arXiv subjects

Jacob Kongsted

Publications and source records attributed to Jacob Kongsted.

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

Perturbatively Corrected Linear Response Selected Configuration Interaction

Selected configuration interaction (SCI) methods have emerged as powerful, lower-cost alternatives to full configuration interaction (FCI) for ground- and excited-state energies. Still, calculating molecular response properties with SCI remains a significant challenge. In this work, we introduce perturbative corrections to the linear response selected configuration interaction (LR-SCI) framework, using an order-by-order Epstein-Nesbet perturbation expansion through second order. We demonstrate that in this theoretical framework, the finite-order perturbative treatment preserves the pole structure of the parent variational LR-SCI theory, which means that although the method can be useful for static properties, it is not suitable for frequency-dependent molecular response properties. Numerical benchmarks targeting the static polarizabilities of water, ethene, boron hydride, and hydrogen chloride demonstrate systematic convergence toward the FCI limit for both ground and excited electronic states. While first-order corrections yield marginal improvements, the inclusion of second-order corrections substantially enhances accuracy over underlying variational treatments and diminishes oscillatory convergence behavior present in the parent variational LR-SCI method. Combined with extrapolation techniques, LR-SCI-PT achieves excellent agreement with high-level coupled-cluster references, establishing a powerful route toward near-FCI quality molecular properties for systems otherwise inaccessible to exact FCI treatments.

physics.chem-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

State-Averaged Quantum Algorithms for Multiconfigurational Surface Chemistry: A Benchmark on Rh@TiO2(110)

Accurate modeling of surface catalytic processes often requires methods capable of describing strong correlation, charge transfer, and multiple closely lying electronic states. While density functional theory remains widely used, its limitations for localized electronic states motivate the use of wavefunction-based approaches and, more recently, quantum computing algorithms. However, the performance of quantum ans\"atze in chemically motivated, multistate settings remains largely unexplored. Here, we benchmark state-averaged factorized unitary coupled cluster with singles and doubles (SA-fUCCSD) and the adaptive, problem-tailored ansatz (SA-ADAPT) using an embedded cluster model of NO adsorption on Rh-doped TiO2(110). The system exhibits pronounced multiconfigurational character and multiple state crossings, providing a stringent test. State-averaged CASSCF serves as a reference, and the quantum ans\"atze are evaluated as solvers for the corresponding CASCI problem within a fixed orbital basis. We find that SA-fUCCSD improves with increasing circuit depth but requires many parameters and shows sensitivity to initialization. In contrast, SA-ADAPT achieves near-CASSCF accuracy with significantly fewer operators. A modified operator selection scheme, incorporating multiple operators per iteration, substantially accelerates convergence. Our results demonstrate the efficiency of adaptive ans\"atze for multistate problems and establish a controlled benchmark for quantum algorithms in chemically motivated systems beyond minimal models.

quant-ph↗

arXiv2025

Cost-effective scalable quantum error mitigation for tiled Ans\"atze

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 Ans\"atze (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↗

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

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

Linear Response Selected Configuration Interaction

In this work, we extend selected configuration interaction (SCI) methods beyond energies and expectation values by introducing a linear response (LR) framework for molecular response properties. Existing SCI approaches are capable of approximating the energy of the full configuration interaction (FCI) wave function with high accuracy but at a much lower cost. However, conventional determinant selection will, by design, mainly select determinants that are expected to improve energies, and this can lead to the omission of many determinants that are important for wave function response. We address this by introducing two new selection criteria motivated by linear response theory. Using these extended determinant selection criteria, we demonstrate that LR-SCI can systematically converge toward the FCI limit for static polarizabilities. Using a damped LR formulation, we compute the water K-edge X-ray absorption spectrum in active spaces up to (10e, 58o). Finally, we use LR-SCI to compute NMR spin-spin coupling constants for water, where we find that accuracy beyond that offered by CCSDT can be achieved. Overall, LR-SCI offers a promising route to compute response properties with near-FCI accuracy to systems beyond the reach of exact FCI.

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

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

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

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{\"o}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↗

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↗

arXiv2024

Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers

The promise of quantum computing to circumvent the exponential scaling of quantum chemistry has sparked a race to develop chemistry algorithms for quantum architecture. However, most works neglect the quantum-inherent shot noise, let alone the effect of current noisy devices. Here, we present a comprehensive study of quantum linear response (qLR) theory obtaining spectroscopic properties on simulated fault-tolerant quantum computers and present-day near-term quantum hardware. This work introduces novel metrics to analyze and predict the origins of noise in the quantum algorithm, proposes an Ansatz-based error mitigation technique, and highlights the significant impact of Pauli saving in reducing measurement costs and noise. Our hardware results using up to cc-pVTZ basis set serve as proof-of-principle for obtaining absorption spectra on quantum hardware in a general approach with the accuracy of classical multi-configurational methods. Importantly, our results exemplify that substantial improvements in hardware error rates and measurement speed are necessary to lift quantum computational chemistry from proof-of-concept to an actual impact in the field.

quant-ph↗

arXiv2024

Divergences in classical and quantum linear response and equation of motion formulations

Calculating molecular properties using quantum devices can be done through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naive, projected, self-consistent, and state-transfer. In the naive and projected parameterizations, the metric is not the identity, and we show that it depends on the redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noise-less setting. Further, this leads to significant variance when calculations include statistical noise from finite quantum sampling.

quant-ph↗

arXiv2024

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH$_2$ in the series of STO-3G/6-31G/6-31G* basis sets and of H$_4$ and H$_2$O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H$_4$, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

quant-ph↗