• Convergence Security Journal
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• v.19 no.3
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• pp.61-70
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• 2019

Recently, developments on quantum computers and cloud computing have been actively conducted. Quantum computers have been known to show tremendous computing power and Cloud computing has high accessibility for information and low cost. For quantum computers, quantum error correcting codes are essential. Similarly, cloud computing requires homomorphic encryption to ensure security. These two techniques, which are used for different purposes, are based on similar assumptions. Then, there have been studies to construct quantum homomorphic encryption based on quantum error correction code. Therefore, in this paper, we propose a scheme which can process the homomorphic encryption like quantum computation by modifying the QECCs. Conventional quantum homomorphic encryption schemes based on quantum error correcting codes does not have error correction capability. However, using the proposed scheme, it is possible to process the homomorphic encryption like quantum computation and correct the errors during computation and storage of quantum information unlike the homogeneous encryption scheme with quantum error correction code.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.1
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• pp.31-40
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• 2022

This paper proposes an augmented QSBC(Quantum Short-Block Code) that preserves the function of the existing QSBC and adds a single bit-flip error correction function due to Pauli X and Y errors. The augmented QSBC provides the diagnosis and automatic correction of a single Pauli X error by inserting additional auxiliary qubits and Toffoli gates as many as the number of information words into the existing QSBC. In this paper, the general expansion method of the augmented QSBC using seed vector and the realization method of the Toffoli gate of the single bit-flip error automatic correction function reflecting the scalability are also presented. The augmented QSBC proposed in this paper has a trade-off with a coding rate of at least 1/3 and at most 1/2 due to the insertion of auxiliary qubits.

• Electronics and Telecommunications Trends
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• v.38 no.5
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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.

• ETRI Journal
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• v.46 no.5
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• pp.759-773
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• 2024

Fault-tolerant quantum computation requires error-correcting codes that enable reliable universal quantum operations. This study introduces a novel approach that executes the logical Hadamard with low-space requirements while preserving the original definition of logical operators within the framework of the rotated surface codes. Our method leverages a boundary deformation method to rotate the logical qubit transformed by transversal Hadamard. Following this, the original encoding of the logical qubit is reinstated through logical flipand-shift operations. The estimated space-time cost for a logical Hadamard operation with a code distance d is 5d² + 3d² . The efficiency enhancement of the proposed method is approximately four times greater than those of previous approaches, regardless of the code distance. Unlike the traditional method, implementing a logical Hadamard requires only two patches instead of seven. Furthermore, the proposed method ensures the parallelism of quantum circuits by preventing interferences between adjacent logical data qubits.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.8
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• pp.3-14
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• 2013

We demonstrate a fashion of quantum channel combining and splitting, called polar quantum channel coding, to generate a quantum bit (qubit) sequence that achieves the symmetric capacity for any given binary input discrete quantum channels. The present capacity is achievable subject to input of arbitrary qubits with equal probability. The polarizing quantum channels can be well-conditioned for quantum error-correction coding, which transmits partially quantum data through some channels at rate one with the symmetric capacity near one but at rate zero through others.

• Journal of Satellite, Information and Communications
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• v.12 no.1
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• pp.38-42
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• 2017

This paper introduces the concept of a dual hash function to amplify security in a quantum key distribution system. We show the use of the relationship between quantum error correction and security to provide security amplification. Also, in terms of security amplification, the approach shows that phase error correction offers better security. We describe the process of enhancing security using the universal hash function using the BB84 protocol, which is a typical example of QKD. Finally, the deterministic universal hash function induces the security to be evaluated in the quantum Pauli channel without depending on the length of the message.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.34 no.2
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• pp.157-166
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• 2024

Probability of decryption failure of a public key cryptography based on LWE(learning with errors) is determined by its architecture and parameter settings. Since large decryption failure probability leads to attacks[1] on scheme as well as degradation of performance, TiGER[2], a Ring-LWE(R)-based KEM proposed for the first round of KpqC, tried to reduce the decryption failure probability by using error correction code Xef and D2 encoding method. However, D'Anvers et al. has shown that the commonly assumed independence of each bit error is not established since in the case of an encryption scheme based on Ring-LWE(R) using an error correction code, there is error dependency which is not negligible[3]. In this paper, since TiGER does not consider the error dependency, we calcualte the decryption failure probability of TiGER by considering the error dependency. In addition, we found that the bit error probability is incorrectly calculated in TiGER, so we present the correct calculation.

• ETRI Journal
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• v.45 no.3
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• pp.462-478
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• 2023

In quantum computing, the use of Pauli frames through software traces of classical computers improves computation efficiency. In previous studies, error correction and Pauli operation tracking have been performed simultaneously using integrated Pauli frames in the physical layer. In such a complex processing structure, the number of simultaneous operations processed in the physical layer exponentially increases as the distance of the surface code encoding logical qubit increases. This study proposes a Pauli frame management architecture partitioned into two layers for a lattice surgery-based surface code and describes its structure and operation rules. To evaluate the effectiveness of our method, we generated a random circuit according to the gate ratios constituting the commonly known quantum circuits and compared the generated circuit with the existing Pauli frame and our method. Simulations show a decrease of about 5% over traditional methods. In the case of experiments that only increase the code distance of the logical qubit, it can be seen that the effect of reducing the physical operation through the logical Pauli frame becomes more important.