Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination
Saved in:
| Title: | Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination |
|---|---|
| Authors: | Kyungbae Jang, Yujin Oh, Hwajeong Seo |
| Source: | Applied Sciences, Vol 14, Iss 19, p 8579 (2024) |
| Publisher Information: | MDPI AG |
| Publication Year: | 2024 |
| Collection: | Directory of Open Access Journals: DOAJ Articles |
| Subject Terms: | quantum computers, information set decoding, Gauss–Jordan elimination, Grover’s search, Technology, Engineering (General). Civil engineering (General), TA1-2040, Biology (General), QH301-705.5, Physics, QC1-999, Chemistry, QD1-999 |
| Description: | Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover’s algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover’s search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works. |
| Document Type: | article in journal/newspaper |
| Language: | English |
| Relation: | https://www.mdpi.com/2076-3417/14/19/8579; https://doaj.org/toc/2076-3417; https://doaj.org/article/b94346b6a324428b90e755f833367c81 |
| DOI: | 10.3390/app14198579 |
| Availability: | https://doi.org/10.3390/app14198579 https://doaj.org/article/b94346b6a324428b90e755f833367c81 |
| Accession Number: | edsbas.CF3700DC |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover’s algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover’s search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works. |
|---|---|
| DOI: | 10.3390/app14198579 |