# Shot-frugal and Robust quantum kernel classifiers

arXiv: https://arxiv.org/abs/2210.06971 · HTML: https://mlsanity.com/paper/2210.06971/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 55 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [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)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (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)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [Adaptive shot allocation for fast convergence in variational quantum algorithms](https://mlsanity.com/paper/2108.10434/) (2021)
- [Quantum Multiple Kernel Learning](https://mlsanity.com/paper/2011.09694/) (2020)
- [An example of use of Variational Methods in Quantum Machine Learning](https://mlsanity.com/paper/2208.04316/) (2022)

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

- [AQKA: Active Quantum Kernel Acquisition Under a Shot Budget](https://mlsanity.com/paper/2605.14672/) (2026)
- [Adaptive Measurement Allocation for Learning Kernelized SVMs Under Noisy Observations](https://mlsanity.com/paper/2605.22275/) (2026)
- [Statevector-to-Hardware Reconstruction of a Four-Qubit ZZ Quantum Kernel: A Single-Backend Case Study of Three Execution Jobs](https://mlsanity.com/paper/2607.20377/) (2026)

## Abstract (arXiv)

Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and because of the constraints of near-term quantum hardware. We emphasize that for classification tasks, the aim is reliable classification and not precise kernel evaluation, and demonstrate that the former is far more resource efficient. Furthermore, it is shown that the accuracy of classification is not a suitable performance metric in the presence of noise and we motivate a new metric that characterizes the reliability of classification. We then obtain a bound for N which ensures, with high probability, that classification errors over a dataset are bounded by the margin errors of an idealized quantum kernel classifier. Using chance constraint programming and the subgaussian bounds of quantum kernel distributions, we derive several Shot-frugal and Robust (ShofaR) programs starting from the primal formulation of the Support Vector Machine. This significantly reduces the number of quantum measurements needed and is robust to noise by construction. Our strategy is applicable to uncertainty in quantum kernels arising from any source of unbiased noise.