Vibrational Sample-Based Quantum Diagonalization with Unitary-Cluster-Jastrow Ansätze on IBM QPUs

Abstract

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 H₂O, CH₂O, and CH₂ClF (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.

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BibTeX RIS

BibTeX

@misc{kumar2026vibrational,
  title = {{Vibrational Sample-Based Quantum Diagonalization with Unitary-Cluster-Jastrow Ansätze on IBM QPUs}},
  author = {Kunal Kumar and Erik Lötstedt and Yuri Kobayashi and Seiji Yunoki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09532},
  eprint = {2610.09532},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09532},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Vibrational Sample-Based Quantum Diagonalization with Unitary-Cluster-Jastrow Ansätze on IBM QPUs
AU  - Kunal Kumar
AU  - Erik Lötstedt
AU  - Yuri Kobayashi
AU  - Seiji Yunoki
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09532
UR  - https://arxiv.org/abs/2610.09532
AB  - 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 H_2O, CH_2O, and CH_2ClF (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.
ER  -

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