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Equation 28 · Part 3 · Error Correction Is the Whole Problem in Quantum Computing

Symbol d

Λ  =  PL(d)PL(d+2).\Lambda \;=\; \frac{P_L(d)}{P_L(d+2)} .
dd

What this part means

d is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

d is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

so that each increase of the code distance by two multiplies the protection by a factor conventionally written Λ  =  PL(d)PL(d+2)\Lambda \;=\; \frac{P_L(d)}{P_L(d+2)} . Below threshold means Λ\Lambda > 1 . Above threshold, adding qubits makes the logical qubit worse, because each additional physical qubit contributes more error than the larger code removes. This is the sense in which qubit count is not merely an incomplete figure of merit but can be an actively misleading one.

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Learn the underlying idea

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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