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Published equation contexts

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

Why this formula appears here

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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PL(d+2)P_L(d+2)

Denominator: P_L(d+2)

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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

Equation 28 · Quantum Information

Error Correction Is the Whole Problem in Quantum Computing

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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