 24 of 24)

- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Highly comparative feature-based time-series classification](https://mlsanity.com/paper/1401.3531/) (2014)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [Quantum Data Encoding: A Comparative Analysis of Classical-to-Quantum Mapping Techniques and Their Impact on Machine Learning Accuracy](https://mlsanity.com/paper/2311.10375/) (2023)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [A Survey on the Robustness of Computer Vision Models against Common Corruptions](https://mlsanity.com/paper/2305.06024/) (2023)
- [A Unified Framework for Trace-induced Quantum Kernels](https://mlsanity.com/paper/2311.13552/) (2023)
- [Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data](https://mlsanity.com/paper/2412.07915/) (2024)
- [Variational Quantum Approximate Support Vector Machine with Inference Transfer](https://mlsanity.com/paper/2206.14507/) (2022)
- [Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training](https://mlsanity.com/paper/2401.02879/) (2024)
- [Frequency learning for image classification](https://mlsanity.com/paper/2006.15476/) (2020)
- [Quantum Fourier Transform Based Kernel for Solar Irrandiance Forecasting](https://mlsanity.com/paper/2511.17698/) (2025)

## Abstract (arXiv)

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive noise. We introduce Spectral Phase Encoding (SPE), a hybrid construc- tion combining a discrete Fourier transform (DFT) front-end with a diagonal phase-only embedding aligned with the geometry of diagonal quantum maps. Within a unified framework, we compare QK-DFT against alternative quantum variants (QK-PCA, QK-RP) and classi- cal SVM baselines under identical clean-data hyperparameter selection, quantifying robustness via dataset fixed-effects regression with wild cluster bootstrap inference across heterogeneous real-world datasets. Across the quantum family, DFT-based preprocessing yields the smallest degradation rate as noise increases, with statistically sup- ported slope differences relative to PCA and RP. Compared to classical baselines, QK-DFT shows degradation comparable to linear SVM and more stable than RBF SVM under matched tuning. Hardware exper- iments confirm that SPE remains executable and numerically stable for overlap estimation. These results indicate that robustness in quan- tum kernels depends critically on structure-aligned preprocessing and its interaction with diagonal embeddings, supporting a robustness-first perspective for NISQ-era quantum machine learning.