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International Conference on Genetic and Evolutionary Computing

Construction and Complete Circuit for Quantum Low Density Parity Check Code

Shengmei Zhao, Baoyu Zheng

Published Sep 1, 2008• 0 citations
Publisher

Abstract

Quantum error correction is the basic technique for realization of quantum communication and quantum computation. So far, the theories of quantum error correction have become more and more perfect, and many counterpart of classical error correction coding technique have been found in quantum area. In this article, we proposed a new method of construction of parity check matrix of quantum low density parity check (LDPC) codes which based on classical quasi-cyclic LDPC codes, and selected the quantum code (3,8)(16,6) as the example to illustrate the construction of quantum code. We also gave its completing circuit by controlled-not gate and Hadamard gate.

DOI
10.1109/wgec.2008.50

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Quantum error correction is the basic technique for realization of quantum communication and quantum computation. So far, the theories of quantum error correction have become more and more perfect, and many counterpart of classical error correction coding technique have been found in quantum area. In this article, we proposed a new method of construction of parity check matrix of quantum low density parity check (LDPC) codes which based on classical quasi-cyclic LDPC codes, and selected the quantum code (3,8)(16,6) as the example to illustrate the construction of quantum code. We also gave its completing circuit by controlled-not gate and Hadamard gate.
Quantum error correction is the basic technique for realization of quantum communication and quantum computation.So far,the theories of quantum error correction has become more and more perfect,many counterpart of classical error correction coding technique have been found in quantum area.In this paper,we improve a method of construction of parity check matrix in quantum low density parity check(LDPC) codes based on sparse circle sequence,and compare the performance of our construction method with that of MacKay's.The result shows that our method is not only able to remove some disadvantages of B and U construction,but also to reserve their advantages and improve the efficiency of coding and decoding.
With the development of quantum error correction techniques, many counterparts of classical error correction coding techniques have been found in quantum area. As the quantum counterpart of a good error correction code in classical communications, quantum low density parity check code becomes a promising coding technique in quantum error correction area. In this paper, a construction method of quantum low density parity check code (quantum LDPC) based on Projective Geometry is proposed, and the quantum code QLDPC [21,6] is selected as an example to illustrate the whole construction procedures. By numerical simulation, the error correction performance of QLDPC [21,6] is discussed over the bit-flipping channel. It is shown that this method is available and has some advantages.
In this paper, a construction method of quantum low density parity check codes (quantum LDPC) which based on classical quasi-cyclic sparse sequence is proposed, and the quantum code QLDPC(3,8)(16,6) and QLDPC(3,8)(64,24) are selected as examples to illustrate this construction method. The performances of this kind quantum LDPC codes are discussed over the bit-flipping channel by numerical simulations. The results show that these quantum codes have good ability to correct error in quantum channel.
CSS code is a simple,efficient quantum error correction code construction,and has been found applications in construction of varieties of quantum codes,so far.In this paper,we propose a new construction method of quantum parity check matrix codes based on CSS by taking advantage of the method used in classical quasi-cyclic LDPC codes.Using quick encoding algorithm,we can obtain the quantum code based on this proposed method.At last,a quantum code(3,8)(16,6) is selected as the example to illustrate the process of construction,and its encoding circuit by Controlled-not gate and Hadard gate is also presented.
This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an orthogonal structure suitable for quantum error correction. By utilizing algebraic techniques, short cycles are eliminated, which improves error correction performance. Additionally, this method is extended to non-binary LDPC codes and spatially-coupled LDPC codes, demonstrating that both the girth and orthogonality can be preserved. The results of this study enable the design of high-performance quantum error-correcting codes without the need for random search.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.