HHL Analysis and Simulation Verification Based on Origin Quantum Platform

Abstract

Solving large-scale linear equations is of great significance in many engineering fields, such as weather forecasting and bioengineering. The classical computer solves the linear equations, no matter adopting the elimination method or Kramer’s rule, the time required for solving is in a polynomial relationship with the scale of the equation system. With the advent of the era of big data, the integration of transistors is getting higher and higher. When the size of transistors is close to the order of electron diameter, quantum tunneling will occur, and Moore’s Law will not be followed. Therefore, the traditional computing model will not be able to meet the demand. In this paper, through an in-depth study of the classic HHL algorithm, a small-scale quantum circuit model is proposed to solve a 2×2 linear equations, and the circuit diagram and programming are used to simulate and verify on the Origin Quantum Platform. The fidelity under different parameter values reaches more than 90%. For the case where the matrix to be solved is a sparse matrix, the quantum algorithm has an exponential speed improvement over the best known classical algorithm.