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arXiv:2505.13625 · Nature Communications

Classical criticality via quantum annealing

Pratik Sathe, Andrew D. King, Susan M. Mniszewski, Carleton Coffrin, Cristiano Nisoli, Francesco Caravelli

Published Jan 15, 2026• 3 citations
arXivHTMLPDF

Abstract

Quantum annealing provides a powerful platform for simulating magnetic materials and realizing statistical physics models, presenting a compelling alternative to classical Monte Carlo methods. We demonstrate that quantum annealers can accurately reproduce phase diagrams and simulate critical phenomena without suffering from the critical slowing down that often affects classical algorithms. To illustrate this, we study the piled-up dominoes model, which interpolates between the ferromagnetic 2D Ising model and Villain's fully frustrated "odd model". We map out its phase diagram and employ finite-size scaling and Binder cumulants on a quantum annealer to study critical exponents for thermal phase transitions. Our method achieves systematic temperature control by tuning the energy scale of the Hamiltonian, eliminating the need to adjust the physical temperature of the quantum hardware. This work demonstrates how, through fine-tuning and calibration, a quantum annealer can be employed to apply sophisticated finite-size scaling techniques from statistical mechanics. Our results establish quantum annealers as robust statistical physics simulators, offering a novel pathway for studying phase transitions and critical behavior.

DOI
10.1038/s41467-025-67568-w

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Quantum annealing provides a powerful platform for simulating magnetic materials and realizing statistical physics models, presenting a compelling alternative to classical Monte Carlo methods. We demonstrate that quantum annealers can accurately reproduce phase diagrams and simulate critical phenomena without suffering from the critical slowing down that often affects classical algorithms. To illustrate this, we study the piled-up dominoes model, which interpolates between the ferromagnetic 2D Ising model and Villain's fully frustrated "odd model". We map out its phase diagram and employ finite-size scaling and Binder cumulants on a quantum annealer to study critical exponents for thermal phase transitions. Our method achieves systematic temperature control by tuning the energy scale of the Hamiltonian, eliminating the need to adjust the physical temperature of the quantum hardware. This work demonstrates how, through fine-tuning and calibration, a quantum annealer can be employed to apply sophisticated finite-size scaling techniques from statistical mechanics. Our results establish quantum annealers as robust statistical physics simulators, offering a novel pathway for studying phase transitions and critical behavior.
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A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials.These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher.In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits.This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short-and long-range orders and fractional order parameters.We show that a large-scale finite-field quantum annealing experiment is possible on 468 logical spins of this model embedded into the quantum hardware.We determine microscopic spin configurations using an iterative quantum annealing protocol and develop mean-field boundary conditions to attenuate finitesize effects and defects.We not only recover all phases of the Shastry-Sutherland Ising model-including the well-known fractional magnetization plateau in a longitudinal field-but also predict the spin behavior at the critical points with significant ground-state degeneracy and in the presence of defects.The results lead us to establish the connection to the diffuse neutron scattering experiments by calculation of the static structure factors.
The current state of Monte Carlo work on phase transitions and critical phenomena is reviewed. Both classical and quantum Monte Carlo results are discussed with emphasis on statistical lattice-model studies involving the highly accurate calculation of critical exponents. It is shown that finite-size scaling is an effective method whereby not only simple lattice models but also those of complex practical magnetic materials can be treated. For models allowing crossover phenomena, it is shown that both finite-size scaling theory and conventional power-law functions must be used in carrying out a Monte Carlo analysis.
A comprehensive study of the two-dimensional (2D) compass model on the square lattice is performed for classical and quantum spin degrees of freedom using Monte Carlo and quantum Monte Carlo methods. We employ state-of-the-art implementations using Metropolis, stochastic series expansion, and parallel tempering techniques to obtain the critical ordering temperatures and critical exponents. In a preinvestigation we reconsider the classical compass model where we study and contrast the finite-size scaling behavior of ordinary periodic boundary conditions against annealed boundary conditions. It is shown that periodic boundary conditions suffer from extreme finite-size effects which might be caused by closed-loop excitations on the torus. These excitations also appear to have severe effects on the Binder parameter. On this footing we report on a systematic Monte Carlo study of the quantum compass model. Our numerical results are at odds with recent literature on the subject which we trace back to neglecting the strong finite-size effects on periodic lattices. The critical temperatures are obtained as Tc=0.1464(2)J{T}_{c}=0.1464(2)JTc​=0.1464(2)J and Tc=0.055(1)J{T}_{c}=0.055(1)JTc​=0.055(1)J for the classical and quantum versions, respectively, and our data support a transition in the 2D Ising universality class for both cases.
We study the ferromagnetic Ising model on a two-dimensional transition lattice that continuously interpolates between the Lieb and kagome lattices via a geometric deformation parameterized by the angle θ. The exchange couplings follow a distance-dependent decay controlled by an exponent n, enabling us to disentangle the interplay between geometry and interaction range. Using extensive Monte Carlo simulations and Binder cumulant analysis, we map the phase diagram T_{c}(θ) and show that the critical temperature increases monotonically as the lattice acquires higher effective connectivity. In the large-n limit, the system approaches a nearest-neighbor regime in which the Monte Carlo critical temperatures converge to the known exact values of the Lieb and kagome limits. Finite-size scaling and data collapse confirm that the entire interpolation belongs to the two-dimensional Ising universality class. Beyond demonstrating the robustness of the critical behavior across the Lieb-kagome transition, the present framework suggests natural extensions. The continuous geometric interpolation between the nonfrustrated Lieb lattice and the frustrated kagome lattice offers a suitable platform to explore antiferromagnetic interactions, where the interplay between frustration and long-range couplings may induce nontrivial ordering.