Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization
arXiv:2206.05343 · doi:10.1098/rsta.2021.0414
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 () 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.
arXiv comment20 pages, 14 figures; v2 close to published version
References in corpus (47)
- Quantum Computing in the NISQ era and beyond
- Quantum Simulation
- Ising formulations of many NP problems
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Quantum Spin Liquids
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Noise-Induced Barren Plateaus in Variational Quantum Algorithms
- From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
- Quantum Simulators: Architectures and Opportunities
- Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
- Studying Two Dimensional Systems With the Density Matrix Renormalization Group
- Signature of magnetic monopole and Dirac string dynamics in spin ice
- Observation of topological phenomena in a programmable lattice of 1,800 qubits
- Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO
- Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator
- Improving Variational Quantum Optimization using CVaR
- Fractional magnetization plateaus and magnetic order in the Shastry Sutherland magnet TmB4
- Efficient variational simulation of non-trivial quantum states
- Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
- Frustration and quantum criticality
- Quantum Optimization with a Novel Gibbs Objective Function and Ansatz Architecture Search
- Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
- Applying the Quantum Approximate Optimization Algorithm to the Tail Assignment Problem
- Ground States of the Ising Model on the Shastry-Sutherland Lattice and the Origin of the Fractional Magnetization Plateaus in Rare-Earth Tetraborides
- 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
- Qubit spin ice
- Empirical performance bounds for quantum approximate optimization
- The Quantum Alternating Operator Ansatz on Maximum k-Vertex Cover
- Error propagation in NISQ devices for solving classical optimization problems
- Simulating the Shastry-Sutherland Ising Model using Quantum Annealing
- Numerical study of magnetization processes in rare-earth tetraborides
- Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice
- Electronic Transport on the Shastry-Sutherland Lattice in Ising-type Rare Earth Tetraborides
- Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
- Degeneracy of the 1/8 plateau and antiferromagnetic phases in the Shastry-Sutherland magnet TmB4
- Scaling Quantum Approximate Optimization on Near-term Hardware
- Quantum Spin Glasses
- Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice
- Extraction of the interaction parameters for RuCl from neutron data using machine learning
- Quantifying the efficiency of state preparation via quantum variational eigensolvers
- On Circuit Depth Scaling For Quantum Approximate Optimization
- Efficient subgraph-based sampling of Ising-type models with frustration
- Magnetic three states of matter: A quantum Monte Carlo study of spin liquids
- 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 -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