Equation 27 · Part 6 · Error Correction Is the Whole Problem in Quantum Computing

fraction

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

fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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