A quantum-enhanced solution method for multi classification problems

Abstract

With the increasing data size of multi classification problems, the running efficiency of classical algorithms is seriously affected. In the paper, in order to improve the implementation efficiency of the algorithm, we propose a quantum-enhanced solution method for multi classification problems. The method mainly introduces the quantum-enhanced technology into the classical algorithm. Aiming at the two steps of solving Euclid distance and kernel function in the classical algorithm, the paper relates the classical inner product principle with the amplitude evolution of quantum states. On the basis of quantizing the sample data, a general quantum circuit that can calculate the inner product is designed and constructed. The circuit can make full use of the advantages of quantum parallel computing to achieve exponential acceleration of computing efficiency. Aiming at solving linear equations in the classical algorithm, a quantum circuit based on the quantum singular value estimation is designed and constructed. The circuit makes use of the acceleration advantage of quantum computing in matrix computing to achieve polynomial acceleration of matrix computing. The experimental results show that the method can not only find the optimal solution for multi classification problems, but also greatly improve the operation efficiency of the algorithm. Compared with the classical methods, the method has at least polynomial improvement in time complexity and spatial complexity.