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Equation 14 · Part 3 · Error Correction Is the Whole Problem in Quantum Computing

=

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

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 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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