Kagome Lattices

Quantum Material Advancement Shallow Variational Science Ground State of Frustrated Kagome Lattice Magnet Probed by Quantum Eigensolver

To understand complicated magnetic materials, quantum magnetism model research continues. Researchers led by Abdellah Tounsi, Nacer Eddine Belaloui, and Abdelmouheymen Rabah Khamadja have made significant progress in simulating the antiferromagnetic Heisenberg model on the kagome lattice. Using a Variational Quantum Eigensolver (VQE) built on quantum hardware, the team from Constantine Quantum Technologies and Frères Mentouri University Constantine 1 in Algeria, Purdue University in the US, and the University of Science and Technology Houari Boumediene in Algeria accurately identified the system's ground state.

The geometrically frustrated kagome lattice is notable for its remarkable magnetic properties, including topological phases and quantum spin liquids relevant to quantum computing. Because Due to its frustration, preparing this system's ground state is difficult. Researchers focused on minimum kagome cells: triangles and stars. This study advances the use of near-term quantum computers (NISQ devices) to characterise the ground state of an antiferromagnetic Heisenberg model.

A hardware-efficient robust computation method

A shallow, hardware-efficient quantum circuit (ansatz) is a key innovation of this work. It was necessary to mitigate NISQ device noise and short coherence periods. A naturally Euclidean parameter space was envisioned for the ansatz. This novel design uses the Fubini-Study metric to guarantee a singularity-free parameter space and streamline optimisation. The circuit structure is naturally trainable and hardware-efficient.

By making the Fubini-Study metric diagonal and constant in the ansatz, the researchers produced a stable optimisation environment that simplifies training. Because of this approach, the quantum natural gradient and normal gradient match.

Quantum Natural Gradient Descent Implicit adaptation

The researchers developed Implicit-Adaptive Quantum Natural Gradient Descent (I-AQNGD) to speed up the search for the lowest energy state.

I-AQNGD maintains the benefits of Adaptive Quantum Natural Gradient Descent by not measuring the Fubini-Study metric at each iteration. Backtracking search for dynamic step size adaptation is added to natural gradient. Tests indicated that I-AQNGD maintains competitive runtime and converges faster in less iterations than SPSA. The adaptive feature uses backtracking search to achieve faster convergence without relying on the starting point, according to the study.

Accurate Ground State Determination and Noise Resilience

The VQE implementation accurately determined the ground state energy for the investigated systems. The VQE for the triangular kagome cell converged to -0.749(1) J, as predicted by theory. The ground state energy of the star-shaped kagome lattice (12 qubits) was found to be −0.666(2) J, shedding light on frustrated magnetic systems. The team applied the VQE algorithm on the IBMQ Yorktown quantum processor and achieved 99.7% gate fidelity for single qubit gates and 94.2% for two-qubit gates, a significant achievement in noisy quantum devices for condensed matter physics.

Despite quantum computer noise, the technique worked. The custom ansatz precisely recovered spin correlation terms during VQE without complex error mitigation techniques.

By analysing spin-spin correlations and the static spin structure factor, scientists characterised the dimer state beyond energy predictions. In addition to being noise-resistant, this structural characterisation provides fresh information on the quantum states' structure and potential for unique magnetic properties. Even without error mitigation, spin correlation and spin structure factor might qualitatively characterise the dimer state.

Error Reduction Methods

The researchers employed error mitigation (EM) post-optimization methods like qubit-wise readout error mitigation (REM) and zero noise extrapolation (ZNE) to increase findings accuracy.

The results suggest that EM techniques improve observable estimations greatly. REM increased local dimer identification while not changing the variational concept. ZNE allows the violation of the Rayleigh-Ritz variational principle, hence it cannot provide an energy upper bound. However, ZNE often had the best accuracy across devices when used separately, especially with quadratic extrapolation. As seen by infrequent undershoots, REM and ZNE may overlap.

Future Quantum Materials Research Path

This paper establishes a trustworthy method for studying complex quantum many-body systems with near-term quantum computers. VQE's ability to prepare the ground state of kagome lattice pieces with shallow circuits even with high noise suggests a promising path.