Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies

TL;DR

This paper proposes a hybrid quantum computation scheme combining noiseless subsystems and non-Abelian holonomies to achieve robust, all-geometric universal quantum computation resistant to decoherence and imperfections.

Contribution

It introduces a novel all-geometric universal quantum computation method using non-adiabatic, non-Abelian holonomies within a four-qubit noiseless subsystem.

Findings

Scheme is robust against symmetry-breaking imperfections

Provides implementation details for the hybrid approach

Demonstrates stability of the method in noisy environments

Abstract

Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In this paper, we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on non-adiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.