A Construction of Quantum Stabilizer Codes from Classical Codes and Butson Hadamard Matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929426561761280 |
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| author | Sarac, Bulent Acar, Damla |
| author_facet | Sarac, Bulent Acar, Damla |
| contents | In this paper, we give a constructive proof to show that if there exist a classical linear code C is a subset of F_q^n of dimension k and a classical linear code D is a subset of F_q^k^m of dimension s, where q is a power of a prime number p, then there exists an [[nm, ks, d]]_q quantum stabilizer code with d determined by C and D by identifying the stabilizer group of the code. In the construction, we use a particular type of Butson Hadamard matrices equivalent to multiple Kronecker products of the Fourier matrix of order p. We also consider the same construction of a quantum code for a general normalized Butson Hadamard matrix and search for a condition for the quantum code to be a stabilizer code. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Construction of Quantum Stabilizer Codes from Classical Codes and Butson Hadamard Matrices Sarac, Bulent Acar, Damla Quantum Physics Quantum Algebra In this paper, we give a constructive proof to show that if there exist a classical linear code C is a subset of F_q^n of dimension k and a classical linear code D is a subset of F_q^k^m of dimension s, where q is a power of a prime number p, then there exists an [[nm, ks, d]]_q quantum stabilizer code with d determined by C and D by identifying the stabilizer group of the code. In the construction, we use a particular type of Butson Hadamard matrices equivalent to multiple Kronecker products of the Fourier matrix of order p. We also consider the same construction of a quantum code for a general normalized Butson Hadamard matrix and search for a condition for the quantum code to be a stabilizer code. |
| title | A Construction of Quantum Stabilizer Codes from Classical Codes and Butson Hadamard Matrices |
| topic | Quantum Physics Quantum Algebra |
| url | https://arxiv.org/abs/2407.13527 |