Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines

Abstract

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.

11 pages, 4 figures, 2 tables