INTERLEAVED SERIAL CONCATENATION OF QUANTUM CONVOLUTIONAL CODES: GATE IMPLEMENTATION AND ITERATIVE ERROR ESTIMATION ALGORITHM

摘要

A new construction of quantum codes has been proposed. It is based on interleaved serial concatenation of quantum convolutional codes. To describe the iterative error estimation algorithm, a trellis based representation of quantum codes has been introduced. With this tool at hand, it is possible to perform the Sum-Product algorithm for calculating efficiently the extrinsic probability of commutation / anti-commutation of the error with any element of the normalizer group N(S) using some prior on physical and logical errors. Derivation of the iterative algorithm naturally follows from the fact that physical qubits of the outer code are logical qubits of the inner code. This theoretical construction has been illustrated with an example for which performance has been evaluated overrnthe depolarizing channel. While this example is too basic to have performances equivalent to that of good classical turbo-codes, it opens the way to new designs of quantum codes relying on the existence of efficient iterative algorithms for error estimation Fully grown examples are under investigation.rnThis work has been funded in part by "ACI securite informatique - projet reseaux quantiques", and received computing support from Institute for Quantum Computing and SHARCNET. H.O. would like to thank C Negrevergne and D. Poulin for many enjoyable discussions, and R. Laflamme for constant encouragement.