Simulations of Frustrated Ising Hamiltonians with 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 ($\lesssim 100$) 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.

20 pages, 14 figures; v2 close to published version

References in corpus (17)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Fractional magnetization plateaus and magnetic order in the Shastry Sutherland magnet TmB4
• Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
• Ice Rule and Emergent Frustration in Particle Ice and Beyond
• Evidence of the Berezinskii-Kosterlitz-Thouless Phase in a Frustrated Magnet
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Empirical performance bounds for quantum approximate optimization
• Error propagation in NISQ devices for solving classical optimization problems
• Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice
• Scaling Quantum Approximate Optimization on Near-term Hardware
• Extraction of the interaction parameters for $\alpha -$RuCl${}_3$ from neutron data using machine learning
• On Circuit Depth Scaling For Quantum Approximate Optimization
• Efficient subgraph-based sampling of Ising-type models with frustration
• Signatures of a Quantum Griffiths Phase close to an Electronic Nematic Quantum Phase Transition
• Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization

Cited by in corpus (6)

• A Review on Quantum Approximate Optimization Algorithm and its Variants
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization
• High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices
• Modelling noise in global Molmer-Sorensen interactions applied to quantum approximate optimization
• High-fidelity dimer excitations using quantum hardware