Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization

TL;DR

This paper explores using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers to efficiently prepare ground states of frustrated Ising models, demonstrating promising results on small systems and potential for larger, complex materials.

Contribution

It introduces a practical approach to ground state preparation of frustrated magnetic materials using QAOA, validated on a trapped-ion quantum computer, advancing quantum materials research.

Findings

QAOA can find ground states with modest measurements (~100) even in frustrated systems.

Successful demonstration of QAOA on a trapped-ion quantum computer for a nine-spin model.

Ground state probabilities close to theoretical predictions, showing viability of the method.

Abstract

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland, and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements ($\lesssim100$) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.