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arXiv:2607.22850 · Journal of Chemical Theory and Computation

ViBra: Configuration Interaction for Anharmonic Vibrational Spectroscopy and Quantum-Sampled Configuration Spaces

Raphael F. Ligorio, Marco Antonio Barroca, Alan Duriez, Mathias B. Steiner

quant-phphysics.chem-phphysics.comp-phSubmitted Jul 24, 2026• Announced Jul 28, 2026• 0 citations
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Abstract

Quantum-centric workflows are a promising route to improving the accuracy of property predictions in computational chemistry and materials science. By integrating quantum sampling algorithms with classical solvers, electronic structure calculations have recently demonstrated their potential even on noisy intermediate-scale quantum devices. In principle, the method of Vibrational Configuration Interaction (VCI) is suitable for integration with quantum sampling algorithms as well. However, demonstrations of computational workflows for quantum-centric, vibrational property predictions are still lacking. Here, we introduce a methodology for performing anharmonic vibrational structure calculations that can be deployed in a hybrid, quantum-classical mode. Starting from a quartic force field, the approach combines a Vibrational Self-Consistent Field (VSCF) with VCI in either Full, Selected (S-VCI), or Symmetry-Adapted (SA-VCI) mode. In S-VCI, an Epstein-Nesbet perturbative screening significantly reduces the configuration space while retaining high predictive accuracy. A state-list input enables the integration of externally generated vibrational configurations as a seed space. As a proof-of-concept, we demonstrate a hybrid, quantum-classical computational workflow, in which a quantum sampling algorithm provides the seed. Our vibrational wave function analysis package ViBra, equipped with a graphical interface, is available at https://github.com/raphafe96/ViBra.

Comments
48 pages, 6 figures, 6 tables

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Quantum-centric workflows are a promising route to improving the accuracy of property predictions in computational chemistry and materials science. By integrating quantum sampling algorithms with classical solvers, electronic structure calculations have recently demonstrated their potential even on noisy intermediate-scale quantum devices. In principle, the method of Vibrational Configuration Interaction (VCI) is suitable for integration with quantum sampling algorithms as well. However, demonstrations of computational workflows for quantum-centric, vibrational property predictions are still lacking. Here, we introduce a methodology for performing anharmonic vibrational structure calculations that can be deployed in a hybrid, quantum-classical mode. Starting from a quartic force field, the approach combines a Vibrational Self-Consistent Field (VSCF) with VCI in either Full, Selected (S-VCI), or Symmetry-Adapted (SA-VCI) mode. In S-VCI, an Epstein-Nesbet perturbative screening significantly reduces the configuration space while retaining high predictive accuracy. A state-list input enables the integration of externally generated vibrational configurations as a seed space. As a proof-of-concept, we demonstrate a hybrid, quantum-classical computational workflow, in which a quantum sampling algorithm provides the seed. Our vibrational wave function analysis package ViBra, equipped with a graphical interface, is available at https://github.com/raphafe96/ViBra.
This review provides a detailed anatomical dissection of Quantum-Selected Configuration Interaction (QSCI), a hybrid quantum-classical algorithm introduced by Kanno et al. (2026) that leverages noisy quantum devices solely for sampling important electron configurations from an input state, followed by exact classical diagonalization of the Hamiltonian in the resulting reduced subspace. We systematically evaluate its methodological innovations, noise resilience, and strict adherence to the variational principle. A comprehensive comparison is drawn with at least twelve competing or complementary paradigms in NISQ-era quantum chemistry and classical selected configuration interaction (SCI), including VQE and its adaptive/excited-state variants, Quantum Subspace Expansion (QSE), ASCI, CIPSI, MCCI, FCIQMC, DMRG, Classically-Boosted VQE, and time-evolved input extensions (TE-QSCI). Pros and cons are articulated with reference to recent critical analyses highlighting sampling inefficiencies and subspace compactness. The review further explores the ontological status of configuration selection via quantum measurement and the epistemological guarantees afforded by classical post-processing. Possible extensions—hybrid adaptive pipelines, subspace recycling for molecular dynamics, and integration with machine-learned wavefunctions—are proposed. Also available on Academia.edu: https://www.academia.edu/attachments/133411942/download_file?s=portfolio
The fundamental challenge in electronic structure theory is the factorial scaling of the Full Configuration Interaction (FCI) method. While Quantum-Selected Configuration Interaction (QSCI) has emerged as a promising alternative that utilizes quantum hardware to navigate this Hilbert space, benchmarking studies have identified significant scaling bottlenecks, specifically multinomial sampling inefficiencies and poor wavefunction compactness. This work presents the "hybrid adaptive pipeline" framework, which reconfigures the division of labor between quantum and classical systems. By utilizing quantum processors exclusively as initialization oracles to establish a topological seed of static correlation, and delegating the intensive recovery of dynamic correlation to classical iterative refinement algorithms (such as CIPSI or MCCI), this approach overcomes the limitations of pure sampling-based methods. The hybrid pipeline preserves the essential variational upper-bound guarantee while enabling the efficient, noise-resilient simulation of complex molecular systems on contemporary quantum-centric supercomputing architectures. KSCCN Mamun, SM (2026) …………………………….1 Hybrid Adaptive Pipelines in Quantum Chemistry: Synthesizing Quantum-Selected Configuration Interaction with Classical Iterative Refinement Also available on Academia.edu: https://www.academia.edu/attachments/133434503/download_file?s=portfolio
Scientific simulations demand methods combining scalability with predictive accuracy. Density Functional Theory (DFT) on High-Performance Computing (HPC) enables large-scale electronic-structure simulations but is limited by approximations affecting strongly correlated systems and band-gap predictions. Quantum computing offers a pathway to address this, though current Noisy Intermediate-Scale Quantum (NISQ) hardware remains constrained by qubit resources, noise, and execution cost. This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver. Large systems are partitioned to isolate a chemically relevant active space, treated via the Variational Quantum Eigensolver (VQE), while the remaining degrees of freedom are described by DFT. The framework incorporates active-space selection, embedded Hamiltonian construction, symmetry preservation, operator mapping, self-consistent density updating, and modular classical-quantum coupling. We focus on noiseless quantum simulation to systematically evaluate accuracy, convergence, active-space dependence, computational cost, and HPC scalability without hardware noise. Detailed profiling identifies computational bottlenecks and highlights limitations of CPU-based quantum simulation. A QPU runtime-estimation methodology is additionally developed to assess execution requirements on actual quantum hardware. Results demonstrate quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability. Noisy quantum simulation and QPU execution remain key future directions, providing a pathway toward practical, scalable HPC-quantum hybrid simulations as hardware matures.
Quantum-selected configuration interaction (QSCI) is a novel quantum-classical hybrid algorithm for quantum chemistry calculations. This method identifies electron configurations having large weights for the target state using quantum devices and allows CI calculations to be performed with the selected configurations on classical computers. In principle, the QSCI algorithm can take advantage of the ability to handle large configuration spaces while reducing the negative effects of noise on the calculated values. At present, QSCI calculations are limited by qubit noise during the input state preparation and measurement processes, restricting them to small active spaces. These limitations make it difficult to perform calculations with quantitative accuracy. The present study demonstrates a computational scheme based on multireference perturbation theory calculations on a classical computer, using the QSCI wave function as a reference. This method was applied to ground and excited state calculations for two typical aromatic molecules, naphthalene and tetracene. The incorporation of the perturbation treatment was found to provide improved accuracy. Extension of the reference space based on the QSCI-selected configurations as a means of further improvement was also investigated.
We extend sample-based quantum diagonalization (SQD) to anharmonic vibrational spectra and use it to benchmark how vibrational ansätze scale on present-day hardware under a direct one-hot encoding (up to 72 qubits). Five particle-conserving circuits are warm-started through vibrational coupled-cluster (VCC) t1, t2 amplitudes: UVCCSD, the compact heuristic circuit (CHC), and three unitary-cluster-Jastrow ansätze introduced here, VLUCJ, Vg-uCJ, and VIm-uCJ. A self-consistent configuration-recovery loop reconstructs correlated states from hardware samples in the low-retention regime where naïve post-selection breaks down, enabling the calculation of ground-state energies for H2_22​O, CH2_22​O, and CH2_22​ClF (3-9 modes). We compare harmonic-oscillator and vibrational self-consistent-field (VSCF, "modal") reference bases. In the small-modal-basis regime relevant for near-term devices, the modal basis is typically more accurate than the harmonic-oscillator representation; empirically, it also yields substantially better-converged hardware sampling for deep circuits at these qubit counts. Across ansätze, we find a clear retention/accuracy tradeoff when scaling: the new VLUCJ circuit is the most hardware-robust, retaining the largest fraction of physically valid one-hot outcomes, whereas the more expressive uCJ variants and UVCCSD can recover more correlation when retention is sufficient. Finally, we extend the recovery protocol to excited states by targeting a chosen per-mode VSCF occupation and warm-starting it with a state-specific VCC calculation, and we demonstrate the calculation of one representative fundamental vibrational frequency per molecule on IBM QPUs.
In this work, we present the integration of Qiskit Nature's quantum chemistry solvers into the Atomic Simulation Environment (ASE), enabling hybrid quantum-classical workflows for force-driven atomistic simulations. This coupling allows the use of the Variational Quantum Eigensolver (VQE) and its adaptive variant (ADAPT-VQE) not only for ground-state energy calculations, but also for geometry optimisation, vibrational frequency analysis, strain evaluation, and molecular dynamics, all managed through ASE's calculator interface. By applying ADAPT-VQE to multi-electron systems such as BeH2, we obtain vibrational and structural properties in close agreement with high-level classical CCSD calculations within the same minimal basis. These results demonstrate that adaptive variational quantum algorithms can deliver stable and chemically meaningful forces within an atomistic modelling workflow, enabling downstream applications such as molecular dynamics and active-learning accelerated simulations.