Hybrid classical-quantum linear solver using Noisy Intermediate-Scale
  Quantum machines
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 $\mathcal{O}(N\log(N))$ time on a quantum circuit made of
$\mathcal{O}(\log(N))$ 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.
Chih-Chieh Chen Shiue-Yuan Shiau Ming-Feng Wu Yuh-Renn Wu