Characterizing the Interaction Graph of a Multi-Spin Network in Diamond*

Optically dark electronic spins in diamond surrounding optically addressable nitrogen vacancy (NV) centers can act as qubits in a multi-spin quantum register to help realize more powerful quantum devices. While recent experiments have shown initialization and control of electronic spins near a NV center, the system size has been limited to spins directly coupled to it. In this work we demonstrate our ability to further scale up a quantum register of electronic spins in diamond by harnessing spins beyond the coherence limit of the central NV center. We map out an unknown graph of interacting spins in the environment of a single NV center, and we achieve complete characterization of a four-spin network within a finite frequency range and above a practical coupling strength threshold. This will enable us to polarize a dark spin that is beyond the practical control limit of the central NV center, which could be used for sensing of distant electronic spins. The control tools we develop and our results provide a roadmap to engineer larger solid-state quantum registers, and further advance their capabilities for quantum sensing, device characterization, and simulation.