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On quantum methods for machine learning problems part II: Quantum classification algorithms

Farid Mansurovich Ablayev, Marat Ablayev, Joshua Zhexue Huang +3 more

This is a review of quantum methods for machine learning problems that consists of two parts. The first part, “quantum tools”, presented some of the fundamentals and introduced several quantum tools based on known quantum search algorithms. This second part of the review presents several classification problems in machine learning that can be accelerated with quantum subroutines. We have chosen supervised learning tasks as typical classification problems to illustrate the use of quantum methods for classification.This is a review of quantum methods for machine learning problems that consists of two parts. The first part, “quantum tools”, presented some of the fundamentals and introduced several quantum tools based on known quantum search algorithms. This second part of the review presents several classification problems in machine learning that can be accelerated with quantum subroutines. We have chosen supervised learning tasks as typical classification problems to illustrate the use of quantum methods for classification.

Big Data Mining and AnalyticsDec 19, 201935 citations

Summary of Part I

Alexander A. Lisyansky, E. S. Andrianov, Alexey P. Vinogradov +1 more

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 20240 citations

On quantum methods for machine learning problems part I: Quantum tools

Farid Mansurovich Ablayev, Marat Ablayev, Joshua Zhexue Huang +3 more

This is a review of quantum methods for machine learning problems that consists of two parts. The first part, “quantum tools”, presents the fundamentals of qubits, quantum registers, and quantum states, introduces important quantum tools based on known quantum search algorithms and SWAP-test, and discusses the basic quantum procedures used for quantum search methods. The second part, “quantum classification algorithms”, introduces several classification problems that can be accelerated by using quantum subroutines and discusses the quantum methods used for classification.This is a review of quantum methods for machine learning problems that consists of two parts. The first part, “quantum tools”, presents the fundamentals of qubits, quantum registers, and quantum states, introduces important quantum tools based on known quantum search algorithms and SWAP-test, and discusses the basic quantum procedures used for quantum search methods. The second part, “quantum classification algorithms”, introduces several classification problems that can be accelerated by using quantum subroutines and discusses the quantum methods used for classification.

Big Data Mining and AnalyticsDec 19, 201965 citations

Overview of Part II

Lukas Burgholzer, Robert Wille

Springer eBooksJan 1, 20260 citations

Summary of Part II

Lukas Burgholzer, Robert Wille

Springer eBooksJan 1, 20260 citations

Polynomial unconstrained binary optimisation â part 2

Fred Glover, Jin‐Kao Hao, Gary A. Kochenberger

The class of problems known as quadratic zero-one (binary) unconstrained optimisation has provided access to a vast array of combinatorial optimisation problems, allowing them to be expressed within the setting of a single unifying model. A gap exists, however, in addressing polynomial problems of degree greater than 2. To bridge this gap, we provide methods for efficiently executing core search processes for the general polynomial unconstrained binary (PUB) optimisation problem. A variety of search algorithms for quadratic optimisation can take advantage of our methods to be transformed directly into algorithms for problems where the objective functions involve arbitrary polynomials. Part 1 of this paper (Glover et al., 2011) provided fundamental results for carrying out the transformations and described coding and decoding procedures relevant for efficiently handling sparse problems, where many coefficients are 0, as typically arise in practical applications. In the present part 2 paper, we provide special algorithms and data structures for taking advantage of the basic results of part 1. We also disclose how our designs can be used to enhance existing quadratic optimisation algorithms.The class of problems known as quadratic zero-one (binary) unconstrained optimisation has provided access to a vast array of combinatorial optimisation problems, allowing them to be expressed within the setting of a single unifying model. A gap exists, however, in addressing polynomial problems of degree greater than 2. To bridge this gap, we provide methods for efficiently executing core search processes for the general polynomial unconstrained binary (PUB) optimisation problem. A variety of search algorithms for quadratic optimisation can take advantage of our methods to be transformed directly into algorithms for problems where the objective functions involve arbitrary polynomials. Part 1 of this paper (Glover et al., 2011) provided fundamental results for carrying out the transformations and described coding and decoding procedures relevant for efficiently handling sparse problems, where many coefficients are 0, as typically arise in practical applications. In the present part 2 paper, we provide special algorithms and data structures for taking advantage of the basic results of part 1. We also disclose how our designs can be used to enhance existing quadratic optimisation algorithms.

International Journal of MetaheuristicsJan 1, 201111 citations

Problems for Part I

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Problems for Part I

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