The Grover algorithm with large nuclear spins in semiconductors

TL;DR

This paper proposes implementing the Grover quantum search algorithm using large nuclear spins in semiconductors, utilizing multiphoton transitions and quadrupolar splitting to control and distinguish spin states.

Contribution

It introduces a method to perform Grover's algorithm with large nuclear spins by leveraging multiphoton transitions and a generalized rotating frame for effective Hamiltonian modeling.

Findings

Effective implementation of Grover's algorithm with nuclear spins I=1/2 to 9/2.

The generalized rotating frame accurately models spin dynamics for large quadrupolar splitting.

Better agreement between approximate and exact calculations with increased quadrupolar splitting.

Abstract

We show a possible way to implement the Grover algorithm in large nuclear spins 1/2<I<9/2 in semiconductors. The Grover sequence is performed by means of multiphoton transitions that distribute the spin amplitude between the nuclear spin states. They are distinguishable due to the quadrupolar splitting, which makes the nuclear spin levels non-equidistant. We introduce a generalized rotating frame for an effective Hamiltonian that governs the non-perturbative time evolution of the nuclear spin states for arbitrary spin lengths I. The larger the quadrupolar splitting, the better the agreement between our approximative method using the generalized rotating frame and exact numerical calculations.