Decoherence Rate as a Function of FCLT Necessity Depth: Pre-Registered φ-Structured Decoherence Gradient Prediction and Empirical Test Protocol for Multi-Qubit Quantum Systems

Abby Davis

Published May 13, 2026• 0 citations

Abstract

Fibonacci Causal Loop Theory (FCLT) predicts that decoherence rate Γ scales inversely with necessity depth D: Γ(D) = Γ₀ × φ^(−D), and the ratio of decoherence rates at adjacent necessity depths satisfies Γ(D+1)/Γ(D) = 1/φ ≈ 0.618. This formalizes FCLT Prediction 12 (pre-registered in FCLT Complete Manuscript v16, DOI: 10.5281/zenodo.20087640). The derivation follows directly from the QNM quality factor confirmations: P73 confirmed Q = φ³ (D=3, Schwarzschild) and P73e confirmed Q = φ⁴ (D=4, Kerr). Since Q = ω₀/Γ, the decoherence scaling law Γ(D) = Γ₀ × φ^(−D) follows with zero free parameters. The prediction is testable in NMR quantum simulators, trapped-ion arrays, and superconducting qubit platforms where decoherence rates can be measured across multiple organizational depth levels. Confirmation criterion: δ < 0.05. Classification: technology-gap pending validated D(x,t) measurement protocol. FCLT scorecard unchanged: 20 confirmed / 5 falsified / 24 tech-gap / 4 gray zone.

DOI: 10.5281/zenodo.20149732

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