From Qubits to QCuries: A Quantum Computing Framework for Tc-99m Ultra-Precise Optimization

Abstract Technetium-99m (⁹⁹ᵐTc) radiopharmaceuticals account for more than 80% of diagnostic nuclear medicine procedures, yet their design has remained largely empirical, with minimal integration of quantum-mechanical stability. We present a quantum-entropy optimization framework demonstrating a statistically robust inverse correlation (ρ = -0.76 ± 0.05,p < 0.001) between Rényi-2 entropy (S₂) and quantum state purity (Tr[ρ²]) across ⁹⁹ᵐTc decay pathways. To formalize this relationship and for further research, we propose QCuries (Quantum Curies) as a unit for quantifying quantum-augmented activity, defined as 1 QCurie = 1 Curie × (1 - e⁻ᴿᵉ[ρ]), which reduces to the classical Curie under full decoherence. Our hybrid quantum-classical neural networks (QNN–ANN), trained on ab initio Nikiforov–Uvarov solutions and data from Nuclear information repositories, achieves a 32% accuracy gain over classical ANN baselines in stability and information-theoretic parameter predictions. Predicted phenomena include a 660-attosecond coherence threshold for β⁻ decay, high-purity α emissions (98% at 0.25 nat entropy), and >18% deviations from linear dosimetry in high-entropy regimes(S₂ > 1.5 nat). These results reveal a computationally defined ‘quantum Goldilocks zone’(0.5 < S₂ < 1.5 nat; 0.7-1.2 QCuries), which may guide the optimization of diagnostic tracers pending clinical validation. While clinical validation remains ongoing, this framework provides a physics-grounded path toward more predictive radiopharmaceutical design and may guide future regulatory standards.