Evaluating NISQ Devices with Quadratic Nonresidues

TL;DR

This paper introduces a quantum algorithm for finding quadratic nonresidues, proposes a challenge to demonstrate quantum advantage on NISQ devices, and evaluates current quantum hardware performance on this task.

Contribution

It presents a novel quantum algorithm for quadratic nonresidues, a challenge for quantum advantage, and an empirical evaluation on NISQ devices.

Findings

Quantum algorithm solves QNR in polynomial time.

Quantum devices outperform classical methods on the QNR challenge.

Empirical performance data of NISQ devices on the QNR test.

Abstract

We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We show that QNR is in Exact Quantum Polynomial time, while it is still unknown whether QNR is in P. Second, we present a challenge to create a probability distribution over the quadratic nonresidues. Due to the theoretical complexity gap, a quantum computer can achieve a higher success rate than any known method on a classical computer. A device beating the classical bound indicates quantum advantage or a mathematical breakthrough. Third, we derive a simple circuit for the smallest instance of the quadratic nonresidue test and run it on a variety of currently available NISQ devices. We then present a comparative statistical evaluation of the NISQ devices tested.