Ans\"atz Expressivity and Optimization in Variational Quantum Simulations of Transverse-field Ising Model Across System Sizes

Quantum Physics [Submitted on 22 Apr 2026] Ansätz Expressivity and Optimization in Variational Quantum Simulations of Transverse-field Ising Model Across System Sizes Ashutosh P. Tripathi, Nilmani Mathur, Vikram Tripathi We explore the application of the Variational Quantum Eigensolver (VQE) to investigate the ground state properties, particularly the entanglement entropy, of the Transverse Field Ising Model (TFIM) in one, two, and three dimensions, considering systems of up to 27 spins. By benchmarking VQE results against exact diagonalization and analyzing the entanglement properties across different system sizes and geometries, we assess the algorithm's effectiveness in capturing critical phenomena. Using results of TFIM, we also investigate how VQE's expressivity and optimization influence the simulation of highly entangled quantum states. We employ different ansätze: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational ansätz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization. We further discuss the implications for scaling these methods to larger quantum systems. Comments: 26 pages, 11 figures, 2 tables Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Lattice (hep-lat) Report number: TIFR/TH/26-16 Cite as: arXiv:2604.20961 [quant-ph]   (or arXiv:2604.20961v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.20961 Focus to learn more Submission history From: Ashutosh P. Tripathi [view email] [v1] Wed, 22 Apr 2026 18:00:11 UTC (2,307 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech hep-lat 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?)