Utility-Scale Quantum Computation of Ground-State Energy in a 100+ Site Planar Kagome Antiferromagnet via Hamiltonian Engineering

TL;DR

This paper demonstrates the first large-scale quantum computation of the ground-state energy in a 103-site Kagome antiferromagnet using a hybrid VQE approach and Hamiltonian engineering on IBM quantum processors, showing scalability for complex 2D systems.

Contribution

It introduces a Hamiltonian engineering strategy and a hybrid VQE method enabling efficient quantum simulation of large frustrated 2D systems.

Findings

Achieved ground-state energy estimate matching thermodynamic limit

Entangled up to 103 qubits with high fidelity

Demonstrated scalability of VQE for large 2D frustrated systems

Abstract

We present experimental quantum computation of the ground-state energy in a 103-site flat Kagome lattice under the antiferromagnetic Heisenberg model (KAFH), with IBM's Heron r1 and Heron r2 quantum processors. For spin-1/2 KAFH, our per-site ground-state energy estimate is $-0.417\,J$, which, under open-boundary corrections, matches the energy in the thermodynamic limit, i.e., $-0.4386\,J$. To achieve this, we used a hybrid approach that splits the conventional Variational Quantum Eigensolver (VQE) into local (classical) and global (quantum) components for efficient hardware utilization. More importantly, we introduce a Hamiltonian engineering strategy that increases coupling on defect triangles to mimic loop-flip dynamics, allowing us to simplify the ansatz while retaining computational accuracy. Using a single-repetition, hardware-efficient ansatz, we entangle up to 103 qubits with high fidelity to determine the Hamiltonian's lowest eigenvalue. This work demonstrates the scalability of VQE for frustrated 2D systems and lays the foundation for future studies using deeper ansatz circuits and larger lattices on utility quantum processors.