Solving Linear Systems of Equations on a Trapped Ion Quantum Computer

Solutions to linear systems of equations are the key to many technologically relevant applications, including artificial intelligence, data processing, and system modeling. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm has been shown to provide exponential speed-up over classical methods for solving these systems [1]. Here we present the results of an experimental demonstration of the HHL algorithm on a trapped ion quantum computer. We develop an optimized, 4-qubit circuit to correctly solve a system of two and four equations. The process fidelity of our trapped ion quantum computer is high enough to accurately identify the solution without the use of error mitigation.