Simulation of Grover's quantum search algorithm in a Ising nuclear spin chain quantum computer with first and second nearest neighbour couplings

TL;DR

This paper demonstrates the implementation and analysis of Grover's quantum search algorithm on a nuclear spin chain quantum computer, considering realistic Ising interactions, and explores how fidelity varies with Rabi frequency.

Contribution

It presents a numerical simulation of Grover's algorithm on a spin chain with first and second nearest neighbor couplings, including fidelity analysis and optimal Rabi frequencies.

Findings

Fidelity exhibits maxima at specific Rabi frequencies satisfying the (2πk)-condition.

Performance is affected by second nearest neighbor interactions.

Numerical results guide optimal parameter choices for realistic quantum hardware.

Abstract

We implement Grover's quantum search algorithm on a nuclear spin chain quantum computer, taking into Ising type interactions between nearest and second nearest neighbours into account. The performance of the realisation of the algorithm is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtained pronounced maxima at frequencies which fulfil the condition of the (2\pi k)-method with respect to the second nearest neighbour interactions.