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Related Experiment Video

Updated: Sep 3, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum Linear System Algorithm for General Matrices in System Identification.

Kai Li¹, Ming Zhang², Xiaowen Liu¹

¹College of Information and Communication, National University of Defense Technology, Xi'an 710006, China.

Entropy (Basel, Switzerland)

|July 27, 2022

Summary

This study introduces a novel quantum algorithm for solving linear systems of equations. The new method offers a significant speedup for general matrices, advancing quantum computation capabilities.

Keywords:

linear systems of equations quantum algorithm system identification time complexity

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Area of Science:

Quantum Computing
Linear Algebra
Numerical Analysis

Background:

Solving linear systems (Ax=b) is fundamental in classical computation.
Existing quantum algorithms have limitations regarding matrix properties and efficiency.

Purpose of the Study:

To develop a more efficient quantum algorithm for solving linear systems of equations.
To address limitations of current quantum linear system solvers.

Main Methods:

A modified quantum scheme based on singular value estimation.
Development of a quantum circuit for homogeneous linear equations.

Main Results:

Achieved a runtime of O(κ^2 log(mn)/ϵ) for general m x n matrices.
Demonstrated sparsity-independent and non-square matrix applicability.
Reported exponential improvement for homogeneous linear equations.

Conclusions:

The proposed quantum scheme offers a universal quantum linear system solver.
This research enhances the applicability and efficiency of quantum algorithms for linear algebra problems.