Complete Weight Distribution and MacWilliams Identities for Asymmetric Quantum Codes
Chuangqiang Hu, Shudi Yang, Stephen S.-T. Yau
TL;DR
This paper extends the theory of quantum error-correcting codes by introducing new weight enumerators and deriving MacWilliams identities, enabling improved bounds for asymmetric quantum codes.
Contribution
It introduces double and complete weight enumerators for asymmetric quantum codes and derives their MacWilliams identities, advancing the theoretical framework.
Findings
Derived MacWilliams identities for new weight enumerators
Established bounds for asymmetric quantum codes
Extended classical coding theory to quantum context
Abstract
In 1997, Shor and Laflamme defined the weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. We extend their work by introducing our double weight enumerators and complete weight enumerators. The MacWilliams identities for these enumerators can be obtained similarly. With the help of MacWilliams identities, we obtain various bounds for asymmetric quantum codes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography