The content discusses the use of quotient space quantum codes for constructing quantum error-correcting codes. It presents necessary and sufficient conditions for selecting invariant subspaces, new bounds for quantum codes, and proofs related to the construction of these codes. The approach offers a clear mathematical form for studying quantum error correction, providing insights into the unification of different types of quantum codes.
Additive and nonadditive codes are explored, along with their methods of construction and error correction capabilities. The concept of normed quotient spaces is introduced to establish distance metrics for these codes. The letter also delves into circuit design, decoding methods, and unique advantages offered by this new approach.
The author presents detailed examples of constructing various types of quantum codes using the proposed method. Special cases are discussed, such as nondegenerate and degenerate codes, along with their implications. New bounds are derived based on measurement conditions, expanding the understanding of quantum error correction.
Furthermore, the content addresses critical topics like symplectic inner product definitions, characteristic groups in commutative groups, and characterization of invariant subspaces using coset representatives. The Singleton bound is also discussed in the context of quantum error correction.
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by Jing-Lei Xia lúc arxiv.org 03-08-2024
https://arxiv.org/pdf/2311.07265.pdfYêu cầu sâu hơn