Equation 6 · Part 2 · Error Correction Is the Whole Problem in Quantum Computing

Symbol k

[[n, k, d]]

k

What this part means

the n -.

Its job in the formula

k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol kArticle meaning

Where the article explains it

A code is defined not by listing its states but by naming a set of commuting Pauli operators $S_i$ — the stabiliser generators — whose joint +1 eigenspace is the code space: $S_i$ \, | $\psi_L$ $\rangle$ = + | $\psi_L$ $\rangle$ , $\qquad$ i = 1, $\dots$ , n - k .

The passage around this formula

An [[n, k, d]] code encodes k logical qubits into n physical qubits with distance d . The stabiliser generators are measured repeatedly. Because each $S_i$ commutes with every other and with the logical operators, measuring them extracts no information about which encoded state is present. What it extracts is whether an error has anticommuted with a given check — a single classical bit per generator, per round. That bit string is the syndrome.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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