Performance of quantum registers in diamond in the presence of spin impurities

TL;DR

This paper provides a theoretical analysis of the performance of small quantum registers in diamond, focusing on coherence and fidelity of quantum operations in the presence of spin impurities and environmental interactions.

Contribution

It introduces a detailed theoretical model for multi-qubit NV center registers considering impurity interactions and predicts coherence and fidelity under various conditions.

Findings

Coherence properties depend on impurity density and geometry.

Fidelities for GHZ and Bell operations are quantified.

Decoupling pulses improve quantum operation performance.

Abstract

The Nitrogen Vacancy Center in diamond coupled to addressable surrounding nuclear spins forms a versatile building block for future quantum technologies. While previous activities focused on sensing with only a single or very few spins in operation, recently multi-qubit registers have been successfully implemented for quantum information processing. Further progress requires a detailed understanding of the performance of quantum protocols for consecutive gate operations and thus, beyond established treatments for relaxation and dephasing. Here, we provide such a theoretical analysis for a small spin registers with up to four spins built out of NV and environmental constituents in presence of ensembles of interacting impurity spins. Adapting a cluster correlation expansion, we predict coherence properties as well as fidelities for GHZ- and Bell-gate operations also in presence of decoupling pulses. The influence of the volume density and the geometry of the spin-bath consisting of the substitutional nitrogen- or $^{13}C$ atoms are also taken into account.