  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
