Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2603.13882 · Quantum Science and Technology

Investigating Lipkin-Meshkov-Glick Model and Criticality-Enhanced Metrology in a Coherent Ising Machine

Shuang-Quan Ma, Jing-Yi-Ran Jin, Chen-Rui Fan, Chuan Wang, Qing Ai

quant-phSubmitted Mar 14, 2026• Announced Mar 17, 2026• 1 citation
arXivHTMLPDF

Abstract

Quantum criticality has received extensive attention due to its ability to significantly enhance quantum sensing. But its realization and control in many-body quantum systems remain challenging. We present an effective scheme to simulate the Lipkin-Meshkov-Glick (LMG) model using a coherent Ising machine (CIM) composed of a network of degenerate optical parametric oscillators (DOPO). In our work, the spin variables of the LMG model are mapped onto the phases of DOPO pulses, and the spin-spin interactions are realized by all-to-all couplings among them. Through our investigation of the critical behavior in the antiferromagnetically coupled LMG model in the thermodynamic limit, i.e., $N\rightarrow\infty$, and its application in quantum sensing near the critical point, we verify that the CIM does not only effectively capture the second-order quantum phase transition (QPT) at the critical point but also reconstructs its complete phase diagram under ferromagnetic coupling. Furthermore, we demonstrate how the critical dynamics of this simulation platform can be utilized for quantum-enhanced metrology, achieving a measurement precision that diverges near the critical point of the LMG model. These results highlight the capability of the CIM as a flexible experimental platform for investigating the QPT in the fundamental quantum magnetic models, providing valuable insights into quantum simulation and critical phenomena.

Journal reference
Quantum Sci. Technol. 11 025019 (2026)
DOI
10.1088/2058-9565/ae4d82

Related papers

Quantum Phase Transitions in Coherent Ising Machines: XY Model for Demonstration

Shuang-Quan Ma, Jing-Yi-Ran Jin, Qing Ai

In this work, we study the detection of quantum phase transitions (QPTs) in coherent Ising machines (CIMs) through a spectral mapping between the one-dimensional XY spin model and a network of degenerate optical parametric oscillators (DOPOs). This exact correspondence reveals that the DOPO spectrum faithfully encodes the critical behavior of anisotropic and isotropic XY chains, while a strongly anisotropic regime provides a controlled near-transverse-field-Ising realization, with the energy gap closing precisely at the critical point. The ground-state energy density and its derivatives are analyzed, and the resulting singularities in magnetic susceptibility accurately pinpoint the quantum critical points of the corresponding spin model. These results show that CIMs not only serve as powerful platforms for solving combinatorial optimization problems but also provide a versatile tool for probing universal quantum critical phenomena, bridging quantum-spin models and photonic quantum systems.

quant-pharXiv:2512.23248•Advanced Quantum Technologies•Dec 30, 2025•0 citations

Quantum model for coherent Ising machines: Discrete-time measurement feedback formulation

Atsushi Yamamura, Kazuyuki Aihara, Y. Yamamoto

Recently, the coherent Ising machine (CIM) as a degenerate optical parametric oscillator (DOPO) network has been researched to solve Ising combinatorial optimization problems. We formulate a theoretical model for the CIM with discrete-time measurement feedback processes, and perform numerical simulations for the simplest network, composed of two degenerate optical parametric oscillator pulses with the antiferromagnetic mutual coupling. We evaluate the extent to which quantum coherence exists during the optimization process.

arXiv:1706.02454•Physical Review A•Nov 14, 2017•47 citations

Precision magnetometry exploiting excited state quantum phase transitions

Qian Wang, Ugo Marzolino

Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the Lipkin-Meshkov-Glick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The Lipkin-Meshkov-Glick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the Lipkin-Meshkov-Glick model.

arXiv:2306.01126•SciPost Physics•Aug 9, 2024•3 citations

Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network

Yoshitaka Haribara, Shoko Utsunomiya, Y. Yamamoto

We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential equations. We also discuss the advanced CIM with quantum measurement-feedback control and various problems which can be solved by CIM.

Entropy•Apr 19, 2016•70 citations

Quantum metrology in Lipkin-Meshkov-Glick critical systems

Giulio Salvatori, Antonio Mandarino, Matteo G. A. Paris

The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address quantum metrology in LMG systems and show how criticality may be exploited to improve precision. At first we focus on the characterization of LMG systems themselves, i.e., the estimation of anisotropy, and address the problem by considering the quantum Cram\'er-Rao bound. We evaluate the quantum Fisher information of small-size LMG chains made of $N=2,$ 3, and 4 lattice sites and also analyze the same quantity in the thermodynamical limit. Our results show that criticality is indeed a resource and that the ultimate bounds to precision may be achieved by tuning the external field and measuring the total magnetization of the system. We then address the use of LMG systems as quantum thermometers and show that (i) precision is governed by the gap between the lowest energy levels of the systems and (ii) field-dependent level crossing is a metrological resource to extend the operating range of the quantum thermometer.

arXiv:1406.5766•Physical Review A•Aug 15, 2014•136 citations

The Lipkin-Meshkov-Glick model: 'quasi-local' quantum criticality in nuclear physics

C. Hooley, P. D. Stevenson

Motivated by recent work on local quantum criticality in condensed matter systems, we study the Lipkin-Meshkov-Glick (LMG) model of nuclear physics as a simple model of a kind of 'quasi-local' quantum criticality. We identify a new crossover temperature, T*(V,W), between linear and nonlinear dynamics, which is analogous to the crossover between the renormalized classical and quantum critical regimes in the condensed-matter case. This temperature T* typically vanishes logarithmically as the quantum phase transition is approached, except near the quantum tricritical point where it becomes linear. We also note a further analogy with condensed-matter quantum criticality: the LMG model exhibits quantum order-by-disorder phenomena, of the type often associated with phase reconstruction near quantum critical points.

arXiv:1102.1583•Feb 8, 2011•1 citation
Quantum criticality has received extensive attention due to its ability to significantly enhance quantum sensing. But its realization and control in many-body quantum systems remain challenging. We present an effective scheme to simulate the Lipkin-Meshkov-Glick (LMG) model using a coherent Ising machine (CIM) composed of a network of degenerate optical parametric oscillators (DOPO). In our work, the spin variables of the LMG model are mapped onto the phases of DOPO pulses, and the spin-spin interactions are realized by all-to-all couplings among them. Through our investigation of the critical behavior in the antiferromagnetically coupled LMG model in the thermodynamic limit, i.e., N→∞N\rightarrow\inftyN→∞, and its application in quantum sensing near the critical point, we verify that the CIM does not only effectively capture the second-order quantum phase transition (QPT) at the critical point but also reconstructs its complete phase diagram under ferromagnetic coupling. Furthermore, we demonstrate how the critical dynamics of this simulation platform can be utilized for quantum-enhanced metrology, achieving a measurement precision that diverges near the critical point of the LMG model. These results highlight the capability of the CIM as a flexible experimental platform for investigating the QPT in the fundamental quantum magnetic models, providing valuable insights into quantum simulation and critical phenomena.
In this work, we study the detection of quantum phase transitions (QPTs) in coherent Ising machines (CIMs) through a spectral mapping between the one-dimensional XY spin model and a network of degenerate optical parametric oscillators (DOPOs). This exact correspondence reveals that the DOPO spectrum faithfully encodes the critical behavior of anisotropic and isotropic XY chains, while a strongly anisotropic regime provides a controlled near-transverse-field-Ising realization, with the energy gap closing precisely at the critical point. The ground-state energy density and its derivatives are analyzed, and the resulting singularities in magnetic susceptibility accurately pinpoint the quantum critical points of the corresponding spin model. These results show that CIMs not only serve as powerful platforms for solving combinatorial optimization problems but also provide a versatile tool for probing universal quantum critical phenomena, bridging quantum-spin models and photonic quantum systems.
Recently, the coherent Ising machine (CIM) as a degenerate optical parametric oscillator (DOPO) network has been researched to solve Ising combinatorial optimization problems. We formulate a theoretical model for the CIM with discrete-time measurement feedback processes, and perform numerical simulations for the simplest network, composed of two degenerate optical parametric oscillator pulses with the antiferromagnetic mutual coupling. We evaluate the extent to which quantum coherence exists during the optimization process.
Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the Lipkin-Meshkov-Glick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The Lipkin-Meshkov-Glick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the Lipkin-Meshkov-Glick model.
The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address quantum metrology in LMG systems and show how criticality may be exploited to improve precision. At first we focus on the characterization of LMG systems themselves, i.e., the estimation of anisotropy, and address the problem by considering the quantum Cram\'er-Rao bound. We evaluate the quantum Fisher information of small-size LMG chains made of N=2,N=2,N=2, 3, and 4 lattice sites and also analyze the same quantity in the thermodynamical limit. Our results show that criticality is indeed a resource and that the ultimate bounds to precision may be achieved by tuning the external field and measuring the total magnetization of the system. We then address the use of LMG systems as quantum thermometers and show that (i) precision is governed by the gap between the lowest energy levels of the systems and (ii) field-dependent level crossing is a metrological resource to extend the operating range of the quantum thermometer.
Motivated by recent work on local quantum criticality in condensed matter systems, we study the Lipkin-Meshkov-Glick (LMG) model of nuclear physics as a simple model of a kind of 'quasi-local' quantum criticality. We identify a new crossover temperature, T*(V,W), between linear and nonlinear dynamics, which is analogous to the crossover between the renormalized classical and quantum critical regimes in the condensed-matter case. This temperature T* typically vanishes logarithmically as the quantum phase transition is approached, except near the quantum tricritical point where it becomes linear. We also note a further analogy with condensed-matter quantum criticality: the LMG model exhibits quantum order-by-disorder phenomena, of the type often associated with phase reconstruction near quantum critical points.