On the time-optimal implementation of quantum Fourier transform for qudits represented by quadrupole nucleus

TL;DR

This paper investigates the minimal time required to implement the quantum Fourier transform on qudits with 3 to 8 levels, using NMR-controlled quadrupole nuclei, highlighting differences between integer and half-integer spins.

Contribution

It provides a numerical optimization approach to determine time-optimal QFT implementation for qudits with varying dimensions and spin types.

Findings

Minimum implementation time varies with qudit dimension.

Differences observed between integer and half-integer spin cases.

Optimization results guide efficient quantum gate design.

Abstract

We consider the problem of time-optimal realization of the quantum Fourier transform gate for a single qudit with number of levels d from 3 to 8. As a qudit the quadrupole nucleus with spin I > 1/2 controlled by NMR is considered. We calculate the dependencies of the gate error on the duration of radio-frequency pulse obtained by numerical optimization using Krotov-based algorithm. It is shown that the dependences of minimum time of QFT gate implementation on qudit dimension are different for integer and half-integer spins.