We propose a realistic hybrid classical-quantum linear solver to solve systems of linear equations of a specific type, and demonstrate its feasibility using Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs in O(Nlog(N)) time on a quantum circuit made of O(log(N)) qubits. The input and output are classical data, and so can be easily accessed. It is robust against noise, and ready for implementation in applications such as machine learning.
@article{arxiv.1903.10949,
title = {Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines},
author = {Chih-Chieh Chen and Shiue-Yuan Shiau and Ming-Feng Wu and Yuh-Renn Wu},
journal= {arXiv preprint arXiv:1903.10949},
year = {2019}
}