Qubit Roadmap Extrapolator

Growth Model

Logistic ceiling M 1,000,000 qubits

Milestone target 1,000,000 qubits

Fit Diagnostics

Annual growth rate

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Fit quality R²

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Milestone reached in

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Cursor: 2016 — 5 qubits (IBM Q5, first public device)

How it works

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.

Historical qubit count Fitted projection Milestone / cursor

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