Kagome Lattice Heisenberg Model Ground State Probed with Shallow Variational Quantum Eigensolver

The quest to understand complex magnetic materials drives ongoing research into fundamental models of quantum magnetism, and a team led by Abdellah Tounsi, Nacer Eddine Belaloui, and Abdelmouheymen Rabah Khamadja, all from Constantine Quantum Technologies and Frères Mentouri University Constantine 1 in Algeria, now reports a significant advance in simulating one such model. They investigate the antiferromagnetic Heisenberg model on the kagome lattice, a geometrically frustrated system known for its exotic magnetic properties, using a variational quantum eigensolver implemented on actual quantum hardware. This work demonstrates the ability to accurately determine the ground state of the system with a relatively simple quantum circuit, and importantly, the method exhibits resilience to the noise inherent in current quantum computers, offering a pathway towards simulating increasingly complex materials and deepening our understanding of quantum magnetism. The team, which also includes researchers from the University of Science and Technology Houari Boumediene in Algeria and Purdue University in the USA, achieves this through a carefully designed quantum circuit and an innovative optimisation strategy that accelerates the search for the lowest energy state.

Scientists demonstrate that the VQE implementation accurately determines the ground state energy of the triangular kagome cell, converging to −0. 749(1) J, consistent with established theoretical predictions. The team successfully implemented the VQE algorithm on the IBMQ Yorktown quantum processor, achieving 99. 7% fidelity for single qubit gates and 94.

2% for two-qubit gates, representing a significant advancement in utilising noisy intermediate-scale quantum (NISQ) devices for condensed matter physics problems. Analysis of the star-shaped kagome lattice reveals a ground state energy of −0. 666(2) J, providing new insights into the behaviour of frustrated magnetic systems, and the study establishes a robust methodology for exploring complex quantum many-body systems using near-term quantum computers. The findings contribute to a deeper understanding of quantum magnetism and pave the way for investigating more complex materials with potential applications in quantum technologies.

Kagome Lattice Ground State Preparation via VQE

This work presents a breakthrough in preparing and characterising the ground state of the antiferromagnetic Heisenberg model on minimal kagome lattices, a triangle and a star, using a variational quantum eigensolver (VQE) implemented on real quantum hardware. Scientists achieved robust ground state preparation using a shallow, hardware-efficient circuit designed with a naturally Euclidean parameter space, minimising the impact of noise. The custom ansatz accurately recovers essential spin correlation terms for each edge without requiring explicit error mitigation techniques, demonstrating enhanced stability. A key innovation lies in the construction of the ansatz using the Fubini-Study metric, ensuring a singularity-free parameter space and simplifying the optimisation process.

This design results in the natural gradient coinciding with the normal gradient, complemented by a backtracking search for dynamic step size adaptation, termed Implicit-Adaptive Quantum Natural Gradient Descent (I-AQNGD). Experiments reveal that I-AQNGD achieves faster convergence in fewer iterations compared to simultaneous perturbation stochastic approximation (SPSA), while maintaining competitive runtime with an analytically constant metric. Further enhancing the results, the team applied error mitigation techniques including zero noise extrapolation (ZNE) and qubit-wise readout error mitigation (REM). While acknowledging limitations of ZNE regarding the Rayleigh-Ritz principle, the research details conditions under which REM preserves its validity. Beyond energy estimation, scientists successfully characterised the dimer state by measuring spin-spin correlations and the static spin structure factor, demonstrating resilience to noise and providing insights into the quantum state’s structure and potential for exhibiting exotic magnetic properties. This work establishes a powerful method for exploring quantum magnetism and paves the way for investigating more complex quantum spin liquids and topological phases relevant to quantum computing.

Kagome Lattice Ground State Preparation Demonstrated

This work presents a successful demonstration of ground state preparation for the antiferromagnetic Heisenberg model on minimal kagome lattices, specifically triangles and kagome stars, using a variational quantum eigensolver implemented on real quantum hardware. Researchers developed a custom quantum circuit, designed with a naturally Euclidean parameter space, that accurately recovers essential spin correlation properties without requiring complex error mitigation techniques. This circuit’s design, leveraging the Fubini-Study metric, ensures a stable optimisation landscape and facilitates faster convergence compared to standard optimisation methods. The team achieved this through an implicit adaptive natural gradient descent, which dynamically adjusts step sizes for efficient parameter optimisation.

The study further explores and applies error mitigation techniques, including zero noise extrapolation and qubit-wise readout error mitigation, to improve the accuracy of results. While acknowledging limitations in the applicability of the Rayleigh-Ritz principle with zero noise extrapolation, the authors detail conditions under which readout error mitigation preserves its validity. These findings demonstrate the feasibility of using near-term quantum computers to study complex quantum many-body systems, offering a pathway towards understanding the fundamental properties of frustrated magnets like the kagome lattice. Future research directions could focus on extending this approach to larger, more complex kagome lattices and exploring the potential for discovering novel quantum phases of matter.