Quantum simulation of interlayer charge ordering in Kagome frustrated-magnet

Abstract

The interplay between interlayer coupling and quantum fluctuations governs charge ordering and defect dynamics in Kagome systems, yet these parameters are intrinsically entangled in existing Kagome metals and artificial spin-ice platforms, preventing their independent control. Here we realize a bilayer Kagome frustrated-magnet simulator comprising 1,536 connected spins on D-Wave quantum annealer, in which the effective quantum drive, $Γ_{\rm eff}$, and interlayer exchange, $J_{\perp}$, are independently programmable. We observe an interlayer-driven transition from ferroelectric to antiferroelectric Ice-II charge order at a critical coupling $(J_\perp/J_1)^*\approx0.04$, a phenomenon absent in single-layer geometries. Monte Carlo calculations show the transition persists in the classical limit, allowing the experimentally observed critical coupling to quantify the quantum renormalization induced by fluctuations. Applying resulting phase diagram to Kagome charge-density-wave materials places KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ deep within the ordered antiferroelectric regime, while locating CsV$_3$Sb$_5$ near the phase boundary, providing a natural explanation for its metastable $2\times2\times4$ stacking order. We further show that restricting charge-correlation measurements to ice-rule configurations resolves a systematic underestimation of ordering in conventional analyses, enabling direct reinterpretation of resonant X-ray, XMCD, STM and anomalous Hall experiments. Finally, we demonstrate that the same charge-sector reorganization framework explains near-degenerate plateau states in the metallic Kagome spin-ice HoAgGe and yields experimentally testable predictions for nanomagnetic, Kagome-metal and van der Waals frustrated systems. These results establish programmable quantum annealers as scalable simulators of emergent charge order and monopole physics in frustrated quantum matter.