Stabilizer Quantum Codes: A Unified View based on Forney-style Factor Graphs Export

@article{citeulike:3955734, abstract = {Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure that enables efficient and close-to-optimal iterative decoding. In this paper we focus on stabilizer QECCs, a class of QECCs whose construction is rendered non-trivial by the fact that the stabilizer label code, a code that is associated with a stabilizer QECC, has to satisfy a certain self-orthogonality condition. In order to design graphical models of stabilizer label codes that satisfy this condition, we extend a duality result for Forney-style factor graphs (FFGs) to the stabilizer label code framework. This allows us to formulate a simple FFG design rule for constructing stabilizer label codes, a design rule that unifies several earlier stabilizer label code constructions.}, archivePrefix = {arXiv}, author = {Vontobel, Pascal O.}, citeulike-article-id = {3955734}, citeulike-linkout-0 = {http://arxiv.org/abs/0807.3566}, citeulike-linkout-1 = {http://arxiv.org/pdf/0807.3566}, eprint = {0807.3566}, keywords = {graphs, physics, quantum, quantum-information}, month = {Jul}, posted-at = {2009-01-26 23:35:47}, priority = {2}, title = {Stabilizer Quantum Codes: A Unified View based on Forney-style Factor Graphs}, url = {http://arxiv.org/abs/0807.3566}, year = {2008} }

TY - JOUR ID - citeulike:3955734 L3 - citeulike-article-id:3955734 N2 - Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure that enables efficient and close-to-optimal iterative decoding. In this paper we focus on stabilizer QECCs, a class of QECCs whose construction is rendered non-trivial by the fact that the stabilizer label code, a code that is associated with a stabilizer QECC, has to satisfy a certain self-orthogonality condition. In order to design graphical models of stabilizer label codes that satisfy this condition, we extend a duality result for Forney-style factor graphs (FFGs) to the stabilizer label code framework. This allows us to formulate a simple FFG design rule for constructing stabilizer label codes, a design rule that unifies several earlier stabilizer label code constructions. TI - Stabilizer Quantum Codes: A Unified View based on Forney-style Factor Graphs KW - graphs KW - physics KW - quantum KW - quantum-information AU - Vontobel, Pascal PY - 2008/Jul/22/ UR - http://arxiv.org/abs/0807.3566 ER -