Error-mitigation techniques for quantum simulations of spin defects on quantum computers

Recently, we formulated a quantum defect embedding theory [1,2] for hybrid classical-quantum calculations of the electronic structure of spin defects, where one defines an effective Hamiltonian describing the electronic states of the defects within the environment of a periodic solid. Here we focus on finding the ground and excited states of the effective Hamiltonian representing a nitrogen-vacancy center in diamond and a divacancy in silicon carbide, on a quantum computer. We use two techniques, a variational quantum eigensolver (VQE) [3] and a quantum subspace expansion [4]. We show that by combining partial constraints on electron occupation to overcome the unphysical state problem [5] of VQE and zero noise extrapolation [6], we can obtain reasonably accurate results on near-term-noisy architectures not only for ground state properties of the spin-defects, but also for their excited state properties.

[1] Ma, He, et al. npj Computational Materials 6.1 (2020): 1-8.

[2] Ma, He, et al. JCTC 17.4 (2021): 2116-2125.

[3] Peruzzo, Alberto, et al. Nature communications 5.1 (2014): 1-7.

[4] McClean, Jarrod R., et al. Physical Review A 95.4 (2017): 042308.

[5] Sawaya, Nicolas PD, et al. JCTC 12.7 (2016): 3097-3108.

[6] Li, Ying, and Simon C. Benjamin. Physical Review X 7.2 (2017): 021050.