23 research outputs found
Algebraic techniques in designing quantum synchronizable codes
Quantum synchronizable codes are quantum error-correcting codes that can
correct the effects of quantum noise as well as block synchronization errors.
We improve the previously known general framework for designing quantum
synchronizable codes through more extensive use of the theory of finite fields.
This makes it possible to widen the range of tolerable magnitude of block
synchronization errors while giving mathematical insight into the algebraic
mechanism of synchronization recovery. Also given are families of quantum
synchronizable codes based on punctured Reed-Muller codes and their ambient
spaces.Comment: 9 pages, no figures. The framework presented in this article
supersedes the one given in arXiv:1206.0260 by the first autho
Algebraic techniques in designing quantum synchronizable codes
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces
Quantum Synchronizable Codes From Finite Geometries
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that, in principle, such a code can be constructed through a combination of a classical linear code and its subcode if the two are both cyclic and dual-containing. However, finding such classical codes that lead to promising quantum synchronizable error-correcting codes is not a trivial task. In fact, although there are two families of classical codes that are proved to produce quantum synchronizable codes with good minimum distances and highest possible tolerance against misalignment, their code lengths have been restricted to primes and Mersenne numbers. In this paper, examining the incidence vectors of projective spaces over the finite fields of characteristic 2, we give quantum synchronizable codes from cyclic codes whose lengths are not primes or Mersenne numbers. These projective geometric codes achieve good performance in quantum error correction and possess the best possible ability to recover synchronization, thereby enriching the variety of good quantum synchronizable codes. We also extend the current knowledge of cyclic codes in classical coding theory by explicitly giving generator polynomials of the finite geometric codes and completely characterizing the minimum weight nonzero codewords. In addition to the codes based on projective spaces, we carry out a similar analysis on the well-known cyclic codes from Euclidean spaces that are known to be majority logic decodable and determine their exact minimum distances
Parsing a sequence of qubits
We develop a theoretical framework for frame synchronization, also known as
block synchronization, in the quantum domain which makes it possible to attach
classical and quantum metadata to quantum information over a noisy channel even
when the information source and sink are frame-wise asynchronous. This
eliminates the need of frame synchronization at the hardware level and allows
for parsing qubit sequences during quantum information processing. Our
framework exploits binary constant-weight codes that are self-synchronizing.
Possible applications may include asynchronous quantum communication such as a
self-synchronizing quantum network where one can hop into the channel at any
time, catch the next coming quantum information with a label indicating the
sender, and reply by routing her quantum information with control qubits for
quantum switches all without assuming prior frame synchronization between
users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication
in the IEEE Transactions on Information Theor
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.