基于测量的量子计算研究进展

张诗豪; 张向东; 李绿周

doi:10.7498/aps.70.20210923

摘要

相比于量子门电路模型, 基于测量的量子计算模型为实现普适量子计算提供了另一途径, 且经过近二十年的发展其内涵已得到了极大丰富. 本文对基于测量的量子计算模型的研究历史和现状进行综述. 首先简要介绍该模型的基本理论, 包括量子图态等资源态的概念和工作原理、模型的计算普适性和经典模拟方法、在相关量子信息处理领域的应用等. 接着从量子物理特性的角度概括基于测量的量子计算模型和量子多体系统之间的紧密联系, 包括量子纠缠、互文性、量子关联、对称保护拓扑序和量子物质相等作为计算资源所发挥的独特作用. 然后, 总结实现基于测量的量子计算模型的不同技术路线和实验成果. 这些理论和实验方面的进展是不断推动可扩展容错量子计算机研制的力量源泉. 最后, 对该领域未来的研究方向进行讨论和展望, 希望能启发读者进一步学习和探索相关课题.

关键词:

Abstract

Compared with the quantum gate circuit model, the measurement-based quantum computing model provides an alternative way to realize universal quantum computation, and relevant contents have been greatly enriched after nearly two decades of research and exploration. In this article, we review the research history and status of the measurement-based quantum computing model. First, we briefly introduce the basic theories of this model, including the concept and working principles of quantum graph states as resource states, the model’s computational universality and classical simulation methods, and relevant applications in the field of quantum information processing such as designing quantum algorithms and fault-tolerant error correction schemes. Then, from the perspective of quantum physical properties, which include the specific roles of quantum entanglement, contextuality, quantum correlations, symmetry-protected topological order, and quantum phases of matter as computing resources, the close relationship between measurement-based quantum computing model and quantum many-body system is presented. For example, a type of measurement-based computing model for exploiting quantum correlations can show a quantum advantage over the classical local hidden variable models, or certain symmetry-protected topological order states enable the universal quantum computation to be conducted by using only the measurements of single-qubit Pauli operators. Next, a variety of different technical routes and experimental progress of realizing the measurement-based quantum computing model are summarized, such as photonic systems, ion traps, superconducting circuits, etc. These achievements in various physical areas lay the foundation for future scalable and fault-tolerant quantum computers. Finally, we discuss and prospect the future research directions in this field thereby inspiring readers to further study and explore the relevant subjects.

Keywords:

作者及机构信息

1.
中山大学计算机学院, 量子计算与计算机理论研究所, 广州　510006

2.
北京理工大学物理学院, 先进光电量子结构设计与测量教育部重点实验室, 北京　100081

通信作者: 李绿周, lilvzh@mail.sysu.edu.cn

基金项目: 国家自然科学基金(批准号: 61772565, 62102464)、广东省基础与应用基础研究基金(批准号: 2020B1515020050)、广东省重点研发项目(批准号: 2018B030325001)和中国博士后科学基金(批准号: 2020M683049, 2021T140761)资助的课题

Authors and contacts

1.
Institute of Quantum Computing and Computer Theory, School of Computer Science and Engineering, Sun Yat-Sen University, Guangzhou 510006, China

2.
Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Li Lü-Zhou, lilvzh@mail.sysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61772565, 62102464), the Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2020B1515020050), the Key Research and Development project of Guangdong Province, China (Grant No. 2018B030325001), and the China Postdoctoral Science Foundation (Grant Nos. 2020M683049, 2021T140761)

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施引文献

图 1 不同类型的图态　(a)线性簇态; (b)星形图态; (c)马蹄形簇态; (d)可扩展的二维方格图态

Fig. 1. Different types of graph states: (a) A linear cluster state; (b) a star-graph state; (c) a horseshoe cluster state; (d) the scalable 2D square graph state.

下载: 全尺寸图片幻灯片

图 2 单向量子计算执行量子门操作　(a)输入态$ \left| + \right\rangle $经过${R_z}( - \alpha )$旋转和Hadamard门作用; (b)以测量纠缠态的方式等价地实现(a); (c)为(b)的扩展, 制备并测量4-qubit线性簇态以实现任意的单量子比特旋转门; (d)以4-qubit星形簇态执行CNOT门

Fig. 2. Realization of quantum gates in the 1 WQC model: (a) Input state $ \left| + \right\rangle $ undergoes a ${R_z}( - \alpha )$ rotation and a Hadamard gate; (b) a circuit equivalent to (a) by measuring an entangled state; (c) a generalization of (b) to prepare and measure a 4-qubit linear cluster state for implementing arbitrary single-qubit rotation gates; (d) a circuit performing the CNOT gate via a star cluster state.

下载: 全尺寸图片幻灯片

图 3 基于传态的方案实现单量子比特门　(a)一方远程制备态$U\left| \alpha \right\rangle $并通过Bell测量和泡利修正传给另一方, 注意U和Bell测量可以直接合并成新的联合测量; (b)利用制备好的资源态$(I \otimes U)\left| {{\beta _{{\text{00}}}}} \right\rangle $来间接执行$U\left| \alpha \right\rangle $

Fig. 3. Teleportation-based scheme for implementing any sing-qubit gate: (a) State $U\left| \alpha \right\rangle $is remotely prepared at one site and teleported to another site via Bell measurement and Pauli corrections, note here U and Bell measurement can be directly combined into a new joint measurement; (b) the scheme to indirectly implement $U\left| \alpha \right\rangle $ via a prepared resource state $(I \otimes U)\left| {{\beta _{{\text{00}}}}} \right\rangle $.

下载: 全尺寸图片幻灯片

图 4 利用关联的计算模型. 经典控制计算机提供k个测量设置中的1个作为对关联多方资源态中个体的经典输入(蓝色箭头), 并且接收l个测量结果中的1个(红色箭头)作为输出

Fig. 4. A computational model exploiting correlations. The classical control computer provides one of k measurement settings as the classical input (blue arrows) to each of the parties in the correlated resource state and receives one of l possible measurement results (red arrows) as the output.

下载: 全尺寸图片幻灯片

map

[1]	Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (New York: Cambridge University Press) pp1−12
[2]	Barenco A, Bennett C H, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J A, Weinfurter H 1995 Phys. Rev. A 52 3457 Google Scholar
[3]	Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188 Google Scholar
[4]	Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312 Google Scholar
[5]	Prevedel R, Walther P, Tiefenbacher F, Böhi P, Kaltenbaek R, Jennewein T, Zeilinger A 2007 Nature 445 65 Google Scholar
[6]	Lanyon B, Jurcevic P, Zwerger M, Hempel C, Martinez E, Dür W, Briegel H, Blatt R, Roos C F 2013 Phys. Rev. Lett. 111 210501 Google Scholar
[7]	Tame M, Özdemir Ş, Koashi M, Imoto N, Kim M 2009 Phys. Rev. A 79 020302 Google Scholar
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[12]	Pathumsoot P, Matsuo T, Satoh T, Hajdušek M, Suwanna S, Van Meter R 2020 Phys. Rev. A 101 052301 Google Scholar
[13]	Hein M, Eisert J, Briegel H J 2004 Phys. Rev. A 69 062311 Google Scholar
[14]	Briegel H J, Browne D E, Dür W, Raussendorf R, Van den Nest M 2009 Nat. Phys. 5 19 Google Scholar
[15]	Preskill J 2018 Quantum 2 79 Google Scholar
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