Research progress of measurement-based quantum computation

Zhang Shi-Hao; Zhang Xiang-Dong; Li Lü-Zhou

doi:10.7498/aps.70.20210923

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:

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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Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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 $

Figure 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 $.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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
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[15]	Preskill J 2018 Quantum 2 79 Google Scholar
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[20]	Perdrix S 2005 Int. J. Quantum Inf. 3 219 Google Scholar
[21]	Jorrand P, Perdrix S 2005 Proc. SPIE 5833 44 Google Scholar
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[23]	Gross D, Eisert J, Schuch N, Perez-Garcia D 2007 Phys. Rev. A 76 052315 Google Scholar
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