The five-qubit error-correcting code, also known as the "perfect code," is a quantum error correction code that can correct arbitrary errors on a single qubit within a five-qubit quantum state. It is a fundamental example of how quantum information can be protected from decoherence and other types of noise that can occur in quantum systems.
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The five-qubit code encodes one logical qubit into five physical qubits and corrects an arbitrary error on one physical qubit. In a nondegenerate realization, the identity and fifteen one-qubit Pauli operators take the two-dimensional code into sixteen mutually orthogonal syndrome subspaces, filling the 32-dimensional physical Hilbert space.
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