A Construction of Quantum Stabilizer Codes from Classical Codes and Butson Hadamard Matrices

• URL: http://arxiv.org/abs/2407.13527v1
• Date: Thu, 18 Jul 2024 14:00:38 GMT
• Title: A Construction of Quantum Stabilizer Codes from Classical Codes and Butson Hadamard Matrices
• Authors: Bulent Sarac, Damla Acar,
• Abstract summary: We show that if there exist a classical linear code C is a subset of F_qn of dimension k, then there exists an [[nm, ks, d]]_q quantum stabilizer code with d determined by C and D. We 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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