Article
Multidisciplinary Sciences
Ming Gong, Xiao Yuan, Shiyu Wang, Yulin Wu, Youwei Zhao, Chen Zha, Shaowei Li, Zhen Zhang, Qi Zhao, Yunchao Liu, Futian Liang, Jin Lin, Yu Xu, Hui Deng, Hao Rong, He Lu, Simon C. Benjamin, Cheng-Zhi Peng, Xiongfeng Ma, Yu-Ao Chen, Xiaobo Zhu, Jian-Wei Pan
Summary: The study successfully demonstrated the experimental realization of the [5, 1, 3] code, verifying key aspects such as error identification and correction, logical operations, and state decoding.
NATIONAL SCIENCE REVIEW
(2022)
Article
Quantum Science & Technology
Younghun Kim, Jeongsoo Kang, Younghun Kwon
Summary: Surface code is a method of error correction that can be used for a functioning quantum computer. Transmon-based quantum computers, which are a promising candidate for practical use, have errors that occur predominantly as Z type errors. Tailored surface and XZZX codes have been developed to address these errors. This study presents a method for implementing tailored surface code and XZZX code on the specific heavy-hexagon structure of transmon-based quantum computers. The results show improved thresholds for the tailored surface code and XZZX code compared to the regular surface code, even in the absence of bias.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Quantum Science & Technology
Hanwei Xiao, Xiaoguang Chen
Summary: This paper proposes a framework of quantum convolutional codes that can handle continuous errors, by concatenating GKP code and utilizing the output information of the decoding circuit through multiple iterations to further reduce errors.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Quantum Science & Technology
Kai Lin Ong
Summary: The algebraic structures of classical codes can extract their properties and be viewed as ideals of group algebras. It has been proven that this method is efficient when the code generators are idempotents. In quantum error correction, self-orthogonal additive codes over GF(4) are required for the stabilizer formalism, which can be seen as F2-submodules over GF(4) through group algebras. This paper classifies idempotents in the commutative group algebra GF(4)G, and provides a criterion for idempotents to generate stabilizer subgroups. Furthermore, it constructs quantum stabilizer codes for cyclic group Cn (n = 2(m) - 1 and n = 2(m) + 1) and determines the quantum bounds on their burst error minimum distance.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Mathematics
Qiang Zhao, Haokun Mao, Yucheng Qiao, Ahmed A. Abd El-Latif, Qiong Li
Summary: In this paper, a remote quantum error correction code preparation protocol using a cluster state is introduced for blind quantum computation (BQC). The blindness of the protocol in the measurement-based quantum computation model is analyzed. Compared to previous methods, our protocol requires fewer quantum resources as it only requires weak coherent pulses, eliminating the need for quantum memory and limited quantum computing. Theoretical analysis and simulations demonstrate that our protocol requires fewer quantum resources compared to non-coding methods with the same qubit error rate.
Article
Quantum Science & Technology
Cibele Cristina Trinca, J. Carmelo Interlando, Reginaldo Palazzo Jr, Antonio Aparecido de Andrade, Ricardo Augusto Watanabe
Summary: This work presents a procedure for constructing toric quantum error-correcting codes. A new class of infinite family of toric quantum codes is provided by constructing cyclic codes on square lattices. The proposed quantum interleaving technique using the constructed toric quantum codes shows better code rate and coding gain compared to Kitaev's toric quantum codes and Bombin and Martin-Delgado's toric quantum codes.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Computer Science, Information Systems
Manideep Mamindlapally, Andreas Winter
Summary: This article discusses the derivation of Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum error correcting codes using quantum Shannon theoretic methods. It shows that the triple-rate region of possible EACQ codes is contained within the quantum Shannon theoretic rate region of a memoryless erasure channel, which is a polytope. The study demonstrates that a large part of this region can be achieved by certain EACQ codes under certain conditions.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Physics, Multidisciplinary
Rong Yan, Shanqi Pang, Mengqian Chen, Fuyuan Yang
Summary: In this paper, a relation between quantum error-correcting codes and orthogonal arrays with orthogonal partitions is established using the Hamming distance. This relation is a generalization of the existing relation between quantum error-correcting codes and irredundant orthogonal arrays. The construction of pure quantum error-correcting codes is made possible through this relation, leading to the explicit construction of numerous optimal quantum codes. The advantages of this approach include the constructive nature of the results, the purity of the constructed codes, and the reduced number of terms in each basis state. Furthermore, the method developed can be extended to the construction of quantum error-correcting codes over mixed alphabets.
Article
Physics, Multidisciplinary
Youwei Zhao, Yangsen Ye, He-Liang Huang, Yiming Zhang, Dachao Wu, Huijie Guan, Qingling Zhu, Zuolin Wei, Tan He, Sirui Cao, Fusheng Chen, Tung-Hsun Chung, Hui Deng, Daojin Fan, Ming Gong, Cheng Guo, Shaojun Guo, Lianchen Han, Na Li, Shaowei Li, Yuan Li, Futian Liang, Jin Lin, Haoran Qian, Hao Rong, Hong Su, Lihua Sun, Shiyu Wang, Yulin Wu, Yu Xu, Chong Ying, Jiale Yu, Chen Zha, Kaili Zhang, Yong-Heng Huo, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, Jian-Wei Pan
Summary: This article describes an experimental implementation of an error-correcting surface code on a superconducting quantum processor. By executing multiple consecutive error correction cycles, logical errors were significantly reduced, providing a key step towards scalable fault-tolerant quantum computing.
PHYSICAL REVIEW LETTERS
(2022)
Article
Computer Science, Theory & Methods
Boyi He, Qunying Liao
Summary: This paper studies the error-correcting pair for linear codes, focusing on the direct sum code of two linear codes. It provides conditions for the direct sum code to have an error-correcting pair, and discusses the decoding procedure with several examples.
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
(2023)
Article
Computer Science, Theory & Methods
Rene B. Christensen, Carlos Munuera, Francisco R. F. Pereira, Diego Ruano
Summary: This article discusses entanglement-assisted quantum error-correcting codes (EAQECCs) derived from classical one-point algebraic geometry codes from the Hermitian curve. An efficient algorithmic approach for computing the unknown parameter c for this family of EAQECCs is presented. The algorithm allows the construction of EAQECCs with excellent parameters over any field size.
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Boyi He, Qunying Liao
Summary: This paper investigates the error-correcting pair method for linear codes, focusing on MDS linear codes with minimum distance 2$+2$. It is found that MDS linear codes with an error-correcting pair have three possible parameter cases, where one case requires the code to be a generalized Reed-Solomon code.
FINITE FIELDS AND THEIR APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
Aron Rozgonyi, Gabor Szechenyi
Summary: In this theoretical study, we investigate the use of quantum code-based memories to enhance the lifetime of qubits and demonstrate the effectiveness of the quantum phase-flip repetition code as a quantum memory. By considering the gate error probabilities of current quantum computing platforms, we determine the optimal repetition number of quantum error correction cycles required to reach the break-even point and provide guidelines for developing quantum memories in semiconductor quantum devices.
NEW JOURNAL OF PHYSICS
(2023)
Article
Quantum Science & Technology
Regina Finsterhoelzl, Guido Burkard
Summary: We evaluate the performance of small error-correcting codes tailored to different hardware platforms, taking into account hardware-specific errors and connectivity. We investigate the dependence of logical error rate on platform features and benchmark our predictions with experimental results. The results show that the quasi-linear layout of superconducting devices is advantageous for small codes, while the central-spin connectivity of color centers enables lower error rates for codes involving multi-qubit controlled operations.
QUANTUM SCIENCE AND TECHNOLOGY
(2023)
Article
Quantum Science & Technology
Chaobin Liu
Summary: We derive explicit process matrices for a five-qubit code under any unital error channel, providing insights into the code's performance. This is the first explicit effective logical channel derived for a quantum correction code under a broad class of noise models. The process matrix proves that the concatenated code with a symmetric decoder can correct an open set of any type error channels.
QUANTUM INFORMATION PROCESSING
(2023)
Review
Optics
S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, S. L. Braunstein
Article
Optics
Stefano Pirandola, Carlo Ottaviani, Gaetana Spedalieri, Christian Weedbrook, Samuel L. Braunstein, Seth Lloyd, Tobias Gehring, Christian S. Jacobsen, Ulrik L. Andersen
Editorial Material
Multidisciplinary Sciences
Stefano Pirandola, Samuel L. Braunstein
Article
Multidisciplinary Sciences
Samuel L. Braunstein, Stefano Pirandola
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2018)
Article
Multidisciplinary Sciences
Zhi-Wei Wang, Samuel L. Braunstein
NATURE COMMUNICATIONS
(2018)
Article
Multidisciplinary Sciences
Zhi-Wei Wang, Samuel L. Braunstein
SCIENTIFIC REPORTS
(2016)
Article
Multidisciplinary Sciences
Riccardo Laurenza, Samuel L. Braunstein, Stefano Pirandola
SCIENTIFIC REPORTS
(2018)
Article
Astronomy & Astrophysics
Samuel L. Braunstein, Saurya Das, Zhi-Wei Wang
Summary: The study reveals that the apparent horizon and region near r = 0 of an evaporating charged, rotating black hole are timelike, suggesting that natural black holes with rotation have a channel for classical or quantum information to escape to the outside while the black hole shrinks. This has implications for the information loss problem.
INTERNATIONAL JOURNAL OF MODERN PHYSICS D
(2021)
Article
Quantum Science & Technology
Stefano Pirandola, Carlo Ottaviani, Christian S. Jacobsen, Gaetana Spedalieri, Samuel L. Braunstein, Tobias Gehring, Ulrik L. Andersen
Summary: The study explores the application of a quantum relay in quantum communication protocols, showing that classical correlations in the environment can reactivate entanglement distribution protocols by guaranteeing the distribution of a weaker form of entanglement. Additionally, experimental evidence demonstrates that memory effects in the environment can significantly enhance the performance of a quantum relay beyond established limits for quantum and private communications.
NPJ QUANTUM INFORMATION
(2021)
Editorial Material
Astronomy & Astrophysics
Zhi-Wei Wang, Samuel L. Braunstein
Summary: Dennis Sciama suggests that life is highly unlikely in a random universe due to the dependence of life on fundamental constants. However, without a complete understanding of these constants, his argument also implies the potential for an intelligently designed universe.
Article
Physics, Multidisciplinary
Gaetana Spedalieri, Lolita Piersimoni, Omar Laurino, Samuel L. Braunstein, Stefano Pirandola
PHYSICAL REVIEW RESEARCH
(2020)
Article
Quantum Science & Technology
Gaetana Spedalieri, Cosmo Lupo, Samuel L. Braunstein, Stefano Pirandola
QUANTUM SCIENCE AND TECHNOLOGY
(2019)
Article
Optics
Gaetana Spedalieri, Stefano Pirandola, Samuel L. Braunstein
Article
Quantum Science & Technology
Stefano Pirandola, Samuel L. Braunstein, Riccardo Laurenza, Carlo Ottaviani, Thomas P. W. Cope, Gaetana Spedalieri, Leonardo Banchi
QUANTUM SCIENCE AND TECHNOLOGY
(2018)
Proceedings Paper
Engineering, Electrical & Electronic
Carlo Ottaviani, Riccardo Laurenza, Thomas P. W. Cope, Gaetana Spedalieri, Samuel L. Braunstein, Stefano Pirandola
QUANTUM INFORMATION SCIENCE AND TECHNOLOGY II
(2016)
