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Equation 14 · Part 2 · Error Correction Is the Whole Problem in Quantum Computing

Symbol d^2

nphys=2d2−1,n_{\mathrm{phys}} = 2d^{2} - 1 ,
d2d^{2}

What this part means

The square of d: multiply d by itself.

Its job in the formula

d2d^2 is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Distance d is the weight of the smallest undetectable logical error. A distance- d code corrects up to ⌊\lfloor (d-1)/2 ⌋\rfloor errors. For the planar surface code in its standard rotated layout, the physical cost of one logical qubit is nphys=2d2−1n_{\mathrm{phys}} = 2d^{2} - 1 . counting data and measure qubits together. A distance-7 patch therefore occupies ninety-seven physical qubits, and that is a memory holding one logical qubit, doing nothing else. It performs no gate, produces no non-Clifford operation, and reserves no routing space.

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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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