Quantum simulation of coupled-oscillator synchronisation on a 156-qubit superconducting processor

This preprint presents a Kuramoto--XY synchronisation study with heterogeneous natural frequencies, simulator baselines, and ledgered IBM Heron r2 evidence. A Rust/PyO3-assisted pipeline supports entanglement entropy, Krylov complexity, OTOC scrambling, and Floquet discrete-time-crystal diagnostics for 2--16 qubit systems. The manuscript reports finite-size diagnostics consistent with Berezinskii--Kosterlitz--Thouless scaling in the small systems studied, including a periodic-boundary central-charge estimate near c = 1 at n = 8, while explicitly noting finite-size drift at larger sizes. It also records subharmonic Floquet response, non-ergodic level-spacing behaviour for heterogeneous frequencies, and a hardware-anchored scaling analysis that bounds exact Hilbert-space simulation costs. The record archives the manuscript source and PDF. Legacy IBM artefacts are treated as committed artefact-path evidence rather than aggregate validation, and the resource-boundary discussion is not promoted as a broad quantum-advantage claim because classical Rust Kuramoto ODE baselines remain faster in the measured observable-level regime.