Phase transition of Frustrated Ising model via D-wave Quantum Annealing Machine

TL;DR

This paper investigates the phase transition in a frustrated 2D Ising model using D-wave quantum annealing, revealing how frustration affects the objective function's landscape and the limitations of current quantum annealing hardware.

Contribution

It demonstrates the application of D-wave quantum annealing to a frustrated Ising model and analyzes the impact of frustration on phase transition detection and objective function structure.

Findings

Identified ferromagnetic to stripe order phase transition via magnetization and susceptibility.

Observed multi-modal objective function with multiple local minima near phase transition.

Analyzed failure modes of quantum annealing related to chain formation as system size increases.

Abstract

We study the frustrated Ising model on the two-dimensional $L \times L$ square lattice with ferromagnetic (FM) nearest-neighbor and antiferromagnetic diagonal-neighbor interactions using the D-wave quantum annealing machine (D-QAM) with 5000+ qubits composed on structure of the Pegasus graph. As the former Monte Carlo and mean field results, we find the FM to stripe order phase transition, through observations of the magnetization $M$, energy, magnetic susceptibility and structure factor. We also analyze probability which occurs any $M$ at a given interaction for many quantum annealing shots to estimate the shape of objective function $f$. The only one value of $M$ with specific phase is observed in the regions far from phase transition for many quantum annealing shots, while several values of $M$ with different possibilities are appeared in the regimes of phase transition. We guess that $f$ in the regimes of phase transition retains the multi-modal structure with several local minimums, due to the strong degeneracies caused by frustrations. Finally, we discuss fail of the quantum annealing simulations, through analysis of the number of the chains, defined as the same variable with $N$-qubits, as a function of $L$.