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Measurement-based quantum computation beyond the one-way model
Open accessAbstract
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 [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 the citing paper
“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]
In the citing paper
“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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Citations
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Metadata
- 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
- 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
- bronze
- doi.org
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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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