The extended Lipkin model: proposal for implementation in a quantum platform and machine learning analysis of its phase diagram

TL;DR

This paper proposes implementing the Extended Lipkin Model on quantum computers and uses machine learning to analyze its phase diagram, identifying quantum phase transitions with high accuracy.

Contribution

It introduces a quantum computing framework for the ELM and applies machine learning to map its phase diagram, including first- and second-order phase transitions.

Findings

Successful replication of ground-state energy using ADAPT-VQE

Quantum implementation framework with controlled errors

ML-based phase diagram predictions

Abstract

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