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Equation 14 · Part 6 · Error Correction Is the Whole Problem in Quantum Computing

superscript

nphys=2d2−1,n_{\mathrm{phys}} = 2d^{2} - 1 ,
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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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