Auger Spectroscopy via Generative Quantum Eigensolver: A Quantum Approach to Molecular Excitations

Abstract

Auger electron spectroscopy, a way of characterizing electronic structure through core-level decay processes, is widely used in materials characterization; however direct calculation from molecular geometry requires accurate treatment of many excited states, posing a challenge for classical methods. We present a hybrid quantum-classical workflow for calculating Auger spectra that combines the generative quantum eigensolver (GQE) for ground-state preparation, the quantum self-consistent equation-of-motion method for excited-state calculations, and the one-centre approximation for Auger transition rates. GQE uses a GPT-2 model to generate quantum circuits for ground-state optimization, allowing our workflow to benefit from HPC parallelization and GPU-acceleration for favourable scaling with system size. We demonstrate the validity of our workflow by calculating the Auger spectrum of water with the STO-3G basis set and demonstrating qualitative and quantitative agreement with spectra obtained using completely classical full configuration interaction calculations, from the computational literature, and from the experimental literature. We also find that for water, substituting the variational quantum eigensolver (VQE) for GQE results in near-identical spectra, but that the ground state estimator generated by GQE contains about half the total gate count as that generated by VQE.

Figures (6)

• Figure 1: Graphical summary of the Auger workflow used in this study. First, the ground-state reference is prepared with the GQE nakaji_generative_2024. Next, q-sc-EOM provides core-ionized and doubly ionized energies ($E_{\mathrm{IP}}$, $E_{\mathrm{DIP}}$) and transition reduced density matrices asthana_quantum_2023. Finally, the OCA tenorio_multireference_2022 combines these quantities with atomic integrals to produce the Auger spectrum.
• Figure 2: GQE results for the 12-qubit water molecule. The blue solid line is the GQE result, and the dashed grey line is the FCI result obtained using PySCF and the STO-3G basis. The grey region indicates the threshold for chemical accuracy. Simulation data are plotted only until this threshold is reached.
• Figure 3: Auger spectrum of $\mathrm{H_2O}$. (a) Spectrum obtained with the proposed hybrid workflow. (b) Fully classical FCI+OCA reference. (c) Experimental spectrum digitized from Ref. moddeman_determination_1971. We observe close agreement in relative peak intensity and position between all three spectra.
• Figure 4: The Auger spectrum of water calculated using our workflow, but substituting VQE for GQE. This spectrum is nearly identical to the one produced in Fig. \ref{['fig:h2o_auger']}(a), confirming that the GQE ground state is of comparable quality to VQE and that the differences from the FCI reference (Fig. \ref{['fig:h2o_auger']}(b)) originate from the q-sc-EOM approximation for excited states.
• Figure 5: GQE results for the LiH model. The solid blue line is the GQE result, and the dashed grey line is the FCI result obtained by PySCF. The solid grey area indicates the range of chemical accuracy. The result obtained by GQE is within chemical accuracy of the FCI result.