Quantum error correction

Quantum error correction encodes quantum information across multiple physical qubits so errors can be detected and corrected without directly measuring the encoded information.

Quantum error-correcting code: A code that represents logical quantum states in a larger space of physical states so errors can be detected and corrected. These codes provide the mathematical rules for encoding, syndrome measurement, and recovery.
Qubit: A quantum system whose state can represent a superposition of two basis states. Quantum codes distribute information stored in qubits across redundant physical carriers.
Shor code: A nine-qubit quantum code that corrects an arbitrary error on any one physical qubit. It combines bit-flip and phase-flip protection in an early demonstration of quantum error correction.
Dynamical decoupling: A control technique that suppresses unwanted system-environment interactions through sequences of applied operations. Unlike error correction, it suppresses some errors without encoding information across redundant qubits.
Quantum error-correction overhead: The extra physical qubits, operations, and time required to encode and protect logical quantum information. Reducing overhead is essential to making useful logical qubits affordable.
Quantum stabilizer code: A quantum error-correcting code specified by commuting Pauli operators whose shared eigenspaces define its code space. Stabilizer measurements extract error syndromes without revealing encoded logical information.
Quantum superposition: A quantum state formed from a coherent combination of multiple possible basis states. Correction must protect superpositions, not merely classical bit values.
Steane code: A seven-qubit CSS quantum code that corrects any single-qubit error. Its structure supports transversal operations useful in fault-tolerant computation.
Decoherence-free subspace: A subspace of quantum states that is unaffected by a specified class of environmental noise. It avoids selected errors through symmetry rather than detecting syndromes and applying recovery.
Quantum error correction threshold: The maximum physical error rate below which a particular code can suppress logical errors as its size increases. Thresholds depend on noise and architecture, so laboratory performance must be judged in context.

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