NASA Center for Climate Simulation

Abstract

Recent investment from the private sector into quantum computing has led to several commercially available quantum computing devices. Among them the first publicly available quantum gate computer is the IBMQ. Alongside the hardware device is the open source software package QISKit which allows anyone to run a quantum circuit on the IBMQ machines.

There are many algorithms that offer a computational speedup over their best classical counterparts. One such algorithm was developed by Harrow, Hassidim, and Lloyd(HHL) in 2009 to solve linear systems of equations. The best classical algorithm, conjugate gradient scales as O( N log( N ) ) while the HHL algorithm scales as O( log ( N ) ), where N is the size of the linear system.

Here we investigate the feasibility of implementing the HHL algorithm on the IBMQ. We begin with a study of the IBMQ focusing on the decoherence time. This is a measure of how long a qubit will remain in the state it is supposed to be in. Then we discuss the linear systems algorithm and its components. Results for the quantum Fourier transform(QFT) are presented and the improvements to the IBMQ required to run the HHL algorithm are discussed.