Non-Adiabatic Universal Holonomic Quantum Gates Based on Abelian Holonomies

TL;DR

This paper presents a method for implementing non-adiabatic universal holonomic quantum gates using abelian holonomies and Lie-algebraic techniques, avoiding complex secondary procedures and enabling purely non-adiabatic operations.

Contribution

The authors introduce a novel scheme for non-adiabatic holonomic quantum gates that does not require double-loop or spin-echo techniques, simplifying experimental realization.

Findings

Gates are realizable purely in the non-adiabatic regime.

The scheme uses dynamical invariants and Lie-algebraic methods.

It avoids experimental difficulties associated with previous methods.

Abstract

We implement a non-adiabatic universal set of holonomic quantum gates based on abelian holonomies using dynamical invariants, by Lie-algebraic methods. Unlike previous implementations, presented scheme does not rely on secondary methods such as double-loop or spin-echo and avoids associated experimental difficulties. It turns out that such gates exist purely in the non-adiabatic regime for these systems.