Constructing Quantum Convolutional Codes via Difference Triangle Sets
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918337941864448 |
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| author | Nourozi, Vahid Mitchell, David |
| author_facet | Nourozi, Vahid Mitchell, David |
| contents | In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic orthogonality), while keeping the stabilizers sparse and encoding memory small. To construct Z(D), we show that one can use a reflection of the DTS indices of X(D), where X(D) corresponds to a classical convolutional self-orthogonal code (CSOC) constructed from strong DTS supports. The motivation of this approach is to provide a constructive design that guarantees a prescribed minimum distance. We provide numerical results demonstrating the construction for a variety of code rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructing Quantum Convolutional Codes via Difference Triangle Sets Nourozi, Vahid Mitchell, David Information Theory Quantum Algebra In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic orthogonality), while keeping the stabilizers sparse and encoding memory small. To construct Z(D), we show that one can use a reflection of the DTS indices of X(D), where X(D) corresponds to a classical convolutional self-orthogonal code (CSOC) constructed from strong DTS supports. The motivation of this approach is to provide a constructive design that guarantees a prescribed minimum distance. We provide numerical results demonstrating the construction for a variety of code rates. |
| title | Constructing Quantum Convolutional Codes via Difference Triangle Sets |
| topic | Information Theory Quantum Algebra |
| url | https://arxiv.org/abs/2602.13505 |