Vibrational Sample-Based Quantum Diagonalization with Unitary-Cluster-Jastrow Ans\"atze 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 H$_2$O, CH$_2$O, and CH$_2$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.

arXiv:2610.09532 [quant-ph]

(or arXiv:2610.09532v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.09532 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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