From near-term to fault-tolerance: When axis-aligned QLM can outperform classical counterparts in Earth observation

Quantum computing is increasingly viewed as a possible tool for Earth science, yet its practical value beyond quantum hardware development remains uncertain. This paper argues that such value should be assessed through family-specific, axis-specific, and time-horizon-specific claims rather than broad claims of quantum advantage. For near-term quantum devices, we compare quantum vision transformers, quantum graph neural networks, and quantum kernel methods under matched-parameter settings, finding sharply different behaviors across model families.

To guide evaluation, we propose a structural-prior alignment principle: quantum models are most plausible when their designs align with physically structured axes in Earth-observation data. We instantiate this idea with Quantum Spectral Kernel Attention, a spectral-band-group quantum vision transformer that uses fewer parameters than a matched classical vision transformer and directionally outperforms it on SEN12-FLOOD when the training size is at least 100 samples in a three-seed pilot.

For long-term applications, classical simulations suggest that Quantum Oracle Sketching can enable compact quantum sketches of classical Earth-observation data, yielding a 4.4 to 5.8 orders-of-magnitude memory advantage on Pavia Centre and EuroSAT-MS. Overall, this work offers a structured framework for evaluating quantum computing in Earth science and identifies near-term architectural opportunities and longer-term fault-tolerant pathways for compact processing of large, heterogeneous Earth data.