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

## TL;DR

This paper introduces a practical hybrid classical-quantum algorithm for solving certain linear systems, leveraging quantum random walks on NISQ devices, with potential applications in machine learning.

## Contribution

It presents a feasible hybrid quantum-classical linear solver using quantum random walks optimized for NISQ hardware, demonstrated on IBM Q systems.

## Key findings

- Runs in O(N log N) time on quantum circuits
- Uses O(log N) qubits for input/output
- Robust against noise and suitable for machine learning applications

## 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.