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.
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