Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

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 ( ≲ 100 ) 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. This article is part of the theme issue ‘Quantum annealing and computation: challenges and perspectives’.

Quantum annealing and computation: challenges and perspectives

“…The paper entitled ‘Optimization with photonic wave based annealers’ [ 27 ] by Prabhakar et al develops two different types of photonic Ising machines and compares the performances with a state-of-the-art classical solver and a quantum annealer on two combinatorial optimization problems. The paper entitled ‘Simulations of frustrated Ising Hamiltonians using quantum approximate optimization’ [ 28 ] by Lotshaw et al investigates the properties of the ground state of frustrated magnetic materials using QAOA, a quantum computer-based optimization algorithm. In the paper by Dridi et al .…”