Determining the parity of a permutation using an experimental NMR qutrit

TL;DR

This paper demonstrates the first experimental use of a single qutrit, realized with a deuterium nucleus, to determine permutation parity, leveraging quantum contextuality for computational advantage.

Contribution

It introduces an experimental implementation of a quantum algorithm for permutation parity using a single qutrit, highlighting advantages over qubit-based approaches.

Findings

Successful NMR implementation with deuterium nucleus as qutrit

First experimental use of a single qutrit for computation

Shows potential of qutrits for quantum algorithms

Abstract

We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.