Operational scale detection in quantum magnetism via susceptibility analysis: Critical-like behavior at the quantum–classical crossover on NISQ hardware

What defines the operational boundary between quantum information and classical magnetism? We present a model-independent methodology for detecting characteristic scales in quantum systems through generalized susceptibility analysis χ(σ)=|d〈O〉/dσ|, where σ represents observation scales across spatial, temporal, and decoherence dimensions. Through comprehensive experiments on a Rigetti Ankaa-3 quantum processor, we identify an operational threshold at γc=0.6737±0.036 under tested noise profiles, exhibiting exceptional peak clarity κ=8.58—the sharpest signal observed across all phenomena. This pronounced transition, validated through bootstrap analysis and multiple susceptibility metrics, suggests critical-like behavior in the quantum-to-classical crossover, though we carefully refrain from claiming a thermodynamic phase transition. The framework successfully extracts characteristic scales without prior theoretical knowledge: correlation length ξ=8.00 qubits, distinct ordering timescales for ferromagnetic (tc=0.36) versus antiferromagnetic (tc=0.91) systems, and the quantum critical field hc=1.821 in the transverse-field Ising model. Robustness analysis confirms stability across smoothing parameters, methods, and metric definitions. Beyond providing actionable guidance for noisy intermediate-scale quantum-era quantum computing, our findings suggest that magnetic correlations exhibit characteristic transitions at specific decoherence scales—an operational perspective connecting quantum information theory and condensed matter physics. While framing this as methodological advance rather than fundamental physics, the identification of critical-like information-to-physics transitions provides practical diagnostics for quantum device characterization and optimization.