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:2606.20166

Applications of quantum annealing to magnetic dipole hyperfine structure constants: First results beyond energies for atoms

Boni Paul, Subimal Deb, Per Jönsson, Jörgen Ekman, Bhanu Pratap Das

quant-phphysics.atom-phphysics.chem-phSubmitted Jun 18, 2026• Announced Jun 19, 2026• 0 citations
v1 · Jun 18, 2026v2 · Jun 29, 2026
arXivHTMLPDF

Abstract

We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral $\mathrm{Li}$, Li-like $\mathrm{Be}$, neutral $\mathrm{Na}$, and Na-like $\mathrm{Mg}$ using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices ($H_{\mathrm{DC}}$) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and $H_{\mathrm{DC}}$ matrix dimensions.

Related papers

Accurate Computation of Relativistic Excitation Energies Using Quantum Annealing

Kumar Vikrant, Nishanth Baskaran, V. S. Prasannaa +4 more

We report the first results for the computation of relativistic effects in quantum many-body systems using quantum annealers. An average accuracy of 98.9% in the fine structure splitting of boron-like ions with respect to experiments has been achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the D-Wave Advantage hardware. We obtain these results in the framework of the many-electron Dirac theory. We implement QAE through our quantum annealing workflow that includes a novel qubit encoding scheme and a perturbation theory-based decomposition strategy.

arXiv:2212.01801•Dec 4, 2022•1 citation

Experimental computations of atomic properties on a superconducting quantum processor

Akhil Pratap Singh, Kenji Sugisaki, V. S. Prasannaa +3 more

We experimentally compute relativistic and correlation effects in the atomic properties by using a superconducting qubit processor. Specifically, we compute the relativistic ground-state energies and magnetic-dipole hyperfine structure constants for four Li-like atomic systems ranging from very light to moderately heavy to very heavy in terms of nuclear charge. A symmetry-conserving Bravyi-Kitaev transformation is used to reduce the original six-qubit problem to a four-qubit problem, which is experimentally contrived by reducing the hardware requirement by employing a virtual two-qubit gate. It enables the simulation of four-qubit circuits using two physical qubits with additional circuit evaluations. The ground-state wave functions, required for computing atomic properties, are obtained by using quantum state tomography. Our results show that the averaged relative errors for the ground-state energies are ≈ 0.3 ± 1 % . However, for the hyperfine structure constants, the mean values of the relative errors are less than 15 % , with their estimated upper bound of relative errors of ≈ ± 10 % (with the exception of 7.2 ± 47 % for neutral Li 7 ). Notably, our results for the hyperfine structure constants exhibit higher sensitivity to errors as compared to energies; a trend which we also confirm through additional numerical simulations. Published by the American Physical Society 2024

Physical Review A•Dec 30, 2024•4 citations

Computation of relativistic and many-body effects in atomic systems using quantum annealing

V. Vijay Kumar, Nishanth Baskaran, V. S. Prasannaa +4 more

We report results for the computation of relativistic effects in quantum many-body systems using quantum annealers. An average accuracy of 98.9% in the fine-structure splitting of boron-like ions with respect to experiments is achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the D-Wave Advantage 5000-qubit hardware, which is substantially higher than that attained on a gate-based quantum device to date. We obtain these results in the framework of the many-electron Dirac theory. We implement QAE using a hybrid quantum annealing method that includes an alternative qubit encoding scheme and decomposing the problem into smaller ones based on perturbation theory.

Physical Review A•Apr 8, 2024•6 citations

Calculation of the magnetic hyperfine structure constant of alkali metals and alkaline-earth-metal ions using the relativistic coupled-cluster method

Sudip Sasmal

The $Z$-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (${A}_{J}$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The $Z$-vector results are in very good agreement with the experiment. The ${A}_{J}$ values of Li, Na, K, Rb, Cs, ${\mathrm{Be}}^{+}$, ${\mathrm{Mg}}^{+}$, ${\mathrm{Ca}}^{+}$, and ${\mathrm{Sr}}^{+}$ obtained in the $Z$-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the $Z$-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.

arXiv:1706.09640•Physical Review A•Jul 13, 2017•9 citations

Fock-space relativistic coupled-cluster calculations of two-valence atoms

Brajesh Kumar Mani, D. Angom

We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of ${\mathrm{Sr}}^{+}$, ${\mathrm{Ba}}^{+}$, and ${\mathrm{Yb}}^{+}$. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine structure constants of ${\mathrm{Yb}}^{+}$.

arXiv:1009.2963•Physical Review A•Jan 7, 2011•27 citations

Reverse Quantum Annealing for Ground-State Energy Calculation in Molecule

Pradyot Pritam Sahoo

We present the results of our reverse quantum annealing computations of the ground-state energies of alkaline-earth monofluoride molecules. By partitioning the Dirac--Coulomb electronic Hamiltonian into sub-QUBOs and refining forward-annealing solutions through optimized reverse-annealing schedules, residual configuration errors are systematically minimized. The electronic ground-state wave functions and energies are obtained using the Quantum Annealing Eigensolver algorithm. This work provides a pathway for achieving sub-milliHartree chemical accuracy and advancing molecular electronic structure calculations in the quantum annealing paradigm.

quant-pharXiv:2610.39129•Oct 30, 2026•0 citations
We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral Li\mathrm{Li}Li, Li-like Be\mathrm{Be}Be, neutral Na\mathrm{Na}Na, and Na-like Mg\mathrm{Mg}Mg using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices (HDCH_{\mathrm{DC}}HDC​) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and HDCH_{\mathrm{DC}}HDC​ matrix dimensions.
We report the first results for the computation of relativistic effects in quantum many-body systems using quantum annealers. An average accuracy of 98.9% in the fine structure splitting of boron-like ions with respect to experiments has been achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the D-Wave Advantage hardware. We obtain these results in the framework of the many-electron Dirac theory. We implement QAE through our quantum annealing workflow that includes a novel qubit encoding scheme and a perturbation theory-based decomposition strategy.
We experimentally compute relativistic and correlation effects in the atomic properties by using a superconducting qubit processor. Specifically, we compute the relativistic ground-state energies and magnetic-dipole hyperfine structure constants for four Li-like atomic systems ranging from very light to moderately heavy to very heavy in terms of nuclear charge. A symmetry-conserving Bravyi-Kitaev transformation is used to reduce the original six-qubit problem to a four-qubit problem, which is experimentally contrived by reducing the hardware requirement by employing a virtual two-qubit gate. It enables the simulation of four-qubit circuits using two physical qubits with additional circuit evaluations. The ground-state wave functions, required for computing atomic properties, are obtained by using quantum state tomography. Our results show that the averaged relative errors for the ground-state energies are ≈ 0.3 ± 1 % . However, for the hyperfine structure constants, the mean values of the relative errors are less than 15 % , with their estimated upper bound of relative errors of ≈ ± 10 % (with the exception of 7.2 ± 47 % for neutral Li 7 ). Notably, our results for the hyperfine structure constants exhibit higher sensitivity to errors as compared to energies; a trend which we also confirm through additional numerical simulations. Published by the American Physical Society 2024
We report results for the computation of relativistic effects in quantum many-body systems using quantum annealers. An average accuracy of 98.9% in the fine-structure splitting of boron-like ions with respect to experiments is achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the D-Wave Advantage 5000-qubit hardware, which is substantially higher than that attained on a gate-based quantum device to date. We obtain these results in the framework of the many-electron Dirac theory. We implement QAE using a hybrid quantum annealing method that includes an alternative qubit encoding scheme and decomposing the problem into smaller ones based on perturbation theory.
The ZZZ-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (AJ{A}_{J}AJ​) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The ZZZ-vector results are in very good agreement with the experiment. The AJ{A}_{J}AJ​ values of Li, Na, K, Rb, Cs, Be+{\mathrm{Be}}^{+}Be+, Mg+{\mathrm{Mg}}^{+}Mg+, Ca+{\mathrm{Ca}}^{+}Ca+, and Sr+{\mathrm{Sr}}^{+}Sr+ obtained in the ZZZ-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the ZZZ-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.
We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of Sr+{\mathrm{Sr}}^{+}Sr+, Ba+{\mathrm{Ba}}^{+}Ba+, and Yb+{\mathrm{Yb}}^{+}Yb+. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine structure constants of Yb+{\mathrm{Yb}}^{+}Yb+.
We present the results of our reverse quantum annealing computations of the ground-state energies of alkaline-earth monofluoride molecules. By partitioning the Dirac--Coulomb electronic Hamiltonian into sub-QUBOs and refining forward-annealing solutions through optimized reverse-annealing schedules, residual configuration errors are systematically minimized. The electronic ground-state wave functions and energies are obtained using the Quantum Annealing Eigensolver algorithm. This work provides a pathway for achieving sub-milliHartree chemical accuracy and advancing molecular electronic structure calculations in the quantum annealing paradigm.