The Extended Lipkin Model - Proposal for Implementation in a Quantum Platform and Machine Learning Analysis of Its Phase Diagram

Aug 5, 2026

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The document investigates how the Extended Lipkin Model (ELM) can be realized on quantum computing platforms while also enabling an accurate phase-diagram reconstruction. It targets quantum shape phase transitions relevant to nuclear physics, where both first- and second-order transitions can occur depending on model parameters. The study combines variational quantum algorithms for ground-state energies with machine learning methods to classify phases and locate critical points. It further provides a complete implementation framework to run the model with controlled errors, including dynamics and experimental accessibility for small particle numbers.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages23

Reading Time58 min

AccessFree to download

Background and Purpose

Quantum phase transitions in nuclear models

Goals of the study (VQE, platform implementation, ML analysis)

Method and Implementation

ADAPT-VQE ground-state energy calculation

Quantum platform formulation for dynamics

Machine learning for phases and critical points

Results and Conclusions

Reproducing ground-state energy across the phase space

Controlled-error implementation feasibility

ML predictions for the phase diagram

arXiv :2404 . 15558v1 [ quant-ph] 23 Apr 2024 The extended Lipkin model: proposal for implementation in a quantum platform and machine learning analysis of its phase diagram S. Baid 1 , A. S´aiz 1 ,2 , L. Lamata 1 , P. P´erez-Fern´andez2 , A.M. Romero3 ,4,a , A. Rios3 ,4 , J.M. Arias 1 and J.E. Garc´ıa-Ramos5 ,6 1 Departamento de F´ısica At´omica, Molecular y Nuclear, Facultad de F´ısica, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain 2 Departamento de F´ısica Aplicada III, Escuela T´ecnica Superior de Ingenier´ıa, Universidad de Sevilla, E-41092 Sevilla, Spain. 3 Departament de F´ısica Qu`antica i Astrof´ısica (FQA), Universitat de Barcelona (UB), c. Mart´ı i Franqu´es, 1, 08028 Barcelona, Spain 4 Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart´ı i Franqu´es, 1, 08028 Barcelona, Spain 5 Departamento de Ciencias Integradas y Centro de Estudios Avanzados en F´ısica, Matem´atica y Computaci´on, Universidad de Huelva, 21071 Huelva, Spain. 6 Instituto Carlos I de F´ısica Te´orica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain aNew address: Fujitsu Research of Europe, [antonio.marquezromero@fujitsu.com](antonio.marquezromero@fujitsu.com) (Dated: April 25, 2024) Background: In recent years, the implementation of Nuclear Physics models in quantum computers has emerged as a promising and novel area of research. Simultaneously, the study of quantum shape phase transitions in nuclear models has gained significant attention. Specifically, the phase diagram of the Interacting Boson Approximation (IBA) has been extensively explored, particularly in connection with large-particle-number-limit considerations. Interestingly, the Extended Lipkin Model (ELM) serves as a valuable alternative for mimicking the IBA phase diagram and holds the advantage of being more straightforward to implement within a quantum computing platform. Purpose: We explore the ELM and provide: i) calculations of the ground state energy using a variational quantum eigensolver; ii) a comprehensive formulation for implementing the dynamics of the ELM within a quantum computing platform, enabling the experimental exploration of the IBA phase diagram for systems with a small number of particles; and iii) a determination of the phase diagram of the model using different Machine Learning (ML) methods. We note that in the ELM, unlike the usual Lipkin model, both first-and second-order quantum shape phase transitions take place depending on the model parameters. Method: Initially, we employ the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) to calculate the ground-state energy of the ELM. Next, we introduce the essential formulation and procedures required to implement this model effectively in a quantum computing environment. Finally, we use ML techniques to identify the different phases and critical points of the ELM. Results: We successfully reproduce the ground-state energy of the ELM across the complete phase space of the model using the ADAPT-VQE algorithm. We provide the necessary framework for implementing the ELM in a quantum computing platform, ensuring that the model can be executed with controlled errors. Finally, we obtain meaningful ML predictions that allow us to determine the phase diagram of the model. Conclusions: Our findings offer compelling evidence that the implementation of a nuclear model like the ELMin a quantum computing environment is not only feasible but can also be achieved with manageable error rates. This realization opens the door to detailed experimental investigations of the phase diagram of the ELM (and indirectly of the IBA) in a quantum computer, further advancing our understanding of quantum shape phase transitions and nuclear structure. Keywords: Quantum Platforms Nuclear Models ADAPT-VQE Quantum Shape Phase Transitions Interacting Boson Approximation Extended Lipkin Mo

FAQs

What problem does the study address regarding nuclear models on quantum computers?

It addresses how to implement the Extended Lipkin Model on a quantum computing platform and use it to investigate quantum shape phase transitions related to nuclear structure.

How are ground-state energies of the Extended Lipkin Model computed?

Ground-state energies are obtained using the ADAPT-VQE variational quantum eigensolver algorithm.

How does the document determine the ELM phase diagram?

It uses machine learning methods to classify different phases and identify critical points based on the model’s computed features.

Aug 5, 2026

Upload by Noah