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Quantum Error Correction Fault Tolerance

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

arXiv
Authors: Bulent Sarac, Damla Acar

Year

2024

Paper ID

65239

Status

Preprint

Abstract Read

~2 min

Abstract Words

137

Citations

N/A

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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  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2407.13527 [2] arXiv https://arxiv.org/abs/2407.13527 [3] Publisher https://arxiv.org/abs/2407.13527

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