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Equation 5 · Part 4 · Error Correction Is the Whole Problem in Quantum Computing

Symbol n

Si ∣ψL⟩=+∣ψL⟩,i=1,…,n−k.S_i \, |\psi_L\rangle = + |\psi_L\rangle , \qquad i = 1, \dots, n - k .
nn

What this part means

n is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

n is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…by listing its states but by naming a set of commuting Pauli operators SiS_i — the stabiliser generators — whose joint +1 eigenspace is the code space: Si ∣ψL⟩=+∣ψL⟩,i=1,…,n−kS_i \, |\psi_L\rangle = + |\psi_L\rangle , \qquad i = 1, \dots, n - k . An [[n, k, d]] code encodes k logical qubits into n physical qubits with distance d . The stabiliser generators are measured repeatedly. Because each SiS_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…

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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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