Quantum error-correcting code ($\mathcal{C}\subseteq ({\mathbb{C}}^2{)}^{\otimes n}$)

A quantum error-correcting code is a subspace encoding a logical Hilbert space, together with a specified family of noise operators that a common recovery quantum channel reverses on every encoded state. A K-dimensional code carries ${\log }_{2}K$ logical qubits. For a code projector $P$, correctability is characterized by the Knill--Laflamme condition; code distance is defined by the smallest undetectable operator weight, not merely by the number of generators.