# A Unified Framework for Trace-induced Quantum Kernels

arXiv: https://arxiv.org/abs/2311.13552 · HTML: https://mlsanity.com/paper/2311.13552/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (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)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [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)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [On the expressivity of embedding quantum kernels](https://mlsanity.com/paper/2309.14419/) (2023)
- [Quantum tangent kernel](https://mlsanity.com/paper/2111.02951/) (2021)
- [The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning](https://mlsanity.com/paper/2212.11826/) (2022)

## Built on by (most cited first, 12 of 12)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Double descent in quantum kernel methods](https://mlsanity.com/paper/2501.10077/) (2025)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [On the similarity of bandwidth-tuned quantum kernels and classical kernels](https://mlsanity.com/paper/2503.05602/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [Non-variational supervised quantum kernel methods: a review](https://mlsanity.com/paper/2604.07896/) (2026)
- [Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms](https://mlsanity.com/paper/2506.13865/) (2025)
- [Spectral Phase Encoding for Quantum Kernel Methods](https://mlsanity.com/paper/2602.19644/) (2026)
- [Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization](https://mlsanity.com/paper/2607.01080/) (2026)

## Abstract (arXiv)

Quantum kernel methods are promising candidates for achieving a practical quantum advantage for certain machine learning tasks. Similar to classical machine learning, an exact form of a quantum kernel is expected to have a great impact on the model performance. In this work we combine all trace-induced quantum kernels, including the commonly-used global fidelity and local projected quantum kernels, into a common framework. We show how generalized trace-induced quantum kernels can be constructed as combinations of the fundamental building blocks we coin "Lego" kernels, which impose an inductive bias on the resulting quantum models. We relate the expressive power and generalization ability to the number of non-zero weight Lego kernels and propose a systematic approach to increase the complexity of a quantum kernel model, leading to a new form of the local projected kernels that require fewer quantum resources in terms of the number of quantum gates and measurement shots. We show numerically that models based on local projected kernels can achieve comparable performance to the global fidelity quantum kernel. Our work unifies existing quantum kernels and provides a systematic framework to compare their properties.