Shattering the Symmetry Trap in Fixed-Ansatz VQE: An Accelerated ADAPT-VQE Study of Three Pillar Molecules under Bravyi-Kitaev Mapping

Quantum Physics [Submitted on 4 Jun 2026] Shattering the Symmetry Trap in Fixed-Ansatz VQE: An Accelerated ADAPT-VQE Study of Three Pillar Molecules under Bravyi-Kitaev Mapping Hermawan Kresno Dipojono Fixed-ansatz Variational Quantum Eigensolvers (VQE), such as the Unitary Coupled Cluster with Singles and Doubles (UCCSD) framework, frequently suffer from severe initialization paralyzation and zero-gradient traps when evaluated using the non-local Bravyi-Kitaev (BK) fermion-to-qubit mapping. In this work, we systematically demonstrate how the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT-VQE) framework shatters these structural limitations across three distinct electronic and geometric molecular pillars: Lithium Hydride (\text{LiH}), Hydrogen Fluoride (\text{HF}), and Water (\text{H}_2\text{O}), under heavily stretched or asymmetric multi-reference configurations. While conventional UCCSD-VQE flatlines completely at a zero energy shift (0.000000~Ha) due to global phase cancellations inherent to the BK tree structures, our dynamic ADAPT-VQE loop successfully isolates the dominant symmetry-breaking operators using analytical commutator gradients. To bypass the severe \mathcal{O}(N^3) computational bottlenecks of dense matrix exponentiation and Singular Value Decomposition on larger registers, we implement a highly optimized, vector-based Taylor series expansion state-evolution engine. Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction (FCI) convergence within the very first macro-cycle across all three molecular systems, maintaining absolute numerical stability up to a 12-qubit register space. This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments on near-term local architectures. Comments: 8 pages, including raw algorithmic telemetry logs Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05968 [quant-ph]   (or arXiv:2606.05968v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05968 Focus to learn more Submission history From: Hermawan Kresno Dipojono [view email] [v1] Thu, 4 Jun 2026 10:13:23 UTC (15 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)