Equation 27 · Part 4 · Error Correction Is the Whole Problem in Quantum Computing

Symbol p

P_L(d) \;\approx\; A \left( \frac{p}{p_{\mathrm{th}}} \right)^{\left\lfloor (d+1)/2 \right\rfloor} ,

p

What this part means

well below $p_{\mathrm{th}}$ , not marginally below it.

Its job in the formula

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

Full expressionSymbol pArticle meaning

Where the article explains it

The suppression is exponential in d but the prefactor matters enormously in practice, and the useful regime is reached only when p is well below $p_{\mathrm{th}}$ , not marginally below it.

The passage around this formula

The practical form of the promise is a scaling law. Below threshold, the logical error rate per round of a distance- d code falls approximately as $P_L(d) \;\approx\; A \left( \frac{p}{p_{\mathrm{th}}} \right)^{\left\lfloor (d+1)/2 \right\rfloor}$ . so that each increase of the code distance by two multiplies the protection by a factor conventionally written

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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