Implementation of Liouville space search algorithm on strongly dipolar coupled nuclear spins

TL;DR

This paper adapts the Liouville space search algorithm for strongly dipolar coupled nuclear spins, enabling its implementation using transition selective pulses, and demonstrates this experimentally on a four-qubit system.

Contribution

It introduces a modified Liouville space search algorithm suitable for strongly coupled spins, expanding its applicability beyond weakly coupled systems.

Findings

Successful experimental implementation on a four-qubit system.

Algorithm works with transition selective pulses in strongly coupled spins.

Extends quantum search techniques to complex spin systems.

Abstract

Liouville space search algorithm [Bruschweiler, Phys. Rev. Lett. {\bf 85}, 4815(2000).] utilizes mixed initial states of the ensemble, and has been successfully implemented earlier in weakly coupled spins, in which a spin can be identified as a qubit. It has recently been demonstrated that n-strongly coupled spins can be collectively treated as an n-qubit system. Application of algorithms in such systems, requires new approaches using transition selective pulses rather than qubit selective pulses. This work develops a modified version of Liouville space search algorithm, which is applicable for strongly as well as weakly coupled spins. All the steps of the algorithm, can be implemented by using transition selective pulses. Experimental implementation is carried out on a strongly dipolar coupled four qubit system.