Abstract: Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes C, D satisfying C⊥⊂C⊂D through the Calderbank-Shor-Steane (CSS) code construction. In this work, we establish connections between quantum synchronizable codes, subsystem codes, and […]
Abstract: In this article, we consider second-generation (2G) quantum repeaters (QRs) for creating long-distance entanglement in quantum networks. Combining a distance-dependent depolarizing error model with the nonlocal Bell state purification procedure required by 2G QRs leads to an error model consisting of correlated and biased errors. To correct correlated errors, nonsymmetric Calderbank–Steane–Shor (CSS) codes with […]
Abstract: This article proposes a novel low-complexity syndrome-based linear programming (SB-LP) decoding algorithm for decoding quantum low-density parity-check codes. Under the code-capacity model, the SB-LP decoder can be used as a standalone decoder; however, it is particularly powerful when used as a postprocessing step following SB min-sum (SB-MS) decoding. In the latter case, the proposed […]
Quantum error correction and the use of quantum error correction codes are likely to be essential for the realization of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes that are tailored for a particular error model may have much better performance. For more about this article see link below. […]
Trellis decoders are a general decoding technique first applied to qubit-based quantum error correction codes by Ollivier and Tillich in 2006. Here, we improve the scalability and practicality of their theory, show that it has strong structure, extend the results using classical coding theory as a guide, and demonstrate a canonical form from which the […]
We propose and prove an existential theorem for entanglement-assisted asymmetric quantum error correction. Then, we demonstrate its superiority over the conventional one. For more about this transaction see link below. https://ieeexplore.ieee.org/document/9076251
In this article, we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local information is taken into account during the decoding process: the code distance associated with a given logical […]