# Quantum machine learning beyond kernel methods

@article{Jerbi2021QuantumML, title={Quantum machine learning beyond kernel methods}, author={Sofi{\`e}ne Jerbi and Lukas J. Fiderer and Hendrik Poulsen Nautrup and Jonas M. K{\"u}bler and Hans J. Briegel and Vedran Dunjko}, journal={ArXiv}, year={2021}, volume={abs/2110.13162} }

Machine learning algorithms based on parametrized quantum circuits are a prime candidate for near-term applications on noisy quantum computers. Yet, our understanding of how these quantum machine learning models compare, both mutually and to classical models, remains limited. Previous works achieved important steps in this direction by showing a close connection between some of these quantum models and kernel methods, well-studied in classical machine learning. In this work, we identify the…

## 14 Citations

### Exponential concentration and untrainability in quantum kernel methods

- Computer ScienceArXiv
- 2022

This work shows that, under certain conditions, values of quantum kernels over diﬀerent input data can be exponentially concentrated towards some value, leading to an exponential scaling of the number of measurements required for successful training.

### Noisy quantum kernel machines

- Computer SciencePhysical Review A
- 2022

It is shown that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines and an upper bound on the generalization error of the model that involves the average purity of the encoded states is derived.

### Parameterized Quantum Circuits with Quantum Kernels for Machine Learning: A Hybrid Quantum-Classical Approach

- Computer Science, Physics
- 2022

It is concluded that quantum kernels with hybrid kernel methods, a.k.a. quantum Kernel PQCs, offer distinct advantages as a hybrid approach to QML.

### Concentration of Data Encoding in Parameterized Quantum Circuits

- Computer ScienceArXiv
- 2022

It is proved that, under reasonable assumptions, the distance between the average encoded state and the maximally mixed state could be explicitly upper-bounded with respect to the width and depth of the encoding circuit.

### Generalization despite overfitting in quantum machine learning models

- Computer Science
- 2022

This work derives the behavior of a classical interpolating Fourier features models for regression on noisy signals, and shows how a class of quantum models exhibits analogous features, thereby linking the structure of quantum circuits to overparameterization and overﬁtting in quantum models.

### Hyperparameter Importance of Quantum Neural Networks Across Small Datasets

- Computer ScienceDS
- 2022

This work applies the functional ANOVA framework to quantum neural networks to analyze which of the hyperparameters were most inﬂuential for their predictive performance, and introduces new methodologies to study quantum machine learning models and provides new insights toward quantum model selection.

### Power and limitations of single-qubit native quantum neural networks

- Computer ScienceArXiv
- 2022

It is proved that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series, and the exact correlations between the parameters of the trainable gates and the working Fourier coefﬁcients are established.

### Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron

- Computer Science
- 2022

It is proved that, under widely believed complexity theory assumptions, quantum phase learning problem cannot be efficiently solved by machine learning algorithms using classical resources and classical data, and it is proved the universality of quantum kernel Alphatron in efficiently predicting quantum phases.

### Learning quantum processes without input control

- Computer Science
- 2022

A general statistical learning theory for processes that take as input a classical random variable and output a quantum state is introduced, and an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite is provided.

### The effect of the processing and measurement operators on the expressive power of quantum models

- Computer Science
- 2022

This work sketches the determinant role that the processing and measurement operators have on the expressive power of simple quantum circuits and observes that increasing the number of parameterized and entangling gates leads to a more expressive model for certain circuit structures.

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