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Published equation contexts

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

Why this formula appears here

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 PL(d)  ≈  A(ppth)⌊(d+1)/2⌋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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PLP_L

Symbol P_L

PLP_L 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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dd

Symbol d

d 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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AA

Symbol A

A 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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pthp_{\mathrm{th}}

Symbol p_th

ptp_th occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 27 · Quantum Information

Error Correction Is the Whole Problem in Quantum Computing

This equation gives an approximation: it relates the quantities while allowing an approximation.

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 PL(d)  ≈  A(ppth)⌊(d+1)/2⌋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

Meanings in this article

  • pp: well below pthp_{\mathrm{th}} , not marginally below it.
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