Definition
Let us define an stabilizer quantum error-correcting code to encode logical qubits into physical qubits. The rate of such a code is . Its stabilizer is an abelian subgroup of the -fold Pauli group : . does not contain the operator . The simultaneous -eigenspace of the operators constitutes the codespace. The codespace has dimension so that we can encode qubits into it. The stabilizer has a minimal representation in terms of independent generators
The generators are independent in the sense that none of them is a product of any other two (up to a global phase). The operators function in the same way as a parity check matrix does for a classical linear block code.
Read more about this topic: Stabilizer Code
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)