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74 lines
2.6 KiB
TeX
74 lines
2.6 KiB
TeX
\section{Timeline Estimates for Cryptographically Relevant Quantum Computers}
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\label{sec:timeline}
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\subsection{Hardware Roadmaps}
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We survey published roadmaps from leading quantum hardware vendors:
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\begin{table}[ht]
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\centering
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\caption{Quantum hardware roadmaps (published projections as of 2025).}
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\label{tab:roadmaps}
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\begin{tabular}{lrrl}
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\toprule
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\textbf{Vendor} & \textbf{Qubits (2025)} & \textbf{Projected CRQC} & \textbf{Source} \\
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\midrule
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IBM & 1{,}121 (Condor) & 2029--2033 & IBM Quantum Roadmap \\
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Google & 105 (Willow) & 2029--2035 & Google AI Blog \\
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PsiQuantum & --- & 2027--2030 & Photonic approach \\
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IonQ & 36 (Forte) & 2030--2035 & Trapped ion \\
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QuEra & 256 (neutral atom) & 2028--2033 & Neutral atom \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Logical vs. Physical Qubits}
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Current quantum computers use physical qubits with error rates of $\sim$$10^{-3}$.
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Breaking secp256k1 requires $\sim$$2{,}330$ \emph{logical} qubits with error rates
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$< 10^{-10}$. Using surface codes with code distance 27, each logical qubit requires
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$\sim$$1{,}457$ physical qubits~\cite{gidney2021factor}. Therefore:
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\[
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2{,}330 \times 1{,}457 \approx 3{,}394{,}810 \text{ physical qubits}
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\]
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This is approximately $3{,}000\times$ more physical qubits than the largest current
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systems. However, qubit counts have been growing exponentially, and error correction
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improvements may reduce the overhead factor significantly.
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\subsection{Probability Assessment}
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Based on published roadmaps, error correction progress, and the distinction between
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physical and logical qubits, we estimate:
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\begin{table}[ht]
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\centering
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\caption{Cumulative probability of CRQC existence.}
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\label{tab:crqc-probability}
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\begin{tabular}{lr}
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\toprule
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\textbf{Year} & \textbf{P(CRQC exists)} \\
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\midrule
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2028 & $< 1\%$ \\
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2030 & $5\text{--}10\%$ \\
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2033 & $15\text{--}30\%$ \\
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2035 & $30\text{--}50\%$ \\
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2040 & $> 70\%$ \\
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\bottomrule
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\end{tabular}
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\end{table}
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These estimates are consistent with Mosca's inequality~\cite{mosca2018}: if the time
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to deploy quantum-safe cryptography ($d$) plus the shelf life of current secrets
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($l$) exceeds the time until CRQCs exist ($q$), then action is needed now. For
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blockchain, $l = \infty$ (on-chain data never expires), so the condition $d < q$
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must hold---meaning migration must \emph{complete} before CRQCs exist. Given that
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protocol-level cryptographic migrations take 3--5 years to fully deploy, the window
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for action is already closing.
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%% ========================================================================
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%% 6. ECONOMIC ANALYSIS
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%% ========================================================================
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