Variational Quantum Support Vector Machine based on $\Gamma$ matrix expansion and Variational Universal-Quantum-State Generator

TL;DR

This paper introduces a variational quantum support vector machine utilizing a $ ext{Gamma}$ matrix expansion for solving linear equations and a universal quantum circuit for state preparation, advancing quantum machine learning techniques.

Contribution

It presents a novel approach combining $ ext{Gamma}$ matrix expansion with a universal quantum circuit to enhance quantum support vector machines and state generation.

Findings

Effective linear equation solving with $ ext{Gamma}$ matrix expansion

Universal quantum circuit can generate arbitrary quantum states

Potential for quantum FPGA-like applications

Abstract

We analyze a binary classification problem by using a support vector machine based on variational quantum-circuit model. We propose to solve a linear equation of the support vector machine by using a $\Gamma$ matrix expansion. In addition, it is shown that an arbitrary quantum state is prepared by optimizing a universal quantum circuit representing an arbitrary $U(2^N)$ based on the steepest descent method. It may be a quantum generalization of Field-Programmable-Gate Array (FPGA).