Classical Criticality via Quantum Annealing

TL;DR

This paper demonstrates that quantum annealers can accurately simulate phase diagrams and critical phenomena in statistical physics models, providing an efficient alternative to classical methods without critical slowing down.

Contribution

It introduces a method to study critical phenomena on quantum annealers using finite-size scaling and Binder cumulants, with systematic temperature control via Hamiltonian tuning.

Findings

Quantum annealers reproduce phase diagrams accurately.

Finite-size scaling and critical exponents are obtained on quantum hardware.

Quantum annealers serve as robust tools for simulating critical phenomena.

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 for the first time, 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.