A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter.
A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter.
A digital quantum simulation of the Agassi model from nuclear physics is proposed and analyzed. The proposal is worked out for the case with four different sites. Numerical simulations and analytical estimations are presented to illustrate the feasibility of this proposal with current technology. The proposed approach is fully scalable to a larger number of sites. The use of a quantum correlation function as a probe to explore the quantum phases by quantum simulating the time dynamics, with no need of computing the ground state, is also studied. Evidence is given showing that the amplitude of the time dynamics of a correlation function in this quantum simulation is linked to the different quantum phases of the system. This approach establishes an avenue for the digital quantum simulation of useful models in nuclear physics.
A central challenge in nuclear physics is understanding quantum many-body systems governed by the strong nuclear force. The inherent complexity of these systems, combined with the limitations of classical computational methods, underscores the need for new approaches to study nuclear structure and dynamics. Here, we demonstrate that a spin-based digital quantum simulator using nuclear magnetic resonance, where nuclear spins simulate interacting fermions, offers a powerful tool to address this challenge. As a first step, we experimentally simulate the Agassi model, which encapsulates the interplay between collective and single-particle behaviors in finite nuclei. By representing nucleons as both bosons (nucleon pairs) and fermions (individual unpaired nucleons), the Agassi model captures highly non-linear interactions and is particularly suited for studying nuclear phase transitions, such as those between spherical and deformed shapes. We experimentally measure the correlation function as an order parameter during the evolution of the many-body system, successfully detecting a quantum phase transition. Specifically, we observe a sharp transition between the symmetric phase and the broken symmetry phase. This work underscores the potential of quantum simulation as a transformative tool in nuclear physics, particularly for exploring complex quantum many-body systems with applications in nuclear structure and reaction dynamics.
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.Methods: 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 ELM in 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.
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
Protocols combining single-qubit digital operations with analog quantum evolutions bypass large numbers of two-qubit entangling gates, offering a promising approach to variational algorithms and hybrid quantum simulation. Focusing on the digital-analog quantum neural network (DA-QNN) as a representative framework, this work demonstrates that incorporating long-range interactions enhances the efficiency of such hybrid algorithms. Within the analog blocks, an Ising model with power-law interactions is employed to generate entanglement, and this protocol is benchmarked across supervised and unsupervised learning tasks. Beyond discussing the effects of the transverse field and evolution time, the primary analysis focuses on how the interaction range governs the expressibility and trainability of the ansatz. For supervised image classification and many-body phase detection, long-range ansatzes match the performance of their short-range counterparts with fewer DA-QNN layers or shorter evolution times, owing to the rapid information propagation across the system enabled by nonlocal couplings. This resource reduction alleviates the classical optimization overhead and eases experimental implementation. In unsupervised phase detection, although the long-range ansatz does not outperform its short-range counterpart in every regime, the two ansatzes provide complementary signatures that jointly reconstruct the complete phase diagram. These findings establish long-range interacting platforms as a compelling resource for advancing practical, large-scale digital-analog quantum computing.
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up ways for simulating complex dynamics of, e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.