# Importance of Kernel Bandwidth in Quantum Machine Learning

@article{Shaydulin2021ImportanceOK, title={Importance of Kernel Bandwidth in Quantum Machine Learning}, author={R.R. Shaydulin and Stefan M. Wild}, journal={ArXiv}, year={2021}, volume={abs/2111.05451} }

Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. However, recent results overlook the central role hyperparameters play in determining the performance of machine learning methods. In this work we identify the hyperparameter controlling the bandwidth of a quantum kernel and show that it controls the expressivity of the resulting model. We use extensive numerical experiments with multiple quantum kernels and classical datasets…

## 10 Citations

### Bandwidth Enables Generalization in Quantum Kernel Models

- Computer ScienceArXiv
- 2022

Evidence is provided that quantum machine learning methods can generalize well on challenging datasets, including those far outside of the theoretical assumptions.

### 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.

### Quantum kernels to learn the phases of quantum matter

- Computer SciencePhysical Review A
- 2022

This work uses a support vector machine (with a quantum kernel) to predict and characterize second order quantum phase transitions and presents two algorithms, one based on ﬁdelity and onebased on the ﬂdelity per site, to classify the phases of matter in a quantum processor.

### Quantum AI simulator using a hybrid CPU-FPGA approach

- Computer Science
- 2022

This work focuses on quantum kernels empirically designed for image classification and demonstrates a field programmable gate arrays (FPGA) implementation, and shows that the quantum kernel estimation by the heterogeneous CPU–FPGA computing is 470 times faster than that by a conventional CPU implementation.

### 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.

### Unsupervised quantum machine learning for fraud detection

- Computer Science
- 2022

This work develops quantum protocols for anomaly detection and applies them to the task of credit card fraud detection, and observes that quantum FD can challenge equivalent classical protocols at increasing number of features (equal to the number of qubits for data embedding).

### A Survey of Quantum Computing for Finance

- Computer Science
- 2022

A comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems more efficiently and accurately.

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