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Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits

National Science Review 2022年第1期9卷 100-106页

作者： 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 Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics University of Science and Technology of China Shanghai Branch CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics University of Science and Technology of China Shanghai Research Center for Quantum Sciences Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Department of Materials University of Oxford

quantum error correction is an essential ingredient for universal quantum computing.D espite tremendous experimental efforts in the study of quantum error correction,to date,there has been no demonstration in the realis ation of universal quantum error-correcting code,with the subsequent verification of all key features including the identification of an arbitrary physical error,the capability for transversal manipulation of the logical state and state *** address this challenge,we experimentally realise the [5,1,3]code,the so-called smallest perfect code that permits corrections of generic single-qubit *** the experiment,having optimised the encoding circuit,we employ an array of superconducting qubits to realise the [5,1,3] code for several typical logical states including the magic state,an indispensable resource for realising non-Clifford *** encoded states are prepared with an average fidelity of 57.1(3)% while with a high fidelity of 98.6(1)% in the code ***,the arbitrary single-qubit errors introduced manually are identified by measuring the *** further implement logical Pauli operations with a fidelity of 97.2(2)% within the code ***,we realise the decoding circuit and recover the input state with an overall fidelity of 74.5(6)%,in total with 92 *** work demonstrates each key aspect of the [5,1,3] code and verifies the viability of experimental realisation of quantum error-correcting codes with superconducting qubits.

关键词： quantum error-correcting code superconducting qubit five-qubit code error detection logical operation

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Constructing quantum error correcting code via logic function

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Science China(Information Sciences) 2010年第3期53卷 515-523页

作者： ZHONG ShuQin, MA Zhi & XU YaJie Zhengzhou Institute of Information Engineering, University of Information Engineering of China, Zhengzhou 450002, China 1. Zhengzhou Institute of Information Engineering University of Information Engineering of China Zhengzhou 450002 China

We present a systematic way to construct p-ary quantum error correcting codes using logic functions. As a consequence, for a given function with APC distance d′ 2, we can construct quantum codes with parameters ((n, K, d))p and gain a lower bound of K for all 2 d d′. The basic states of the constructed quantum codes can be stated and the sufficient conditions for saturating quantum Singleton bound are also discussed. We give quantum codes [[5, 1, 3]]p with p prime, [[6, 0, 4]], [[6, 2, 3]]p with p > 2 prime and [[2n, 2n - 2, 2]] as examples constructed in this way.

关键词： quantum error-correcting code logic states APC distance

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quantum secret sharing based on quantum error-correcting codes

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Chinese Physics B 2011年第5期20卷 91-95页

作者：张祖荣刘伟涛李承祖 Department of Physics School of ScienceNational University of Defense Technology

quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.

关键词： quantum secret sharing quantum error-correcting code classically enhanced quantumerror-correcting code

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quantum error-correcting codeS FROM QUASI-CYCLIC codeS

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INTERNATIONAL JOURNAL OF quantum INFORMATION 2008年第6期6卷 1263-1269页

作者： Qian, Jianfa Ma, Wenping Wang, Xinmei Xidian Univ Natl Key Lab ISN Xian 710071 Peoples R China

Quasi-cyclic codes form a generalization of cyclic codes, and contain a large number of record breaking codes. In this paper, we provide a method for constructing self-orthogonal quasi-cyclic codes, and obtain a large... 详细信息

关键词： quantum error-correcting code cyclic code self-dual basis quasi-cyclic code self-orthogonal code

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On the construction of stabilizer codes with an arbitrary binary matrix

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quantum INFORMATION PROCESSING 2013年第1期12卷 467-479页

作者： Hwang, Yongsoo Choi, Byung-Soo Jeon, Moongu Gwangju Inst Sci & Technol Dept Informat & Commun Kwangju South Korea Duke Univ Dept Elect & Comp Engn Durham NC USA

This paper proposes a simple framework for constructing a stabilizer code with an arbitrary binary matrix. We define a relation between A (1) and A (2) of a binary check matrix A = (A (1)|A (2)) associated with stabilizer generators of a quantum error-correcting code. Given an arbitrary binary matrix, we can derive a pair of A (1) and A (2) by the relation. As examples, we illustrate two kinds of stabilizer codes: quantum LDPC codes and quantum convolutional codes. By the nature of the proposed framework, the stabilizer codes covered in this paper belong to general stabilizer (non-CSS) codes.

关键词： quantum error-correcting code Stabilizer code Low-density parity check code Convolutional code

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quantum codes from nearly self-orthogonal quaternary linear codes

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DESIGNS codeS AND CRYPTOGRAPHY 2014年第2期73卷 417-424页

作者： Lisonek, Petr Singh, Vijaykumar Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada

Construction X and its variants are known from the theory of classical error control codes. We present instances of these constructions that produce binary stabilizer quantum error control codes from arbitrary quaternary linear codes. Our construction does not require the classical linear code that is used as the ingredient to satisfy the dual containment condition, or, equivalently, is not required to satisfy the self-orthogonality condition. We prove lower bounds on the minimum distance of quantum codes obtained from our construction. We give examples of record breaking quantum codes produced from our construction. In these examples, the ingredient code is nearly dual containing, or, equivalently, is nearly self-orthogonal, by which we mean that is positive but small.

关键词： quantum error-correcting code Linear code Construction X

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Classical access structures of ramp secret sharing based on quantum stabilizer codes

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quantum INFORMATION PROCESSING 2020年第1期19卷 1-16页

作者： Matsumoto, Ryutaroh Nagoya Univ Dept Informat & Commun Engn Nagoya Aichi Japan Aalborg Univ Dept Math Sci Aalborg Denmark

In this paper, we consider to use the quantum stabilizer codes as secret sharing schemes for classical secrets. We give necessary and sufficient conditions for qualified and forbidden sets in terms of quantum stabilizers. Then, we give a Gilbert-Varshamov-type sufficient condition for existence of secret sharing schemes with given parameters, and by using that sufficient condition, we show that roughly 19% of participants can be made forbidden independently of the size of classical secret, in particular when an n-bit classical secret is shared among n participants having 1-qubit share each. We also consider how much information is obtained by an intermediate set and express that amount of information in terms of quantum stabilizers. All the results are stated in terms of linear spaces over finite fields associated with the quantum stabilizers.

关键词： Secret sharing quantum error-correcting code Gilbert-Varshamov bound

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A class of quantum low-density parity check codes by combining seed graphs

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quantum INFORMATION PROCESSING 2013年第6期12卷 2219-2239页

作者： Hwang, Yongsoo Chung, Youngjoo Jeon, Moongu Gwangju Inst Sci & Technol Sch Informat & Commun Kwangju South Korea

This paper proposes a new construction of quantum low-density parity check (LDPC) codes that belong to the class of general stabilizer (non-CSS) codes. The method constructs a binary check matrix associated with the stabilizer generators of a quantum LDPC code. The binary check matrix is obtained from a large bipartite graph built by combining several small bipartite graphs called seed graphs. Computer simulation results show that the proposed code has similar or better performance than other quantum LDPC codes, and can be improved by exploiting the degenerate effect of quantum error-correcting codes.

关键词： quantum error-correcting code General stabilizer (non-CSS) code Low-density parity check code

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Catalytic quantum error Correction

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第6期60卷 3073-3089页

作者： Brun, Todd A. Devetak, Igor Hsieh, Min-Hsiu Univ So Calif Ming Hsieh Dept Elect Engn Los Angeles CA 90089 USA Univ Technol Sydney Fac Engn & Informat Technol Ctr Quantum Computat & Intelligent Syst Broadway NSW 2007 Australia

We develop the theory of entanglement-assisted quantum error-correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to preshared entanglement. Conventional stabilizer codes are equivalent to self-orthogonal symplectic codes. In contrast, EAQEC codes do not require self-orthogonality, which greatly simplifies their construction. We show how any classical binary or quaternary block code can be made into an EAQEC code. We provide a table of best known EAQEC codes with code length up to 10. With the self-orthogonality constraint removed, we see that the distance of an EAQEC code can be better than any standard quantum error-correcting code with the same fixed net yield. In a quantum computation setting, EAQEC codes give rise to catalytic quantum codes, which assume a subset of the qubits are noiseless. We also give an alternative construction of EAQEC codes by making classical entanglement-assisted codes coherent.

关键词： quantum error-correcting code entanglement quantum information theory father protocol

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New quantum codes from matrix-product codes over small fields

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quantum INFORMATION PROCESSING 2020年第8期19卷 1-22页

作者： Song, Hao Li, Ruihu Liu, Yang Guo, Guanmin Air Force Engn Univ Dept Basic Sci Xian 710051 Shaanxi Peoples R China

In this paper, we provide methods for constructing Hermitian dual-containing (HDC) matrix-product codes over F-q2 from some non-singular matrices and a special sequence of HDC codes and determine parameters of obtained matrix-product codes when the input matrix and sequence of HDC codes satisfy some conditions. Then, using some nested HDC BCH codes with lengths n = q(4)-1/a (a = 1 or a = q +/- 1), we construct some HDC matrix-product codes with lengths N = 2n or 3n and derive nonbinary quantum codes with length N from these matrix-product codes via Hermitian construction. Four classes of quantum codes over F-q (3 <= q <= 5) are presented, whose parameters are better than those in the literature. Besides, some of our new quantum codes can exceed the quantum Gilbert-Varshamov (GV) bound.

关键词： Matrix-product code Hermitian dual-containing condition BCH code quantum error-correcting code

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