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Variational quantum support vector machine based on [Formula: see text] matrix expansion and variational

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  • 1Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Tokyo, 113-8656 Japan.

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This study introduces a quantum support vector machine for binary classification using variational quantum circuits. It demonstrates a novel method for solving linear equations and preparing quantum states, potentially generalizing Field-Programmable Gate Arrays (FPGAs).

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Area of Science:

  • Quantum Computing
  • Machine Learning
  • Computational Science

Background:

  • Support Vector Machines (SVMs) are powerful tools for binary classification.
  • Variational quantum circuits offer a promising approach for quantum machine learning.
  • Efficient methods for solving linear equations are crucial in many computational tasks.

Purpose of the Study:

  • To develop and analyze a quantum support vector machine (QSVM) model.
  • To propose a novel method for solving the linear equation inherent in SVMs using matrix expansion.
  • To demonstrate the preparation of arbitrary quantum states via optimization of universal quantum circuits.

Main Methods:

  • Utilizing a variational quantum circuit model for the SVM.
  • Employing a [Formula: see text] matrix expansion to solve the SVM's linear equation.
  • Applying the steepest descent method for optimizing a universal quantum circuit to prepare quantum states.

Main Results:

  • Successful application of a quantum circuit-based SVM for binary classification.
  • Demonstration of a matrix expansion technique for solving linear equations in the QSVM.
  • Validation of arbitrary quantum state preparation through circuit optimization.

Conclusions:

  • The proposed QSVM offers a quantum approach to binary classification.
  • The matrix expansion method provides an efficient way to solve linear equations in QSVMs.
  • The optimized universal quantum circuit represents a potential quantum generalization of Field-Programmable Gate Arrays (FPGAs).