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Published equation contexts

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

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

Equation 14 · 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.

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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