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$0.3 n^{3} + 0.0005\, n^{3} \lg n$

Why this formula appears here

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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n^{3}

Symbol n^3

$n^3$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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n

Symbol n

n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Research cited beside this formula

[14] How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits ↗

Published contexts (1)

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0.3 n^{3} + 0.0005\, n^{3} \lg n

Equation 39 · Quantum Information

Error Correction Is the Whole Problem in Quantum Computing

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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0.3n3+0.0005 n3lg⁡n0.3 n^{3} + 0.0005\, n^{3} \lg n0.3n3+0.0005n3lgn