Computational speed-up in a single qudit NMR quantum information processor

TL;DR

This paper demonstrates experimentally that a single qudit can outperform classical methods in solving a permutation problem using NMR technology, showcasing quantum speed-up with minimal quantum resources.

Contribution

It provides the first experimental realization of a quantum algorithm using a single qudit in NMR, illustrating quantum speed-up without entanglement.

Findings

Single qudit quantum algorithm outperforms classical in permutation problem

Experimental implementation with quadrupolar NMR confirms theoretical speed-up

Demonstrates quantum advantage with minimal quantum systems

Abstract

Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in non-classical correlations such as entanglement or quantum discord. However, it has been recently shown that even a single pure qudit is sufficient to design an oracle-based algorithm which solves a black-box problem faster than any classical approach to the same problem. In particular, the algorithm that we consider determines whether eight permutation functions defined on a set of four elements is positive or negative cyclic. While any classical solution to this problem requires two evaluations of the function, quantum mechanics allows us to perform the same task with only a single evaluation. Here, we present the first experimental demonstration of the considered quantum algorithm with a quadrupolar nuclear magnetic resonance setup using a single four-level quantum system, i.e., a ququart.