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The consequence for resource accounting is decisive. In published estimates for cryptographically relevant algorithms, the magic state factory dominates both the spatial footprint and the runtime. Gidney and Ekerå’s abstract circuit model — which, as they state, ignores overheads from distillation, routing and error correction — uses 3n + 0.002\, n $\lg$ n logical qubits, 0.3 $n^{3}$ + 0.0005\, $n^{3}$ $\lg$ n Toffoli gates and 500 $n^{2}$ + $n^{2}$ $\lg$ n measurement depth to factor n -bit RSA integers [ 14 ] . It is the Toffoli count that sets the demand for distilled states, and it is the distillation of those states that turns a modest logical qubit count into the twenty million noisy physical qubits…

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