Optically addressable defect-based qubits offer significant advantages for room-temperature operation. Two-dimensional (2D) materials, particularly h-BN, have emerged as promising hosts for these qubits due to their scalability and potential for controlled doping. However, challenges remain, including the undetermined chemical nature of existing quantum defects and the lack of reliable theoretical methods for accurate prediction of critical physical parameters in 2D systems. These parameters include deep defect levels, stable high spin states, large zero-field splitting (ZFS), efficient radiative recombination, high intersystem crossing (ISC) rates, and long spin coherence and relaxation times. This work addresses these challenges by developing a first-principles theoretical framework that accurately predicts these parameters, considering many-body interactions and dynamical processes such as radiative and nonradiative recombinations. The authors aim to overcome the limitations of uncontrolled and undetermined chemical nature of existing SPEs and unsatisfactory spin-dependent properties of existing defects in 2D materials by designing promising spin defects using high-integrity theoretical methods. The introduction highlights the need for accurate calculations that include defect charge transition levels, optical excitation and exciton radiative lifetime (accounting for defect-exciton interactions), spin-phonon relaxation time, spin coherence time, and phonon-assisted nonradiative recombination rates. Crucially, the role of spin-orbit-induced ISC, essential for pure spin state initialization in qubit operation, is emphasized as a key area for investigation.

The paper reviews existing research on optically addressable defect-based qubits and their applications in quantum computing. It highlights the progress made in using 2D materials, particularly h-BN, to host stable single-photon emitters (SPEs) and spin triplet defects. The authors cite several studies demonstrating the existence of SPEs and spin triplet defects in h-BN, but also point out the challenges associated with the undetermined chemical nature of these defects and the limitations of current theoretical methods in predicting their properties. The literature review underscores the need for a theoretical framework that accurately predicts key physical parameters of defects in 2D materials. The existing theoretical approaches which were reviewed are computationally expensive and often limited to static properties and mean field approximations, lacking the accuracy required for designing and engineering quantum defects with specific properties for 2D quantum technology applications. Therefore, existing methods lack the ability to address the need for accurate prediction of defect charge transition levels, radiative and nonradiative decay rates, exciton-defect interactions and intersystem crossing rates.

The authors developed a complete theoretical framework to design spin defects in h-BN. This framework involves a multi-step computational process combining several state-of-the-art first-principles methods. The methodology begins with a screening process to identify defects with stable triplet ground states using total energy calculations at both semi-local Perdew-Burke-Ernzerhof (PBE) and hybrid functional levels. Dopant substitution at a divacancy site was considered for four elemental groups. Subsequently, the zero-field splitting (ZFS) was calculated, considering both spin-spin and spin-orbit contributions using a plane-wave-based method and the ORCA code respectively. For single-photon emitter (SPE) identification, the authors screened defects based on optical transitions and radiative lifetime calculations at the random phase approximation (RPA) level. Promising candidates were further investigated using many-body perturbation theory (G0W0) with hybrid functional (PBE0(α)) to obtain more accurate electron correlation and address self-interaction errors. The Bethe-Salpeter equation (BSE) was solved to include excitonic effects due to the strong defect-exciton coupling in 2D systems. The optical properties of defects were explored including absorption spectra, radiative lifetimes, exciton binding energies and exciton wavefunctions. To calculate radiative recombination rates, the authors used Fermi's Golden Rule and considered excitonic effects from BSE. For nonradiative processes, including phonon-assisted spin-conserving and spin-flip processes (intersystem crossing, ISC), a first-principles approach was used. This approach extends beyond the Huang-Rhys approximation by explicitly computing the overlap of phonon wavefunctions. Spin-orbit coupling (SOC) was computed using the ORCA code. The framework also involves the calculation of thermodynamic charge transition levels and defect formation energy to assess the stability of the defects. The authors also implemented and benchmarked methods for computing ZFS and ISC rates by comparing the calculated values for the NV center in diamond with experimental values.

The computational screening process identified TiVV and MoVV as stable triplet defects in h-BN, a rare finding. Both defects exhibited sizable ZFS, larger than that of the NV center in diamond, indicating potential for qubit operation. The calculations predicted that SiV is a strong SPE candidate in h-BN, showing that SiV possesses an exciton radiative lifetime comparable to experimentally observed SPE defects. The calculations of the single-particle energy levels using G0W0 calculations and the optical spectra including exciton effects via BSE showed that TiVV and MoVV have long radiative lifetimes exceeding μs, indicating that these are not good candidates for SPEs. Meanwhile, the optical properties of SiV showed a bright optical transition in the ultraviolet region and a short radiative lifetime (22.8 ns), suggesting its potential as an SPE. The analysis of excited-state dynamics revealed the dominant role of ISC in spin-selective decay pathways for both TiVV and MoVV, making them promising candidates for spin qubit applications. For TiVV, a fast ISC with a rate of 12 GHz is predicted, suggesting an efficient spin purification process. For MoVV, while having lower quantum efficiency than TiVV, the ISC rate is comparable to diamond, indicating feasible optical control. The authors note that although TiVV exhibits a low optical quantum yield, its fast ISC offers a key advantage for pure spin state preparation for qubit operations. The MoVV defect, owing to its more ideal ZPL position and improved quantum efficiency, presents better prospects for optical control that can be further enhanced by techniques such as coupling to optical cavities or applying strain.

The findings of this study demonstrate the importance of accurately considering many-body interactions and dynamical processes, particularly ISC, when searching for spin defects. The successful identification of promising SPE and spin qubit candidates in h-BN highlights the potential of extrinsic defects in 2D materials for quantum information science. The authors' first-principles theoretical framework enables the design of defects with specific properties tailored for quantum applications. The discovery of TiVV and MoVV with large ZFS and efficient ISC expands the range of available spin qubits. The identification of SiV as a strong SPE candidate provides a pathway for developing efficient single-photon sources. The comparison of the computational results with experimental data for the NV center in diamond validates the accuracy and reliability of the theoretical framework. The authors acknowledge the limitations of their approach, such as the 1D effective phonon approximation, and suggest future studies focusing on the calculation of spin coherence time and further experimental verification.

This work establishes a comprehensive theoretical framework for designing and identifying optically addressable spin defects in 2D materials. The framework successfully identified promising spin qubits (TiVV and MoVV) and a single-photon emitter (SiV) in h-BN, demonstrating the potential of extrinsic defects in 2D materials for quantum information science. Future research should focus on investigating spin coherence time, understanding decoherence mechanisms, and performing further experiments to validate the theoretical predictions. The framework opens avenues for the design of defects with specific desired properties, accelerating the development of quantum technology.

The study uses approximations, including the 1D effective phonon approximation for calculating nonradiative recombination rates. While the authors validate this approximation by comparing with full phonon calculations (Supplementary Table 8), this simplification might affect the accuracy of the results. Further refinements to include full phonon calculations would improve the accuracy. The study also focuses primarily on the defects within the context of h-BN, and therefore it is necessary to test and extend the framework to other 2D materials. Additional experimental validation is needed to confirm the theoretical predictions made in this study and to investigate other potential sources of decoherence, particularly the spin coherence times. The work also assumes that the defects are isolated in the h-BN matrix, which may not always be true in real experimental settings.