A Unified Periodic Table for Quantum Coherence: Isotope Engineering as a Materials Roadmap

Quantum coherence underpins quantum technologies, but T₂ is limited by nuclear-spin noise. Two paths extend it: control-level protocols (dynamical decoupling) that suppress noise externally, and materials routes that act at the source—most universally, isotopic purification. Building on our law T₂ ∝ 1/ρ_spin and the initial periodic table at natural abundance [1], we now present a unified table that gives closed-form upper bounds (T_2,max) for all stable elements and integrates realistic enrichment pathways [2]. It shows where purification yields order-of-magnitude gains (diamond, Si, SiC), where hosts are intrinsically constrained (odd-Z elements lacking spin-zero isotopes), and highlights overlooked oxides (CaWO₄, HfO₂, ZnO, SrTiO₃) already showing millisecond-scale coherence that could extend far further with enrichment. Stripe patterns across Z encode global rules: even-Z elements typically offer abundant spin-zero isotopes; odd-Z never do. Coupled with availability classes (separability, records, regulation), the table becomes a design-and-triage tool. By setting theoretical ceilings and a pragmatic roadmap, isotope engineering emerges as a universal design principle for scalable qubits, sensors, and networks. [2]

[1] S. Kanai et al., PNAS 119, e2121808119 (2022). [2] S. Kanai et al., submitted (2025).