2024/04/23 by S. Baid, A. Sáiz, Baid, S. +13 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Neural Networks and Applications #Nuclear Theory (nucl-th) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2404.15558
openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We investigate the Extended Lipkin Model (ELM), whose phase diagram mirrors that of the Interacting Boson Approximation model (IBA). Unlike the standard Lipkin model, the ELM (as the IBA) features both first- and second-order quantum shape phase transitions depending on the model parameters. Our goal is to implement the ELM on a quantum platform, leveraging Machine Learning techniques to identify its quantum phase transitions and critical lines. To achieve this, we offer: i) ground state energy calculations using a variational quantum eigensolver; ii) a detailed formulation for ELM dynamics within quantum computing, facilitating experimental exploration of the IBA phase diagram; and iii) a phase diagram determination using various Machine Learning methods. We successfully replicate the ELM ground-state energy using the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) algorithm across the entire phase space. Our framework ensures ELM implementation on quantum platforms with controlled errors. Lastly, our ML predictions yield a meaningful phase diagram for the model. Keywords: Quantum Platforms Nuclear Models ADAPT-VQE Quantum Shape Phase Transitions Interacting Boson Approximation Extended Lipkin Model Machine Learning