Equation 27 · Part 10 · Error Correction Is the Whole Problem in Quantum Computing

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

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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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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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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.

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Sources cited in the article section

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