A Nuclear Magnetic Resonance Implementation of a Classical Deutsch-Jozsa Algorithm

TL;DR

This paper demonstrates using NMR as a classical computing medium to determine specific Boolean functions in the Deutsch-Jozsa problem, clarifying quantum algorithm comparisons.

Contribution

It introduces a classical NMR implementation of the Deutsch-Jozsa algorithm that reveals actual functions rather than just their classification.

Findings

NMR can be used as a classical computing medium for the Deutsch-Jozsa problem.

The approach determines specific Boolean functions for small cases.

Clarifies issues in comparing quantum and classical black-box algorithms.

Abstract

Nuclear magnetic resonance (NMR) has been widely used as a demonstrative medium for showcasing the ability for quantum computations to outperform classical ones. A large number of such experiments performed have been implementations of the Deutsch-Jozsa algorithm. It is known, however, that in some cases the Deutsch-Jozsa problem can be solved classically using as many queries to the black-box as in the quantum solution. In this paper we describe experiments in which we take the contrasting approach of using NMR as a classical computing medium, treating the nuclear spin vectors classically and utilising an alternative embedding of bits into the physical medium. This allows us to determine the actual Boolean function computed by the black-box for the n=1,2 cases, as opposed to only the nature (balanced or constant) as conventional quantum algorithms do. Discussion of these experiments leads to some clarification of the complications surrounding the comparison of different quantum algorithms, particularly black-box type algorithms.