Implementing quantum Fourier transform using three qubits

TL;DR

This paper demonstrates a method to implement the quantum Fourier transform using three qubits by exploiting Hamiltonian symmetry, with potential for high fidelity and faster gates via counter-driving fields.

Contribution

It introduces a symmetry-based approach for realizing quantum Fourier transform in three-qubit systems, emphasizing entanglement preservation and gate acceleration techniques.

Findings

Fidelity calculations show promising results.

Symmetry allows eigenvector construction independent of physical parameters.

Counter-driving fields can accelerate the gate operation.

Abstract

Using the circulant symmetry of a Hamiltonian describing three qubits, we realize the quantum Fourier transform. This symmetry allows us to construct a set of eigenvectors independently on the magnitude of physical parameters involved in the Hamiltonian and as a result, the entanglement will be maintained. The realization will be leaned on trapped ions and the gate implementation requires an adiabatic transition from each spin product state to Fourier modes. The fidelity was numerically calculated and the results show important values. Finally, we discuss the acceleration of the gate by using the counter-driving field.