The bars are IBM's own published superconducting-processor qubit counts, 2016-2023 (5 → 20 → 50 → 53 → 65 → 127 → 433 → 1121). Two textbook technology-forecasting models are fit to that series by ordinary least squares on a linearized form:
Exponential: N(t) = N0 · e^{r(t-t0)}
linear fit of ln N vs t → slope r, intercept ln N0
Logistic: N(t) = M / (1 + e^{-(c+r(t-t0))})
linear fit of ln(N/(M-N)) vs t, for a chosen ceiling M
Both are the standard S-curve / exponential-diffusion models used in real technology-roadmap forecasting (the same math behind Moore's-law extrapolations). R² is computed by comparing the fitted curve back against the eight real data points in qubit-count space, not the linearized space, so it reflects how well the model tracks the actual roadmap.
- Exponential vs Logistic — unbounded compounding growth vs an S-curve that saturates at a chosen ceiling M (e.g. engineering, cryogenics or error-correction overhead limits).
- Ceiling M — only used by the logistic model; solving N(t)=target has no solution once target ≥ M.
- Milestone target — a qubit count of interest (10³-10⁷); the extrapolator solves the fitted curve for the year it is first crossed.
- Play timeline — a cursor sweeps from 2016 to the projected year, reading the fitted qubit count live off the curve.
Real-world relevance: this is exactly the kind of curve-fit extrapolation behind public "quantum advantage by year X" forecasts — and why they disagree so much: the same eight data points fit an unbounded exponential and a capped S-curve almost equally well over a short historical window, yet project wildly different milestone years.
This 2D companion plots the same fitted curve on a log-scale qubit-count vs. year chart instead of a 3D bar/curve scene — easier to read the exact shape of the extrapolation at a glance.