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Equation 28 · Part 4 · Error Correction Is the Whole Problem in Quantum Computing

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

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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