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Glossary

Quantum glossary

Code distance

Also: [[n,k,d]], distance, code parameters

The smallest number of qubits an error must touch to change the encoded information without being detected.

In the notation [[n, k, d]], n physical qubits encode k logical qubits at distance d. A distance-d code detects any error on up to d − 1 qubits and corrects any on up to ⌊(d − 1)/2⌋. It is not the number of errors the code survives: a distance-3 code corrects one.

corrects t = ⌊(d − 1)/2⌋ errors; Steane code: [[7, 1, 3]]

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Related terms

  • Stabilizer formalism — A way to describe a quantum state by the Pauli operators that leave it unchanged, instead of by its amplitudes.
  • Logical qubit — A qubit encoded redundantly across many physical qubits so that errors can be detected and corrected.
  • Surface code — A quantum error-correcting code laid out on a 2D grid, needing only nearest-neighbour interactions.
  • Error threshold — The physical error rate below which adding more qubits to an error-correcting code makes logical errors rarer, not more common.