Equation 39 · Part 1 · Error Correction Is the Whole Problem in Quantum Computing

Symbol n^3

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

n^{3}

What this part means

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

Its job in the formula

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

Full expressionSymbol n^3Article meaning

The passage around this formula

…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…

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

See this notation across published equations →

Sources cited in the surrounding passage

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

These citations provide research context; check each source for the exact claim it supports.