Quantum codes based on fast pauli block transforms in the finite field

Authors:
Ronghua Shi;Ying Guo;Moon Ho Lee
Affiliations:
School of Information Science & Engineering, Central South University, Changsha, China 410083;School of Information Science & Engineering, Central South University, Changsha, China 410083 and Department of Physics, Tsinghua University, Beijing, China 10084;Institute of Information & Communication, Department of Information & Communication Engineering, Chonbuk National University, Chonju, Korea 561-756
Venue:
Quantum Information Processing
Year:
2010

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Abstract

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.