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Cited by 236Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Measurement-based quantum computation beyond the one-way model

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Gross, D., Eisert, J., Schuch, N., Perez-Garcia, D.·2007·Physical Review A
DOI 10.1103/physreva.76.052315
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Abstract

We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes use of tools from many-body physics---matrix product states, finitely correlated states, or projected entangled pairs states---to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem---how to realize quantum computation---was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting and present a large number of examples. We find computational schemes, which differ from the original one-way computer, for example, in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may, for example, exhibit nonvanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.

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  • BQC uses the concept of one-way quantum computing, a measurement-based model of computation.

    “BQC uses the concept of one-way quantum computing [33-37], a measurement-based model of computation [38, 39] which represents a paradigm shift in the understanding of complex data processing by clearly separating the classical and quantum parts of a computation.”

    From Demonstration of Blind Quantum Computing (2012) · cites this paper as [36]

  • In measurement-based quantum computation, universal resources for reproducing classical outputs of any quantum computation can be systematically constructed beyond 2D-cluster states.

    “in 19,85 it is shown how such universal resources for MQC-beyond the 2D-cluster states-can systematically be constructed.”

    From Measurement-based quantum computation (2009) · cites this paper as [85]

  • Extremal entanglement features such as maximal localizable entanglement exhibited by 2D-cluster states need not be present in universal resources if only classical outputs are considered.

    “The main conclusion of this investigation is that a number of extremal entanglement features (such as e.g. maximal localizable entanglement) exhibited by 2D-cluster states no longer have to be present in universal resources if only classical outputs are considered 19,85 .”

    From Measurement-based quantum computation (2009) · cites this paper as [85]

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Research works printed but not linked: 9

  1. ͓5͔ M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, and H.-J. Briegel, e-print arXiv:quant-ph/0602096, Proceed- ings of the International School of Physics "Enrico Fermi" on "Quantum Computers, Algorithms and Chaos," Varenna, Italy, July, 2005 ͑to be published͒. · arXiv
  2. I. Markov and Y. Shi, e-print arXiv:quant-ph/0511069; · arXiv
  3. P. Jorrand and S. Perdrix, Proceedings of SPIE 5833, 44 ͑2002͒.
  4. ͓19͔ R. Jozsa et al., ͑eds.͒ Quantum Information Proceedings ͑ISO Press, 2006͒
  5. ͓22͔ V. Danos, E. Kashefi, and P. Panangaden, J. ACM 54, 8 ͑2007͒.
  6. S. Richter, Ph.D. thesis, Osnabrück, 1994 ͑unpublished͒;
  7. ͓30͔ B. Schumacher and R. F. Werner, e-print arXiv:quant-ph/ 0405174.
  8. D. Gottesman, Proceedings of the XXII International Coll. Group Theor. Meth. Phys. edited by S. A. Corney et al. ͑International Press, Cambridge, 1999͒;
  9. ͓42͔ G. Grimmett, Percolation ͑Springer, Berlin, 1999͒.

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Related

Authors
Gross, D., Eisert, J., Schuch, N., & Perez-Garcia, D.
Affiliations
  • London Institute for Mathematical Sciences (GB)
  • Max Planck Society (DE)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2007-11-19
Volume
76
Issue
5
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.76.052315
OpenAlex
W2077225059
Cited by
236
References
61
Citations by year
2026: 9 · 2025: 10 · 2024: 6 · 2023: 49 · 2022: 3 · 2021: 11 · 2020: 8 · 2019: 6 · 2018: 11 · 2017: 8 · 2016: 9 · 2015: 8 · 2014: 12 · 2013: 10 · 2012: 17
FWCI
18.15
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, other-oa)
  • Library Open Repository (Universidad Complutense Madrid) (submittedVersion, other-oa)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Microsoft Research
  • Engineering and Physical Sciences Research Council
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
measurement-based quantum computation, one-way quantum computation, local measurements, matrix product states, projected entangled pair states, toric code, long-range correlations, classical simulation, ultracold atoms in optical lattices, linear optical systems

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