arXiv subjects

Stephan P. A. Sauer

Publications and source records attributed to Stephan P. A. Sauer.

At least 19 recordsLinked to original sources

arXiv2026

Implementing QESEM's High-Accuracy Error Mitigation on a Quantum Computer: a Water Potential Energy Surface Study

Quantum error mitigation (QEM) is essential for extracting chemically accurate results from near-term quantum hardware. Many widely used QEM methods rely on uncontrolled heuristics whose bias depends on the specific circuit and noise realization. In this work, we employ QESEM---a characterization-based, unbiased quasi-probabilistic mitigation method---on IBM's Aachen quantum processor to compute the ground-state potential energy surface (PES) of the symmetrically-stretched water molecule. We consider a classically-optimized, single-layer perfect-pairing tiled unitary product state ansatz. We map this ansatz to an 8-qubit register corresponding to a (4,4) active space and the STO-3G basis set. Compared to the statevector reference, we find that raw QPU results typically overestimate the ground-state energy by around 500~mHa across the scanned geometries. On the other hand, QESEM-mitigated results fall approximately within 100~mHa, 30~mHa, or ``chemical accuracy'' ($\sim$1.5~mHa), depending on the target precision. We benchmark QESEM at both loose (0.1~Ha) and tight (0.01~Ha) precision targets, evaluating both individual and merged batches of runs. As the precision target is tightened, the accuracy improves systematically, matching or exceeding results reported in the literature. We further quantify the sampling cost of these results, reporting the number of shots required at each precision level. Our results show how, with the current levels of hardware error, reaching the highest accuracies demands substantial QPU time. The results demonstrate that the characterization-based, unbiased error mitigation provided by QESEM allows to measure quantitatively meaningful potential energy surfaces on current quantum hardware. Concurrently, they highlight the sampling overhead associated with QEM, which remains a central bottleneck en route to larger chemical problems and higher precision.

quant-ph↗

arXiv2026

Analytical Nuclear Gradients and Hessians on Quantum Hardware via Orbital-Optimized VQE with Error Mitigation

Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory. On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations. The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.

physics.chem-ph↗

arXiv2026

Cost-effective scalable quantum error mitigation for tiled Ansätze

We introduce a cost-effective quantum error mitigation technique that builds upon the recent Ansatz-based gate and readout error mitigation method (M0). The technique, tiled M0, leverages the unique structure of tiled Ansätze (e.g., tUPS, QNP, hardware-efficient circuits) to apply a locality approximation to M0 that results in an exponential reduction in the QPU cost of the noise characterization. We validate the technique for molecular ground state energy calculations with the tUPS Ansatz on LiH, molecular hydrogen, water, butadiene, and benzene (4-12 qubits), demonstrating little to no loss in accuracy compared to M0 in noisy simulations. We also show the performance of the technique in quantum experiments, highlighting its potential use in near-term applications.

quant-ph↗

arXiv2026

Benchmarking SOPPA-based methods for the calculation of static and dynamic polarizabilities

Static and frequency-dependent polarizabilities were computed for 41 molecules using RPA, RPA(D), HRPA, HRPA(D), SOPPA, SOPPA(CC2), and SOPPA(CCSD) with the aug-cc-pVTZ basis set and benchmarked against CCSD reference values and available experimental data. The analysis reveals a pronounced distinction between the performance of these methods for aromatic versus non-aromatic molecules. Across all frequencies, HRPA consistently yields substantially larger deviations from CCSD than the other approaches, whereas HRPA(D) and SOPPA(CCSD) provide the most accurate results overall. For static polarizabilities, HRPA(D) performs best for non-aromatic systems, followed by SOPPA(CCSD) and RPA(D), while SOPPA(CCSD) is most accurate for aromatic molecules. In the frequency-dependent regime, HRPA(D) remains the most accurate method for non-aromatic molecules, although RPA(D) shows greater consistency. For aromatic molecules, SOPPA(CCSD) performs best at low frequencies, with RPA offering intermediate accuracy but higher consistency than most other methods; at higher frequencies, RPA becomes the most accurate approach, followed by RPA(D), while SOPPA(CCSD) deteriorates. These trends highlight the importance of doubles corrections in RPA(D) and HRPA(D), which achieve accuracy comparable to or better than SOPPA(CCSD) at lower computational cost. The strong performance of RPA for aromatic molecules is attributed to its characteristic overestimation of the lowest electronic excitation energy. Comparison with experimental data confirms SOPPA(CCSD) as the most reliable method for static polarizabilities, while RPA and HRPA(D) provide the best agreement for frequency-dependent polarizabilities of aromatic systems.

physics.chem-ph↗

arXiv2026

Resource-efficient energy-based operator selection in fermionic ADAPT-VQE via exact Hamiltonian transformation

The energy-based approach to operator selection in ADAPT-VQE relies on reconstructing the one-parameter energy landscape for each operator in the pool. In fermionic implementations, the cost of reconstructing this energy landscape often becomes a bottleneck. We address this issue through an exact Hamiltonian transformation that reformulates the one-parameter energy landscape according to a generator-dependent fragmentation of the transformed Hamiltonian. While our method is mathematically identical to standard fermionic Rotoselect, it effectively reduces its cost by about a factor of two, bringing it close to that of gradient-based ADAPT-VQE. We use this formulation to benchmark the gradient-based and energy-based selection approaches in combination with two ansatz-optimization strategies -- "last", where only the appended operator is optimized, and "full", where the full ansatz is re-optimized -- and with both fixed-orbital and orbital-optimized formulations. The benchmark comprises $\text{LiH}$, $\text{BeH}_2$, and $\text{H}_2\text{O}$ at both equilibrium and stretched geometries. In the most weakly correlated system, pairing energy-based selection with "last" optimization enables the efficient construction of an accurate ansatz, which avoids any VQE optimization. As correlation increases, full ansatz re-optimization and orbital optimization become the main factors governing convergence and overall resource cost. This study shows how exact Hamiltonian transformations provide an effective route to reducing the measurement overhead of fermionic energy-based ADAPT-VQE. Moreover, the benchmark clarifies the relative role of operator scoring approach, re-optimization strategy, and orbital treatment in the performance of ADAPT-VQE.

quant-ph↗

arXiv2026

Orbital-optimized spin-adapted multistate contracted VQE for excited states and properties on quantum hardware

We introduce the orbital-optimized multistate contracted variational quantum eigensolver (oo-MC-VQE) method with spin-adapted operators for the computation of ground and excited states, as well as state-specific and transition properties. The use of spin-adapted operators ensures that the spin symmetry of the reference states is conserved throughout the VQE optimization. In multistate variational approaches, achieving a balanced description of an increasing number of electronic states places growing demands on the expressibility of the underlying ansatz, thereby introducing a fundamental trade-off between accuracy and circuit complexity. We consider the effects of this trade-off explicitly and find that the number of circuit parameters required to obtain accurate results is reported to scale approximately linearly in the number of states. We further present an explicit quantum-circuit implementation of the oo-MC-VQE method and demonstrate its integration with quantum error mitigation techniques. Finally, we execute the method on real quantum devices to compute absorption spectra for two benchmark molecular systems.

quant-ph↗

arXiv2026

A Lanczos-based algorithm for sum-over-states calculations of NMR spin--spin coupling constants at the RPA level of theory: The Fermi-contact term

The analysis of nuclear magnetic resonance parameters, such as the indirect nuclear spin-spin coupling constants, in terms of contributions from localised molecular orbitals is a commonly used approach for gaining a deeper understanding of experimentally observed trends in these parameters. In the vast majority of these studies, contributions from pairs of one occupied and one virtual orbital are calculated and analyzed. Analyses in terms of two pairs of an occupied and a virtual orbital, that would allow for the study of coupling pathways, are much more seldom, as they require calculating the coupling constants as a sum over all excited states. Previous studies have shown that, for the often dominating Fermi-contact contribution to the coupling constants, more or less all excited states have to be calculated when employing a Davidson algorithm, because the most high-lying excited states can also make a significant contribution to the Fermi-contact term. In this study we investigated therefore, whether by employing a Lanczos algorithm one can obtain converged values of the Fermi-contact contribution to the indirect nuclear spin-spin coupling constants already with a significantly smaller percentage of the total number of excited states included in the sum-over-states expression. To this purpose we have extended the recent implementation of a Lanczos algorithm for the RPA/TDHF or TDDFT eigenvalue problem in the Dalton program (L. Zamok et al. J. Chem. Phys. 156, 014102 (2022)). The new procedure was tested on 17 molecules containing first, second and third row atoms. We find that, for most coupling constants, less than 50% of the excited pseudo states are necessary for converging the Fermi-contact term with an error of less than 0.5 Hz. For the few exceptions, typically for molecules with third-row atoms, around 60% were necessary.

physics.chem-ph↗

arXiv2026

Quantum error mitigation using energy sampling and extrapolation enhanced Clifford data regression

Error mitigation is essential for the practical implementation of quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. This work explores and extends Clifford Data Regression (CDR) to mitigate noise in quantum chemistry simulations using the Variational Quantum Eigensolver (VQE). Using the H$_4$ molecule with the tiled Unitary Product State (tUPS) ansatz, we perform noisy simulations with the ibm torino noise model to investigate in detail the effect of various hyperparameters in CDR on the error mitigation quality. Building on these insights, two improvements to the CDR framework are proposed. The first, Energy Sampling (ES), improves performance by selecting only the lowest-energy training circuits for regression, thereby further biasing the sample energies toward the target state. The second, Non-Clifford Extrapolation (NCE), enhances the regression model by including the number of non-Clifford parameters as an additional input, enabling the model to learn how the noisy-ideal mapping evolves as the circuit approaches the optimal one. Our numerical results demonstrate that both strategies outperform the original CDR.

quant-ph↗

arXiv2025

Orbital-Optimized Unitary Coupled Cluster for Indirect Nuclear Spin-Spin Coupling Constants within a Quantum Linear Response Framework

We present a quantum linear response (qLR) approach within an active-space framework for computing indirect nuclear spin-spin coupling constants, a key ingredient in NMR spectra predictions. The method employs the unitary coupled cluster (UCC) ansatz and its orbital-optimized variant (ooUCC), both suitable for quantum computing implementations, to evaluate spin-spin coupling constants via qLR. Test calculations on five small molecules are compared with CASCI, CASSCF, and conventional CCSD results. qLR with UCC/ooUCC yields spin-spin coupling constants comparable to classical methods. We further examine the role of orbital optimization and find that ooUCC markedly affects the computed couplings; orbital-optimized results show better agreement with CCSD. These findings indicate that orbital optimization is important for accurate NMR coupling predictions within quantum-computing-friendly correlated methods.

physics.chem-ph↗

arXiv2025

Vibrational corrections to molecular properties including relativistic corrections at the level of the Zeroth-Order Regular Approximation

The vibrational averaging module of the Dalton Project was extended to work also with the Amsterdam Density Functional (ADF) program, making it possible to calculate vibrational corrections to properties and at the same time include a treatment of relativistic effects for heavier atoms at the level of the Zeroth-Order Regular Approximation (ZORA). To illustrate the importance of the relativistic contributions, zero-point vibrational corrections were calculated for the electric field gradient tensor and the two NMR parameters, the isotropic shielding and the spin-spin coupling constants (SSCC), of selected mercury compounds. For all three properties, the vibrational corrected values performed closest to experimental values, and the magnitudes of the corrections depended on the level of relativity and the basis set in the calculation.

physics.chem-ph↗

arXiv2025

Reduced density matrix and cumulant approximations of quantum linear response

Linear response (LR) is an important tool in the computational chemist's toolbox. It is therefore no surprise that the emergence of quantum computers has led to a quantum version, quantum LR (qLR). However, the current quantum era of near-term intermediary scale quantum (NISQ) computers is dominated by noise, short decoherence times, and slow measurement speed. It is therefore of interest to find approximations that greatly reduce the quantum workload while only slightly impacting the quality of a method. In an effort to achieve this, we approximate the naive qLR with singles and doubles (qLRSD) method by either directly approximating the reduced density matrices (RDMs) or indirectly through their respective reduced density cumulants (RDCs). We present an analysis of the measurement costs behind qLR with RDMs, and report qLR results for model Hydrogen ladder systems; for varying active space sizes of OCS, SeH$_2$, and H$_2$S; and for symmetrically stretched H$_2$O and BeH$_2$. Discouragingly, while approximations to the 4-body RDMs and RDCs seem to produce good results for systems at the equilibrium geometry and for some types of core excitations, they both tend to fail when the system exhibits strong correlation. All approximations to the 3-body RDMs and/or RDCs severely affect the results and cannot be applied.

physics.chem-ph↗

arXiv2025

Hyperfine Coupling Constants on Quantum Computers: Performance, Errors, and Future Prospects

We present the first implementation and computation of electron spin resonance isotropic hyperfine coupling constants (HFCs) on quantum hardware. As illustrative test cases, we compute the HFCs for the hydroxyl radical (OH$^{\bullet}$), nitric oxide (NO$^{\bullet}$), and the triplet hydroxyl cation (OH$^{+}$). Our approach integrates the qubit-ADAPT method with unrestricted orbital optimization in an active space framework. To accurately measure the necessary spin one-electron reduced density matrices on current hardware, we employ a combination of error mitigation, error suppression, and post-selection, including our in-house developed ansatz-based readout and gate error mitigation. The HFCs obtained from the quantum hardware experiments align with results from unrestricted complete active space self-consistent field calculations on classical hardware. These results mark a significant step towards leveraging quantum computing for chemically relevant molecular properties and highlight the critical role of multi-method error strategies in the noisy intermediate-scale quantum era.

quant-ph↗

arXiv2025

Critical Limitations in Quantum-Selected Configuration Interaction Methods

Quantum Selected Configuration Interaction (QSCI) methods (also known as Sample-based Quantum Diagonalization, SQD) have emerged as promising near-term approaches to solving the electronic Schr{ö}dinger equation with quantum computers. In this work, we perform numerical analysis to show that QSCI methods face critical limitations that severely hinder their practical applicability in chemistry. Using the nitrogen molecule and the iron-sulfur cluster [2Fe-2S] as examples, we demonstrate that while QSCI can, in principle, yield high-quality configuration interaction (CI) expansions similar to classical SCI heuristics in some cases, the method struggles with inefficiencies in finding new determinants as sampling repeatedly selects already seen configurations. This inefficiency becomes especially pronounced when targeting high-accuracy results or sampling from an approximate ansatz. In cases where the sampling problem is not present, the resulting CI expansions are less compact than those generated from classical heuristics, rendering QSCI an overall more expensive method. Our findings suggest a significant drawback in QSCI methods when sampling from the ground-state distribution as the inescapable trade-off between finding sufficiently many determinants and generating compact, accurate CI expansions. This ultimately hinders utility in quantum chemistry applications, as QSCI falls behind more efficient classical counterparts.

physics.chem-ph↗

arXiv2025

Redundant parameter dependencies in truncated classic and quantum Linear Response and Equation of Motion theory

Extracting molecular properties from a wave function can be done through the linear response (LR) formalism or, equivalently, the equation of motion (EOM) formalism. For a simple model system, He in a 6-31G basis, it is here shown that calculated excitation energies depend on the specifically chosen orbitals, even when the ground-state is the FCI solution, if the LR is truncated to a singles expansion. This holds for naive, projected, self-consistent, and state-transfer parametrizations of the LR operators. With a focus on the state-transfer parameterization, this problem is shown to also hold for more complicated systems, and is also present when the LR is truncated to singles and doubles. This problem can be alleviated by performing a ground-state constrained trace optimization of the Hessian matrix before performing the LR calculation. It is finally shown that spectra can be further improved for small LR expansions by targeting only a few states in the constrained trace optimization using constrained state-averaged UCC.

physics.chem-ph↗

arXiv2025

A Computational Study of the Vibrational and Rotational g-Factors of the Diatomic Molecules LiH, LiF, CO, CS, SiO and SiS

The purpose of this article is to present theoretical values for the vibrational and rotational g-factors of several diatomic molecules. The calculations have been carried out at the Multi-Configurational Self-Consistent Field (MCSCF) level of theory. To determine the most reliant method and basis set for these calculations also the Hartree-Fock (HF) and Density Functional Theory (DFT) approaches were considered. Different DFT functionals, including B3LYP, BHandHLYP, PBE0, B3PW91 and KT3 have been employed. Furthermore, different active spaces were evaluated to optimize MCSCF. To establish the accuracy of the methods the computed rotational g-factors were compared to experimental values. The benchmark study of CO and CS shows that the MCSCF method provides most reliable results and that the aug-cc-pCV5Z basis set is the most sufficient. The aug-cc-pCVQZ basis set for Li and aug-cc-pV5Z basis set for H gave best results for LiH. The active spaces tested for CO and CS do not yet converge towards the experimental values when more determinants were included. However, if the g-factors are vibrationally averaged, the computed values are seen to move towards the experimental value. Lastly, the g-factors have been vibrationally averaged, and it shows a slight improved agreement between computed values and experimental data.

physics.chem-ph↗

arXiv2025

Exact closed-form expression for unitary spin-adapted fermionic singlet double excitation operators

We derive exact closed-form expressions for the matrix exponential of the anti-Hermitian spin-adapted singlet double excitation fermionic operators. These expressions enable the efficient implementation of such operators within unitary product state frameworks targeting conventional hardware, and allow for the implementation of ansatze that guarantee convergence to specific spin symmetries. Moreover, these exact closed-form expressions might also lay the groundwork for constructing spin-adapted circuits for quantum devices.

quant-ph↗

arXiv2025

Bromine and Iodine in Atmospheric Mercury Oxidation

We investigate the atmospheric oxidation of mercury Hg(0) by halogens, initiated by Br and I to yield Hg(I), and continued by I, Br, BrO, ClO, IO, NO2 and HO2 to yield Hg(II) or Hg(0), using computational methods with a focus on the creation of data for determining the impact of rising iodine levels. We calculate reaction enthalpies and Gibbs free energies using the Coupled Cluster singlets, doublets, and perturbative triplets method (CCSD(T)) with the ma-def2-TZVP basis set and effective core potential to account for relativistic effects. Additionally, we investigate the reaction kinetics using variational transition state theory based on geometric scans of bond dissociations at the CASPT2/ma-def2-TZVP level. We compare the results obtained from the CASPT2 and CCSD(T) methods to help define the uncertainty. Our results provide insights into the mechanisms of these reactions, and the data produced get us closer to determining iodine's impact on mercury depletion events and on the atmosphere as a whole. The reaction *HgBr + Br* -> HgBr2 was found to be twice as fast as HgI* + I* -> HgI2, with reaction rate coefficients of 8.8x10-13 and 4.2x10-13 cm3molecule-1s-1 respectively. The BrHg* + BrO* -> BrHgOBr reaction was about 7.2 times faster than the *HgI + IO* -> IHgOI reaction with their rates being 3.3x10-14 and 4.6x10-15 cm3molecule-1s-1 respectively. We investigate the Hg*XOY (X and Y being halogen) complexes. From the reactions investigated including iodine, the reaction with the most plausible chance of impacting the mercury lifetime in the atmosphere is HgI* + I* -> HgI2.

physics.chem-ph↗

arXiv2024

Self-consistent Quantum Linear Response with a Polarizable Embedding environment

Quantum computing presents a promising avenue for solving complex problems, particularly in quantum chemistry, where it could accelerate the computation of molecular properties and excited states. This work focuses on hybrid quantum-classical algorithms for near-term quantum devices, combining the quantum linear response (qLR) method with a polarizable embedding (PE) environment. We employ the self-consistent operator manifold of quantum linear response (q-sc-LR) on top of a unitary coupled cluster (UCC) wave function in combination with a Davidson solver. The latter removes the need to construct the entire electronic Hessian, improving computational efficiency when going towards larger molecules. We introduce a new superposition-state-based technique to compute Hessian-vector products and show that this approach is more resilient towards noise than our earlier gradient-based approach. We demonstrate the performance of the PE-UCCSD model on systems such as butadiene and para-nitroaniline in water and find that PE-UCCSD delivers comparable accuracy to classical PE-CCSD methods on such simple closed-shell systems. We also explore the challenges posed by hardware noise and propose simple error correction techniques to maintain accurate results on noisy quantum computers.

physics.chem-ph↗