Probing the ground state of the antiferromagnetic Heisenberg model on the kagome lattice using geometrically informed variational quantum eigensolver
Abstract
This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver algorithm on real quantum hardware. We demonstrate that the ground-state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation. We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubitwise readout-error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.
Abdellah Tounsi
Ph.D in Theoretical Physics
PhD in mathematical physics. Working on topological quantum computing.
Nacer Eddine Belaloui
Ph.D student in Theoretical Physics
PhD student in Theoretical Physics. Working at CQTech on Variational Quantum Algorithms.
R. Abdelmouheymen Khamadja
Graduate Research Assistant | Ph.D Student in Quantum Algorithms
Ph.D Student in Quantum Algorithms, and Theoretical Physics Master’s, working withing CQTech on quantum algorithms and simulation.
Mohamed Messaoud Louamri
Ph.D in Theoretical Physics
Theoretical physicist. I worked on variational quantum algorithms, quantum random number generation, and QUBO-based optimization. Currently, focusing on quantum Machine Learning and Quantum Optimization.
Mohamed Taha Rouabah
Associate Professor of Physics
ARISE Fellow, Principal Investigator at Constantine Quantum Technologies, Associate Professor at University of Constantine 1 (Algeria).