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Certain point defects in solids can efficiently be used as qubits forapplications in quantum technology. They have spin states that areinitializable, readable, robust, and can be manipulated optically. Newtheoretical methods are needed to find the best host materials and defectconfigurations. Most methods proposed so far rely either on cluster models orrestrict the many-body treatment of the defects to a subspace ofsingle-particle orbitals. We explore best practices and theory for the use ofquantum Monte Carlo to predict the excitation spectra for spin defects, byusing the negatively charged nitrogen vacancy (NV$^-$) center in diamond as atest system. Quantum Monte Carlo can be used to explicitly simulate electroniccorrelations with larger systems and sets of orbitals than previous methods dueto favourable scaling with respect to system size and computing power. Weconsider different trial wave functions for variational and diffusion MonteCarlo methods, explore the nodal surface errors of the ground and excited statewave functions and study whether the variational principle holds for theexcited states. We compute the vertical excitation energies in differentsimulation cell sizes and extrapolate to infinite system size, and includebackflow corrections to the extrapolated energies. The final results forvertical excitation energies are found to overestimate the experimentalestimates, but the triplet-to-triplet and singlet-to-singlet transitions areaccurate against experiment. Finally, we list further developments for QMCneeded to address the problem of accurately predicting structural and spinproperties of the solid-state defects.

Calculation of the energies of the multideterminant states of the nitrogen vacancy center in diamond with quantum Monte Carlo