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 with Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs in o(N log(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.