Experimental realization of quantum algorithms for linear system inspired by adiabatic quantum computing

TL;DR

This paper demonstrates an experimental implementation of a quantum algorithm inspired by adiabatic quantum computing to solve 8-dimensional linear equations using a 4-qubit NMR system, showcasing practical potential for quantum linear system solutions.

Contribution

It experimentally realizes a quantum linear system solver inspired by adiabatic quantum computing, achieving the solution of higher-dimensional equations with limited qubits.

Findings

Successfully solved 8-dimensional linear equations in a 4-qubit system.

Implemented the algorithm with simplifications for practical feasibility.

Shows potential for solving real-world linear systems with quantum computers.

Abstract

Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we can solve linear equation system via algorithm inspired by adiabatic quantum computing. Here we demonstrate the algorithm and realize the solution of 8-dimensional linear equations $A\textbf{x}=\textbf{b}$ in a 4-qubit nuclear magnetic resonance system. The result is by far the solution of maximum-dimensional linear equation with a limited number of qubits in experiments, which includes some ingenious simplifications. Our experiment provides the new possibility of solving so many practical problems related to linear equations systems and has the potential applications in designing the future quantum algorithms.