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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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Structure of CSS and CSS-T quantum codes

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DESIGNS codeS AND CRYPTOGRAPHY 2024年第10期92卷 2801-2823页

作者： Berardini, Elena Caminata, Alessio Ravagnani, Alberto CNRS 351 Cours Liberat F-33405 Talence France Univ Bordeaux IMB 351 Cours Liberat F-33405 Talence France Univ Genoa Dipartimento Matemat Dipartimento Eccellenza 2023 2027 Via Dodecaneso 35 I-16146 Genoa Italy Eindhoven Univ Technol Eindhoven Netherlands

We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction capability, showing that such pairs are easy to produce with a randomized construction. We then prove that CSS-T codes exhibit the opposite behaviour, showing also that, under very natural assumptions, their rate and relative distance cannot be simultaneously large. This partially answers an open question on the feasible parameters of CSS-T codes. We conclude with a simple construction of CSS-T codes from Hermitian curves. The paper also offers a concise introduction to CSS and CSS-T codes from the point of view of classical coding theory.

关键词： quantum error-correcting code CSS code CSS-T code code parameters

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Application of GRS codes to some entanglement-assisted quantum MDS codes

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quantum INFORMATION PROCESSING 2022年第3期21卷 1-16页

作者： Wang, Guohui Tang, Chunming Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China Guangdong Prov Key Lab Informat Secur Technol Guangzhou 510006 Peoples R China Qinghai Univ Basic Course Teaching & Res Dept Xining 810016 Peoples R China

Entanglement-assisted quantum error-correcting codes (EAQECCs) are a generalization of standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality condition and utilizing pre-shared entanglement between the sender and receiver to boost the rate of transmission. In this paper, we present some constructions of generalized Reed-Solomon codes and calculate the dimension of their hulls. With these generalized Reed-Solomon codes, we obtain four infinite families new constructions of EAQECCs, which are optimal with respect to the Singleton bound for EAQECCs. Notably, the parameters of our EAQECCs are flexible.

关键词： Entanglement-assisted quantum MDS code quantum error-correcting code Generalized Reed-Solomon code

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Channel-optimized quantum communication scheme based on combination code

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MODERN PHYSICS LETTERS A 2024年第16期39卷

作者： Zhao, Li-Yun Chen, Xiu-Bo Gong, Li Xu, Gang Chang, Yan Dong, Zhi-Chao Zhou, Nanrun Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Informat Secur Ctr Beijing 100876 Peoples R China North China Univ Technol Sch Informat Sci & Technol Beijing 100144 Peoples R China Adv Cryptog & Syst Secur Key Lab Sichuan Prov Chengdu 610025 Peoples R China Chengdu Univ Informat Technol Sch Cybersecur Chengdu 610225 Peoples R China Jiuzhou Quantum Technol Co Ltd Hangzhou 311200 Zhejiang Peoples R China Shanghai Univ Engn Sci Sch Elect & Elect Engn Shanghai 201620 Peoples R China

In this paper, a channel-optimized quantum communication scheme with imperfect Bell states is being considered, based on quantum teleportation and error correction codes technology. In this scheme, a novel "combination code" technique is proposed to protect the pre-shared Bell states from storage errors and to safeguard the information-encoded states from noisy channels. Ultimately, it is revealed by Monte Carlo simulation results that the channel fidelity of the proposed channel-optimized quantum communication scheme with imperfect Bell states is significantly advantageous over standard quantum error-correcting code (QECC) and entanglement-assisted quantum error-correcting code (EAQECC) communication schemes.

关键词： quantum error-correcting code quantum entanglement Bell state Monte Carlo simulations combination code

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Lattice surgery-based Surface code architecture using remote logical CNOT operation

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quantum INFORMATION PROCESSING 2022年第6期21卷 217-217页

作者： Lee, Jonghyun Kang, Yujin Ha, Jinyoung Heo, Jun Korea Univ Sch Elect Engn Seoul 02841 South Korea

The lattice surgery approach allows for an efficient implementation of universal quantum gate sets with topological quantum error correcting codes that achieve a high threshold and are composed of only the nearest gate operations and low-weight stabilizers. Here, we propose two types of lattice surgery-based logical qubit architectures using the logical remote-controlled-not operation and circuit mapping method. Our architectures enhanced the qubit efficiency, and when combined with our qubit initialization and routing process, they reduced the running time and quantum volume of several quantum circuits by removing time-expensive logical SWAP operations and enabling fast logical CNOT operations. The quantum volume was compared between three cases, one in which the magic state distillation technique was not applied, one in which the multiple magic state distillation circuits are used to reduce the circuit execution time, and the other in which one magic state distillation circuit are used to reduce the number of qubit used.

关键词： quantum error-correcting code quantum architectures quantum circuit mapping Lattice surgery

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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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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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Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets

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DESIGNS codeS AND CRYPTOGRAPHY 2020年第9期88卷 1893-1907页

作者： Matsumoto, Ryutaroh Tokyo Inst Technol Dept Informat & Commun Engn Tokyo Japan Aalborg Univ Dept Math Sci Aalborg Denmark

We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure.

关键词： Secret sharing quantum error-correcting code Gilbert-Varshamove bound Strong security

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The Ghost in the Radiation: Robust Encodings of the Black Hole Interior (Invited Paper) 2021

The Ghost in the Radiation: Robust Encodings of the Black Ho...

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53rd Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Kim, Isaac H. Tang, Eugene Preskill, John Univ Sydney Sydney NSW Australia CALTECH Pasadena CA 91125 USA

ISBN: (纸本)9781450380539

We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.

关键词： quantum Gravity Black Hole Information quantum error-correcting code quantum Computational Complexity

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New quantum codes Constructed by quantum Caps in PG(3,9) and PG(4,9)

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IEEE ACCESS 2020年 8卷 227894-227900页

作者： Li, Husheng Li, Ruihu Fu, Qiang Air Force Engn Univ Dept Basic Sci Xian 710051 Peoples R China

In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in PG(3, 9) and PG(4, 9) are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code with d = 4, we obtain 278 quantum error-correcting codes. Most of these results break theGVbound, and a number of them are optimal quantum codes or have improved parameters.

关键词： quantum computing quantum mechanics Linear codes error correction codes codecs Generators Licenses quantum cap quantum Hamming bound quantum error-correcting code combinatorial construction

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