Quantum Computing, Quantum Informations, Quantum Error-correcting, and Algebraic Coding Theory

Registration

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Special lecture on Quantum Information Sciences

• Choi, Minjin  (KISTI)

Title: Solving Partial Differential Equations with Variational Quantum Algorithms

Abstract: Variational quantum algorithms (VQAs) are fascinating methods that can be implemented on noisy intermediate-scale quantum devices. Their potential applications, such as investigating molecular structures, simulating quantum systems, and addressing optimization problems, are being actively explored. This talk introduces methods for solving the Poisson equation using VQAs. We also discuss the broader application of VQAs to other partial differential equations, emphasizing their potential in tackling complex physical phenomena.

Talks

Session I - Quantum Computing and Machine Learning 

• Lee, Yonghae  (Kangwon National University)

Title: An Implementation Method for the HHL Algorithm and Its Experimental Test

Abstract: We present a method for the efficient circuit implementation of the HHL algorithm, which plays a crucial role in quantum-assisted machine learning applications. By employing this approach, the number of qubits and quantum gates required can be significantly reduced, thereby improving resource optimization and enhancing the overall performance of the algorithm.

• Park, Jun Sur  (KIAS)

Title: tLaSDI: Thermodynamics-informed latent space dynamics identification

Abstract: We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

• Jang, Deok-Kyu (Kangwon National University)

Title: Quantum Machine Learning: Possibilities, Challenges, and Realities

Abstract: Quantum Machine Learning (QML) combines the principles of quantum computing with machine learning, opening new possibilities for addressing problems that are difficult to solve with classical methods. By leveraging quantum phenomena such as superposition and entanglement, QML offers innovative approaches in fields like optimization, pattern recognition, and complex simulations. However, significant technical and practical challenges remain, requiring further development to fully realize its potential. This talk introduces the core concepts of QML, including quantum data encoding, hybrid quantum-classical models, and Variational Quantum Circuits (VQC). Additionally, the quantum simulator Qiskit is introduced to demonstrate how QML concepts can be explored in practice.

Session II -  Coding Theory

• Han, Sunghyu (KoreaTech)

Title: Recent Developments of MDS Self-Dual Codes over Finite Fields

Abstract: In this presentation, we study recent developments of MDS self-dual codes over finite fields. Fisrt, we give Markus Grassl and T. Aaron Gulliver's construction method for even characteristic. Second, we give Lingfei Jin and Chaoping Xing's construction method for odd characteristic. Third, we give Haode Yan's further developments. Finally, we give various other construction methods.

• Kim, Hyun Jin (Yonsei University)

Title: Quasi-cyclic self-dual Codes with four factors 

Abstract:  In this study, we examine l-quasi-cyclic self-dual codes of length lm over F2, provided that the polynomial X^m − 1 has exactly four distinct irreducible factors in F_2[X]. We find the standard form of generator matrices of codes over the ring R = F_q[X]/(X^m − 1) and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths 2 and 4 over R.

• Jeong, Jihye (Ewha Womans University)

Title: Algorithms for constructing balanced plateaued functions with maximal algebraic degrees 

Abstract: Plateaued functions have received much attention due to their capability to prevent some cryptanalysis. In addition, some cryptographic applications require plateaued functions with balancedness and high algebraic degrees to have a large capacity to secure against some cryptographic attacks. We present explicit methods for constructing plateaued functions with balancedness and maximal algebraic degrees. To obtain the construction methods, we first find a theoretical framework for secondary constructions of plateaued functions. From this theoretical framework, we derive three practical algorithms for constructing plateaued functions. Finally, we obtain infinite families of r-plateaued functions with balancedness and maximal algebraic degrees for every positive integer r from the algorithms. This is a joint work with Prof. Yoonjin Lee (from Ewha Womans University).

Session III -  Quantum Computing and Error-Correction Codes

• Hong, Jihoon (Sogang University)

Title: Trends in Korean Post-Quantum Cryptography Competition and Introduction to the REDOG Algorithm

Abstract: This presentation examines the overall trends of the Korean Post-Quantum Cryptography Competition (KpqC Competition), organized by the National Security Research Institute (NSRI) since 2021. Additionally, it introduces the REDOG cryptographic algorithm, developed by CICAGO Lab(Prof. Jon-Lark Kim, Sogang University), which advanced to the second round of the competition.

• Kim, Ji-Hyeok (Kangwon National University)

Title: Implementation of Quantum Deletion Error Correcting Codes 

Abstract: Errors frequently occur during information storage and transmission in classical and quantum computing systems. This research focused on Quantum Error-Correcting Codes (QECC) and Permutation-Invariant (PI) codes to address these challenges. This study introduces the implementation of a 4-qubit quantum error correction code based on PI codes, which was developed and tested using Qiskit. 

• Choi, Whan-Hyuk (Kangwon National University)

Title: Designing quantum circuits for decoding binary linear codes 

Abstract: In coding theory, finding an efficient algorithm for the decoding process is one of the most important research problems. A quantum computer is an innovative computing device that performs calculations using the principles of quantum mechanics. In this paper, we find a decoding algorithm for binary linear codes using quantum circuits; this is the first time that quantum circuits are used as a primary tool for decoding binary linear codes. Our decoding algorithm is mainly based on Grover’s search algorithm. In detail, we study implementing the exhaustive search using quantum circuits for decoding binary linear codes. For our purpose, we design a modified Grover’s algorithm using three tools: the matrix multiplier, the Hamming weight counter, and the state indicator. We present a quantum decoding algorithm for binary linear codes. We illustrate the modified Grover’s algorithm using the [7, 4, 3] Hamming code, and IBM Quantum Composer implements the quantum decoding algorithm. This is a joint work with Prof. Yoonjin Lee and Prof. Hyunkee Yoo.

Contacts

• KRIMS : krims@kangwon.ac.kr

• Whan-Hyuk Choi : whchoi@kangwon.ac.kr