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Published equation contexts

[[n,k,d]][[n, k, d]]

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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 given check — a single classical bit per generator, per round. That bit string is the syndrome.

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[[n,k,d]][[n, k, d]]

Equation 6 · Quantum Information

Error Correction Is the Whole Problem in Quantum Computing

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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 given check — a single classical bit per generator, per round. That bit string is the syndrome.

Meanings in this article

  • kk: the n -.
  • dd: the distance.
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