Design of quantum Fourier transforms and quantum algorithms by using circulant Hamiltonians

TL;DR

This paper introduces a method to design quantum Fourier transforms and algorithms using engineered circulant Hamiltonians, employing adiabatic evolution for robustness against parameter fluctuations.

Contribution

It presents a novel approach to implement quantum Fourier transforms with circulant Hamiltonians in a single step, enhancing robustness and efficiency.

Findings

Effective single-step quantum Fourier transform implementation.

Robustness against interaction parameter fluctuations.

Utilization of circulant symmetry in Hamiltonian design.

Abstract

We propose a technique for design of quantum Fourier transforms, and ensuing quantum algorithms, in a single interaction step by engineered Hamiltonians of circulant symmetry. The method uses adiabatic evolution and is robust against fluctuations of the interaction parameters as long as the Hamiltonian retains a circulant symmetry.