Experimental Quantum Computing to Solve Systems of Linear Equations

TL;DR

This paper demonstrates the implementation of a quantum algorithm that can solve small systems of linear equations exponentially faster than classical methods, showcasing the potential of quantum computing for large-scale linear algebra problems.

Contribution

The authors experimentally realize the simplest quantum algorithm for solving linear equations using four qubits, illustrating its fundamental working principle.

Findings

Successfully solved 2x2 linear equations on a quantum computer

Demonstrated the feasibility of the quantum linear solver algorithm

Showcased the implementation of all subroutines with four qubits

Abstract

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2*2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.