Pulse Core Lexicon
Quantum Fraction Evolution
Definition
Quantum Fraction Evolution is the sigmoid function giving the share of computation that has passed from classical to quantum at a given time, describing a gradual but accelerating transition to a quantum-dominated computing landscape.
It is the weight in the Transitional Scaling Function, which blends classical and quantum scaling as S⊶(t) = S●(t) × (1 − f⊡(t)) + S⊡(t) × f⊡(t). The book reads the pair as showing that classical and quantum computation are phases of a single recursive trajectory, and the sigmoid shape as capturing why acceleration follows once coherence thresholds are crossed.
f⊡(t) = 1 / (1 + exp(−(t − t⊶)/Δt⊶)), where f⊡(t) is the quantum fraction, t is the current time, t⊶ is the estimated transition point (2027 ± 2 years) and Δt⊶ is the transition width (3.0 ± 1.0 years). The times are [𝕋] and the fraction is [∅].
It feeds the Transitional Scaling Function and connects to Qubit Count Scaling, Quantum Scaling Laws and Quantum Computational Enhancement.
Mathematical Expression
From the book · Chapter 8 · Pattern Recurrence in the Bit Curve and Quantum Scaling
f⊡(t) = 1/(1 + exp(-(t-t⊶)/Δt⊶)) [∅]
Where:
- f⊡(t) [∅] - quantum fraction evolution
- 1 [∅] - unity constant
- exp [∅] - exponential function
- t [𝕋] - current time
- t⊶ [𝕋] - estimated quantum transition point (2027 ± 2 years)
- Δt⊶ [𝕋] - transition width (3.0 ± 1.0 years)
- 2027 [∅] - nominal transition year
- 2 [∅] - transition year uncertainty
- 3.0 [∅] - nominal transition width
- 1.0 [∅] - transition width uncertainty
Technical Details
Category Concept
Chapter Chapter 8
Importance