Kernel methods in Quantum Machine Learning

Mengoni, Riccardo; Pierro, Alessandra Di

doi:10.1007/s42484-019-00007-4

Cited by 43 publications

(25 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Require: Parameter λ in (26), number M of optimized RFs in (26), even number N ∈ 2N of labeled examples in (25), step sizes η t in (145), parameter q min in (59), parameter region W ⊂ R 2M . Ensure: A classifier fv,α in the form of (37) with v 0 , .…”

Section: Supplementary Materialsmentioning

confidence: 99%

See 1 more Smart Citation

Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning

Yamasaki¹,

Sonoda²

2021

Preprint

View full text Add to dashboard Cite

Random features are a central technique for scalable learning algorithms based on kernel methods. A recent work has shown that an algorithm for machine learning by quantum computer, quantum machine learning (QML), can exponentially speed up sampling of optimized random features, even without imposing restrictive assumptions on sparsity and low-rankness of matrices that had limited applicability of conventional QML algorithms; this QML algorithm makes it possible to significantly reduce and provably minimize the required number of features for regression tasks. However, a major interest in the field of QML is how widely the advantages of quantum computation can be exploited, not only in the regression tasks. We here construct a QML algorithm for a classification task accelerated by the optimized random features. We prove that the QML algorithm for sampling optimized random features, combined with stochastic gradient descent (SGD), can achieve state-of-the-art exponential convergence speed of reducing classification error in a classification task under a low-noise condition; at the same time, our algorithm with optimized random features can take advantage of the significant reduction of the required number of features so as to accelerate each iteration in the SGD and evaluation of the classifier obtained from our algorithm. These results discover a promising application of QML to significant acceleration of the leading classification algorithm based on kernel methods, without ruining its applicability to a practical class of data sets and the exponential error-convergence speed.Preprint. Under review.

show abstract

Section: Supplementary Materialsmentioning

confidence: 99%

“…We stress that, despite the efforts to exploit QML for accelerating kernel methods [25], it was challenging to use the exponential speedup without ruining applicability due to the sparsity and lowrankness assumptions, except for the regression achieved with the quantum algorithm in Ref. [15].…”

Section: Introductionmentioning

confidence: 99%

Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning

Yamasaki¹,

Sonoda²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…As of late, Kernel methods attract a lot of interest these days, owing to its force of grouping the data based on the correlation between two input variables or in terms of feature set space [13][14][15]. Kernels can likewise be connected to a number of ML models in order to improve data classification accuracy of the model.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Quantum Kernel Method for Biomedical Data Analysis

Ragab¹,

Ashary²,

Sabir³

et al. 2022

Computers, Materials &Amp; Continua

View full text Add to dashboard Cite

This study presents a novel method to detect the medical application based on Quantum Computing (QC) and a few Machine Learning (ML) systems. QC has a primary advantage i.e., it uses the impact of quantum parallelism to provide the consequences of prime factorization issue in a matter of seconds. So, this model is suggested for medical application only by recent researchers. A novel strategy i.e., Quantum Kernel Method (QKM) is proposed in this paper for data prediction. In this QKM process, Linear Tunicate Swarm Algorithm (LTSA), the optimization technique is used to calculate the loss function initially and is aimed at medical data. The output of optimization is either 0 or 1 i.e., odd or even in QC. From this output value, the data is identified according to the class. Meanwhile, the method also reduces time, saves cost and improves the efficiency by feature selection process i.e., Filter method. After the features are extracted, QKM is deployed as a classification model, while the loss function is minimized by LTSA. The motivation of the minimal objective is to remain faster. However, some computations can be performed more efficiently by the proposed model. In testing, the test data was evaluated by minimal loss function. The outcomes were assessed in terms of accuracy, computational time, and so on. For this, databases like Lymphography, Dermatology, and Arrhythmia were used.

show abstract

“…In this work, we report the implementation of an optimisation-free framework [20,21], based on a kernel approximation strategy [23][24][25][26], on real quantum devices for density estimation and classification 1 . This framework can be used for supervised and unsupervised machine learning tasks, which we exemplify through density estimation and classification.…”

Section: Introductionmentioning

confidence: 99%

Optimisation-free Classification and Density Estimation with Quantum Circuits

Vargas-Calderón,

González,

Vinck-Posada

2022

Preprint

View full text Add to dashboard Cite

We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification and probability density estimation using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework.

show abstract

Kernel methods in Quantum Machine Learning

Cited by 43 publications

References 45 publications

Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning

Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning

Mathematical Modelling of Quantum Kernel Method for Biomedical Data Analysis

Optimisation-free Classification and Density Estimation with Quantum Circuits

Contact Info

Product

Resources

About