Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.09851 · Physical review. B./Physical review. B

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

Kristoffer Simula, Ilja Makkonen

Published Sep 15, 2023• 11 citations
arXivHTMLPDF

Abstract

Certain point defects in solids can efficiently be used as qubits for applications in quantum technology. They have spin states that are initializable, readable, robust, and can be manipulated optically. New theoretical methods are needed to find the best host materials and defect configurations. Most methods proposed so far rely either on cluster models or restrict the many-body treatment of the defects to a subspace of single-particle orbitals. We explore best practices and theory for the use of quantum Monte Carlo to predict the excitation spectra for spin defects, by using the negatively charged nitrogen vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) center in diamond as a test system. Quantum Monte Carlo can be used to explicitly simulate electronic correlations with larger systems and sets of orbitals than previous methods due to favorable scaling with respect to system size and computing power. We consider different trial wave functions for variational and diffusion Monte Carlo methods, explore the nodal surface errors of the ground and excited state wave functions, and study whether the variational principle holds for the excited states. We compute the vertical excitation energies in different simulation cell sizes and extrapolate to infinite system size, and include backflow corrections to the extrapolated energies. The final results for vertical excitation energies are found to overestimate the experimental estimates, but the triplet-to-triplet and singlet-to-singlet transitions are accurate against experiment. Finally, we list further developments for QMC needed to address the problem of accurately predicting structural and spin properties of the solid-state defects.

DOI
10.1103/physrevb.108.094108

Related papers

Multiconfigurational nature of electron correlation within nitrogen vacancy centers in diamond

Yilin Chen, Tonghuan Jiang, Haoxiang Chen +5 more

Diamond is a solid-state platform used to develop quantum technologies, but it has been a long-standing problem that the current understanding of quantum states of nitrogen vacancy (NV) centers in diamond is mostly limited to single-electron pictures. Here, we combine the full configuration interaction quantum Monte Carlo method and the density-matrix functional embedding theory to achieve an accurate description of the many-body quantum states of such defects in diamond. More than 30 electrons and 130 molecular orbitals are correlated, revealing the multiconfigurational nature of the wave functions of the many-body quantum states therein. Such a description explains puzzling experimental measurements in intersystem crossing and charge-state transitions at NV centers in diamond. The calculations not only reproduce the available experimental measurements of the energy gaps between quantum states but also provide benchmarks for states that are still subject to considerable uncertainty.

arXiv:2302.13730•Physical review. B./Physical review. B•Jul 10, 2023•11 citations

Simulating the Electronic Structure of Spin Defects on Quantum Computers

Benchen Huang, Marco Govoni, Giulia Galli

We present calculations of both the ground-and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol.We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H SiC, which are of interest for the realization of quantum technologies.We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation.We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation.We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground-and excited-state properties of spin defects.

arXiv:2112.04435•PRX Quantum•Mar 10, 2022•41 citations

Quantum embedding methods for correlated excited states of point defects: Case studies and challenges

Lukas Muechler, Danis I. Badrtdinov, Alexander Hampel +3 more

A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$), the negatively charged nitrogen-vacancy center in diamond (${\mathrm{NV}}^{\ensuremath{-}}$), and an Fe impurity on the Al site in wurtzite AlN (${\text{Fe}}_{\text{Al}}$). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the ``double-counting'' correction. For ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the ${\mathrm{NV}}^{\ensuremath{-}}$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in ${\text{Fe}}_{\text{Al}}$.

arXiv:2105.08705•Physical review. B./Physical review. B•Jun 6, 2022•64 citations

Properties of nitrogen-vacancy centers in diamond: the group theoretic approach

Jeronimo R. Maze, Ádám Gali, Emre Togan +4 more

We present a procedure that makes use of group theory to analyze and predict the main properties of the negatively charged nitrogen-vacancy (NV) center in diamond. We focus on the relatively low temperature limit where both the spin–spin and spin–orbit effects are important to consider. We demonstrate that group theory may be used to clarify several aspects of the NV structure, such as ordering of the singlets in the ( e 2 ) electronic configuration and the spin–spin and spin–orbit interactions in the ( ae ) electronic configuration. We also discuss how the optical selection rules and the response of the center to electric field can be used for spin–photon entanglement schemes. Our general formalism is applicable to a broad class of local defects in solids. The present results have important implications for applications in quantum information science and nanomagnetometry.

arXiv:1010.1338•New Journal of Physics•Feb 28, 2011•463 citations

Photoexcitation and recombination processes of the neutral nitrogen-vacancy center in diamond from first principles

Gergő Thiering, Ádám Gali

Nitrogen-vacancy (NV) complex in diamond is one of the most prominent solid state defects as the negatively charged NV defect (NV−) is a leading contender for quantum technologies. In quantum information processing applications, NV− is photoexcited that often leads to photoionization to neutral NV defect, NV0, and re-ionization back to NV− should occur to control the S=1 spin of NV−. As a consequence, understanding the photophysics of NV0 is crucial for controlling NV−. Furthermore, recent studies have shown that the S=1/2 electron spin of NV0 can also be initialized and read out at certain conditions that turns single NV0 a potential quantum bit. Quantum optics protocols rest on detailed knowledge on the electronic structure of the given system, which is obviously missing for NV0 in diamond. In this study, we combine the group theory and density functional theory calculations toward exploring the nature of the ground and excited states of NV0. We show that the effective three-electron system of NV0 leads to high correlation effects that make this system very challenging for ab initio simulations.

Journal of Applied Physics•Aug 27, 2024•12 citations

Excited state optimization for strongly correlated quantum defects using ensemble variational Monte Carlo

Kevin G. Kleiner, Lucas K. Wagner

Using the recently introduced ensemble variational Monte Carlo (VMC), we study optimized wave functions for strongly correlated point defects, including nitrogen-vacancy and silicon-vacancy centers in diamond and substitutional iron and chromium impurities in aluminum nitride. We study the effects of fully optimized determinant expansion parameters, orbitals, and Jastrow correlation factors on these systems. We find that orbitals from the hybrid functional PBE0 are much better (have lower objective functional) than semilocal PBE, which results in changes in the excitation energies up to 0.5 eV. Further improvements can be made by directly optimizing the objective functional, resulting in changes in excitation energies up to 0.2 eV. The most important parameter varies from defect to defect, reinforcing the necessity of optimizing all parameters to obtain accurate excited states in strongly correlated defects.

arXiv:2607.27377•Jul 29, 2026•0 citations
Certain point defects in solids can efficiently be used as qubits for applications in quantum technology. They have spin states that are initializable, readable, robust, and can be manipulated optically. New theoretical methods are needed to find the best host materials and defect configurations. Most methods proposed so far rely either on cluster models or restrict the many-body treatment of the defects to a subspace of single-particle orbitals. We explore best practices and theory for the use of quantum Monte Carlo to predict the excitation spectra for spin defects, by using the negatively charged nitrogen vacancy (NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath−) center in diamond as a test system. Quantum Monte Carlo can be used to explicitly simulate electronic correlations with larger systems and sets of orbitals than previous methods due to favorable scaling with respect to system size and computing power. We consider different trial wave functions for variational and diffusion Monte Carlo methods, explore the nodal surface errors of the ground and excited state wave functions, and study whether the variational principle holds for the excited states. We compute the vertical excitation energies in different simulation cell sizes and extrapolate to infinite system size, and include backflow corrections to the extrapolated energies. The final results for vertical excitation energies are found to overestimate the experimental estimates, but the triplet-to-triplet and singlet-to-singlet transitions are accurate against experiment. Finally, we list further developments for QMC needed to address the problem of accurately predicting structural and spin properties of the solid-state defects.
Diamond is a solid-state platform used to develop quantum technologies, but it has been a long-standing problem that the current understanding of quantum states of nitrogen vacancy (NV) centers in diamond is mostly limited to single-electron pictures. Here, we combine the full configuration interaction quantum Monte Carlo method and the density-matrix functional embedding theory to achieve an accurate description of the many-body quantum states of such defects in diamond. More than 30 electrons and 130 molecular orbitals are correlated, revealing the multiconfigurational nature of the wave functions of the many-body quantum states therein. Such a description explains puzzling experimental measurements in intersystem crossing and charge-state transitions at NV centers in diamond. The calculations not only reproduce the available experimental measurements of the energy gaps between quantum states but also provide benchmarks for states that are still subject to considerable uncertainty.
We present calculations of both the ground-and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol.We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H SiC, which are of interest for the realization of quantum technologies.We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation.We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation.We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground-and excited-state properties of spin defects.
A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (CBCN{\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}CB​CN​), the negatively charged nitrogen-vacancy center in diamond (${\mathrm{NV}}^{\ensuremath{-}}$), and an Fe impurity on the Al site in wurtzite AlN (FeAl{\text{Fe}}_{\text{Al}}FeAl​). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the ``double-counting'' correction. For CBCN{\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}CB​CN​ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the ${\mathrm{NV}}^{\ensuremath{-}}$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in FeAl{\text{Fe}}_{\text{Al}}FeAl​.
We present a procedure that makes use of group theory to analyze and predict the main properties of the negatively charged nitrogen-vacancy (NV) center in diamond. We focus on the relatively low temperature limit where both the spin–spin and spin–orbit effects are important to consider. We demonstrate that group theory may be used to clarify several aspects of the NV structure, such as ordering of the singlets in the ( e 2 ) electronic configuration and the spin–spin and spin–orbit interactions in the ( ae ) electronic configuration. We also discuss how the optical selection rules and the response of the center to electric field can be used for spin–photon entanglement schemes. Our general formalism is applicable to a broad class of local defects in solids. The present results have important implications for applications in quantum information science and nanomagnetometry.
Nitrogen-vacancy (NV) complex in diamond is one of the most prominent solid state defects as the negatively charged NV defect (NV−) is a leading contender for quantum technologies. In quantum information processing applications, NV− is photoexcited that often leads to photoionization to neutral NV defect, NV0, and re-ionization back to NV− should occur to control the S=1 spin of NV−. As a consequence, understanding the photophysics of NV0 is crucial for controlling NV−. Furthermore, recent studies have shown that the S=1/2 electron spin of NV0 can also be initialized and read out at certain conditions that turns single NV0 a potential quantum bit. Quantum optics protocols rest on detailed knowledge on the electronic structure of the given system, which is obviously missing for NV0 in diamond. In this study, we combine the group theory and density functional theory calculations toward exploring the nature of the ground and excited states of NV0. We show that the effective three-electron system of NV0 leads to high correlation effects that make this system very challenging for ab initio simulations.
Using the recently introduced ensemble variational Monte Carlo (VMC), we study optimized wave functions for strongly correlated point defects, including nitrogen-vacancy and silicon-vacancy centers in diamond and substitutional iron and chromium impurities in aluminum nitride. We study the effects of fully optimized determinant expansion parameters, orbitals, and Jastrow correlation factors on these systems. We find that orbitals from the hybrid functional PBE0 are much better (have lower objective functional) than semilocal PBE, which results in changes in the excitation energies up to 0.5 eV. Further improvements can be made by directly optimizing the objective functional, resulting in changes in excitation energies up to 0.2 eV. The most important parameter varies from defect to defect, reinforcing the necessity of optimizing all parameters to obtain accurate excited states in strongly correlated defects.