• Journal of Communications and Networks
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• 제15권2호
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• pp.217-221
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• 2013

Quantum low-density parity-check (LDPC) codes based on the Calderbank-Shor-Steane construction have low encoding and decoding complexity. The sum-product algorithm(SPA) can be used to decode quantum LDPC codes; however, the decoding performance may be significantly decreased by the many four-cycles required by this type of quantum codes. All four-cycles can be eliminated using the entanglement-assisted formalism with maximally entangled states (ebits). The proposed entanglement-assisted quantum error-correcting code based on Euclidean geometry outperform differently structured quantum codes. However, the large number of ebits required to construct the entanglement-assisted formalism is a substantial obstacle to practical application. In this paper, we propose a novel class of entanglement-assisted quantum LDPC codes constructed using classical Euclidean geometry LDPC codes. Notably, the new codes require one copy of the ebit. Furthermore, we propose a construction scheme for a corresponding zigzag matrix and show that the algebraic structure of the codes could easily be expanded. A large class of quantum codes with various code lengths and code rates can be constructed. Our methods significantly improve the possibility of practical implementation of quantum error-correcting codes. Simulation results show that the entanglement-assisted quantum LDPC codes described in this study perform very well over a depolarizing channel with iterative decoding based on the SPA and that these codes outperform other quantum codes based on Euclidean geometries.

• 대한수학회보
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• 제56권3호
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• pp.609-619
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• 2019

The methods for constructing quantum codes is not always sufficient by itself. Also, the constructed quantum codes as in the classical coding theory have to enjoy a quality of its parameters that play a very important role in recovering data efficiently. In a very recent study quantum construction and examples of quantum codes over a finite field of order q are presented by La Garcia in [14]. Being inspired by La Garcia's the paper, here we extend the results over a finite field with $q^2$ elements by studying necessary and sufficient conditions for constructions quantum codes over this field. We determine a criteria for the existence of $q^2$-cyclotomic cosets containing at least three elements and present a construction method for quantum maximum-distance separable (MDS) codes. Moreover, we derive a way to construct quantum codes and show that this construction method leads to quantum codes with better parameters than the ones in [14].

• Journal of Communications and Networks
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• 제15권1호
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• pp.71-76
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• 2013

A new class of quantum low-density parity-check (LDPC) codes whose parity-check matrices are dual-containing matrices constructed based on lines of Euclidean geometries (EGs) is presented. The parity-check matrices of our quantum codes contain one and only one 4-cycle in every two rows and have better distance properties. However, the classical parity-check matrix constructed from EGs does not satisfy the condition of dual-containing. In some parameter conditions, parts of the rows in the matrix maybe have not any nonzero element in common. Notably, we propose four families of fascinating structure according to changes in all the parameters, and the parity-check matrices are adopted to satisfy the requirement of dual-containing. Series of matrix properties are proved. Construction methods of the parity-check matrices with dual-containing property are given. The simulation results show that the quantum LDPC codes constructed by this method perform very well over the depolarizing channel when decoded with iterative decoding based on the sum-product algorithm. Also, the quantum codes constructed in this paper outperform other quantum codes based on EGs.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.397-404
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• 2016

In this work, a method is given to construct quantum codes from cyclic codes over F₄ + vF₄ which will be denoted as R throughout the paper, where v² = v and a Gray map is defined between R and where F₄ is the field with 4 elements. Some optimal quantum code parameters and others will be presented at the end of the paper.

• 대한수학회보
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• 제53권6호
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• pp.1617-1628
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• 2016

In this paper, we extend the results given in [3] to a nonchain ring $R_p={\mathbb{F}}_p+v{\mathbb{F}}_p+{\cdots}+v^{p-1}{\mathbb{F}}_p$, where $v^p=v$ and p is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring $R_p$ and study the structure of their duals. We classify cyclic codes containing their duals over $R_p$ by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map ${\pi}$ defined in [4], we give the parameters of the quantum codes of length pn over ${\mathbb{F}}_p$ which are obtained from cyclic codes over $R_p$. Finally, we illustrate the results by giving some examples.

• 전자통신동향분석
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• 제37권2호
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• pp.1-10
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• 2022

Similar to present computers, quantum computers comprise quantum bits (qubits) and an operating system. However, because the quantum states are fragile, we need to correct quantum errors using entangled physical qubits with quantum error correction (QEC) codes. The combination of entangled physical qubits with a QEC protocol and its computational model are called a logical qubit and fault-tolerant quantum computation, respectively. Thus, QEC is the heart of fault-tolerant quantum computing and overcomes the limitations of noisy intermediate-scale quantum computing. Therefore, in this study, we briefly survey the status of QEC codes and the physical implementation of logical qubit over various qubit technologies. In summary, we emphasize 1) the error threshold value of a quantum system depends on the configurations and 2) therefore, we cannot set only any specific theoretical and/or physical experiment suggestion.

• 전자통신동향분석
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• 제33권1호
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• pp.20-33
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• 2018

The calculation speed of quantum computing is expected to outperform that of existing supercomputers with regard to certain problems such as secure computing, optimization problems, searching, and quantum chemistry. Many companies such as Google and IBM have been trying to make 50 superconducting qubits, which is expected to demonstrate quantum supremacy and those quantum computers are more advantageous in computing power than classical computers. However, quantum computers are expected to be applicable to solving real-world problems with superior computing power. This will require large scale quantum computing with many more qubits than the current 50 qubits available. To realize this, first, quantum error correction codes are required to be capable of computing within a sufficient amount of time with tolerable accuracy. Next, a compiler is required for the qubits encoded by quantum error correction codes to perform quantum operations. A large-scale quantum computer is therefore predicted to be composed of three essential components: a programming environment, layout mapping of qubits, and quantum processors. These components analyze how many numbers of qubits are needed, how accurate the qubit operations are, and where they are placed and operated. In this paper, recent progress on large-scale quantum computing and the relation of their components will be introduced.

• 전자통신동향분석
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• 제38권5호
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• pp.34-50
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• 2023

Quantum error correction is a key technology for achieving fault-tolerant quantum computation. Finding the best decoding solution to a single error syndrome pattern counteracting multiple errors is an NP-hard problem. Consequently, error decoding is one of the most expensive processes to protect the information in a logical qubit. Recent research on quantum error decoding has been focused on developing conventional and neural-network-based decoding algorithms to satisfy accuracy, speed, and scalability requirements. Although conventional decoding methods have notably improved accuracy in short codes, they face many challenges regarding speed and scalability in long codes. To overcome such problems, machine learning has been extensively applied to neural-network-based error decoding with meaningful results. Nevertheless, when using neural-network-based decoders alone, the learning cost grows exponentially with the code size. To prevent this problem, hierarchical error decoding has been devised by combining conventional and neural-network-based decoders. In addition, research on quantum error decoding is aimed at reducing the spacetime decoding cost and solving the backlog problem caused by decoding delays when using hardware-implemented decoders in cryogenic environments. We review the latest research trends in decoders for quantum error correction with high accuracy, neural-network-based quantum error decoders with high speed and scalability, and hardware-based quantum error decoders implemented in real qubit operating environments.

• 융합보안논문지
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• 제19권3호
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• pp.61-70
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• 2019

최근 엄청난 계산 능력을 보여주는 양자 컴퓨터와 정보 접근성이 높고 비용이 낮은 클라우드 컴퓨팅에 대한 개발이 활발하게 이루어지고 있다. 이러한 양자 컴퓨터의 경우 양자오류정정부호가 필수적이며, 클라우드 컴퓨팅의 경우 보안성 및 계산성을 확보하기 위해 동형암호가 사용될 수 있다. 각각 다른 목적을 위해 사용되는 이 두 기법은 서로 비슷한 가정을 바탕으로 하고 있어, 양자오류정정부호를 기반으로 동형암호를 구성하는 연구들이 진행되어왔다. 따라서 본 논문에서는 일반적인 양자오류정정부호를 변형하여 동형암호적 양자정보처리가 가능한 기법을 제시한다. 기존의 양자오류정정부호를 이용한 동형암호기법의 경우 부호를 사용하였지만 오류정정 능력이 전혀 없는데 반해, 제시한 양자오류정정부호 기법을 사용하면 동형암호적 양자정보처리가 가능하면서도, 동시에 양자오류정정부호 본연의 기능인 양자정보의 연산, 저장 중의 오류를 정정할 수 있는 장점이 존재한다.

• Nuclear Engineering and Technology
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• 제54권5호
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• pp.1860-1873
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• 2022

Nuclear thermal-hydraulic system analysis codes have been developed to comprehensively model nuclear reactor systems to evaluate the safety of a nuclear reactor system. For analyzing complex systems with finite computational resources, system codes usually solve simplified fluid equations for coarsely discretized control volumes with one-dimensional assumptions and replace source terms in the governing equations with constitutive relations. Wall boiling heat transfer models are regarded as essential models in nuclear safety evaluation among many constitutive relations. The wall boiling heat transfer models of two widely used nuclear system codes, RELAP5 and TRACE, are analyzed in this study. It is first described how wall heat transfer models are composed in the two codes. By utilizing the same method described in Part 1 paper, heat fluxes from the two codes are compared under the same thermal-hydraulic conditions. The significant factors for the differences are identified as well as at which conditions the non-negligible difference occurs. Steady-state simulations with both codes are also conducted to confirm how the difference in wall heat transfer models impacts the simulation results.