Quantum codes based on fast pauli block transforms in the finite field
Ronghua Shi, Ying Guo, Moon Ho Lee · Quantum Information Processing · 2010
Motivated by the fast Pauli block transforms (or matrices) over the finite field GF ( q ) for an arbitrary number q , we suggest how to construct the simplified quantum code on the basis of quadratic residues. The present quantum code, which is the stabilizer quantum code, can be fast generated from an Abelian group with commutative quantum operators being selected from a suitable Pauli block matrix. This construction does not require the dual-containing or self-orthogonal constraint for the standard quantum error-correction code, thus allowing us to construct a quantum code with much efficiency.