Trellis Decoding for Qudit Stabilizer Codes and Its Application to Qubit Topological Codes

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 […]

Improved Gilbert–Varshamov Bound for Entanglement-Assisted Asymmetric Quantum Error Correction by Symplectic Orthogonality

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

Decoding Quantum Error Correction Codes With Local Variation

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 […]