Qubit Count Scaling

Qubit Count Scaling is the exponential growth law for the number of qubits in quantum systems over time, doubling at a fixed period in the manner of Moore's Law for classical computing. It is the main relation among the book's Quantum Scaling Laws, used to project how quantum computational capability develops from historical trends. Combined with improvements in quality, it underlies the book's Timeline to Singularity, which places the critical threshold for recursive intelligence at 2039.9 ± 3.0 years, and the Survival Function that turns those trajectories into a cumulative probability. N⊡(t) = N₀ × 2^((t − t₀)/T⇈), where N⊡(t) is the qubit count at time t, N₀ is the reference count (100, in 2020), t and t₀ are the current and reference times, and T⇈ is the doubling period, 2.0 ± 0.3 years. Times are [𝕋]; the counts and the exponent are [∅]. It belongs to the Quantum Scaling Laws and connects to the Timeline to Singularity, Survival Function, Effective Qubit Count and Physical-to-Logical Qubit Ratio.