# Arbitrary Nuclear Spin Gates in Diamond Mediated by a NV-center Electron Spin

## TL;DR

This paper introduces a protocol enabling arbitrary multi-qubit nuclear spin interactions mediated by an NV-center electron spin, facilitating direct measurement of nuclear many-body correlators and broad applicability to other platforms.

## Contribution

It presents a general method leveraging dynamical decoupling to control nuclear spins via an electron spin, expanding quantum register capabilities.

## Key findings

- Achieves arbitrary N-qubit nuclear spin interactions.
- Enables direct measurement of nuclear many-body correlators.
- Applicable to other platforms like silicon carbide.

## Abstract

We propose a protocol that achieves arbitrary N-qubit interactions between nuclear spins and that can measure directly nuclear many-body correlators by appropriately making the nuclear spins interact with a nitrogen vacancy (NV) center electron spin. The method takes advantage of recently introduced dynamical decoupling techniques and demonstrates that action on the electron spin is sufficient to fully exploit nuclear spins as robust quantum registers. Our protocol is general, being applicable to other nuclear spin based platforms with electronic spin defects acting as mediators as the case of silicon carbide.