Fundamentals of universality in one-way quantum computation
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In this paper, we build a framework allowing for a systematic investigation of the fundamental issue: ' Which quantum states serve as universal resources for measurement-based (one-way) quantum computation? ' We start our study by re-examining what is exactly meant by 'universality' in quantum computation, and what the implications are for universal one-way quantum computation. Given the framework of a measurement-based quantum computer, where quantum information is processed by local operations only, we find that the most general universal one-way quantum computer is one which is capable of accepting arbitrary classical inputs and producing arbitrary quantum outputs—we refer to this property as CQ-universality. We then show that a systematic study of CQ-universality in one-way quantum computation is possible by identifying entanglement features that are required to be present in every universal resource. In particular, we find that a large class of entanglement measures must reach its supremum on every universal resource. These insights are used to identify several families of states as being not universal, such as one-dimensional (1D) cluster states, Greenberger–Horne–Zeilinger (GHZ) states, W states, and ground states of non-critical 1D spin systems. Our criteria are strengthened by considering the efficiency of a quantum computation, and we find that entanglement measures must obey a certain scaling law with the system size for all efficient universal resources. This again leads to examples of non-universal resources, such as, e.g. ground states of critical 1D spin systems. On the other hand, we provide several examples of efficient universal resources, namely graph states corresponding to hexagonal, triangular and Kagome lattices. Finally, we consider the more general notion of encoded CQ-universality, where quantum outputs are allowed to be produced in an encoded form. Again we provide entanglement-based criteria for encoded universality. Moreover, we present a general procedure to construct encoded universal resources.
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There exist several natural notions of 'universality'.
“Afirst feature which is to be emphasized, is that there exist several natural notions of 'universality' 79 .”
From Measurement-based quantum computation (2009) · cites this paper as [79]
Following the entanglement criteria approach, it can be shown that n-particle 1D-cluster states, GHZ states, W-states, Dicke states, and certain ground states of strongly correlated 1D spin systems are not universal resources.
“Following this approach, it can e.g. be shown that n -particle 1D-cluster states, Greenberger-Horne-Zeilinger (GHZ) states, W-states, Dicke states, and certain ground states of strongly correlated 1D spin systems, are not universal resources 79 .”
From Measurement-based quantum computation (2009) · cites this paper as [79]
A universal measurement-based quantum computer is identified as a device which allows for universal state preparation by local operations only.
“Thus, a universal measurement-based quantum computer is then identified as a device which allows for universal state preparation by local operations only 79,80 .”
From Measurement-based quantum computation (2009) · cites this paper as [79]
Every universal resource must be maximally entangled with respect to all types of entanglement.
“Using this intuition, it can be shown that every such universal resource must be maximally entangled with respect to all types of entanglement 79,80 .”
From Measurement-based quantum computation (2009) · cites this paper as [79]
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- Raussendorf R 2003 PhD Thesis Ludwig-Maximillians University München
- Danos V, Kashefi E, Ollivier H and Silva M 2006 Preprint quant-ph/0611273 · arXiv
Cited by
Sorted by citations
Measurement-based quantum computation
Briegel, H. J., Browne, D. E., Dür, W., Raussendorf, R., & Van den Nest, M. (2009) · Nature Physics · doi:10.1038/nphys1157 · Cited by 1,090 · see citing works
Self-citationThe resource theory of quantum reference frames: manipulations and monotones
Gour, G., & Spekkens, R. W. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/3/033023 · Cited by 423 · see citing works
Measurement-based quantum computation beyond the one-way model
Gross, D., Eisert, J., Schuch, N., & Perez-Garcia, D. (2007) · Physical Review A · doi:10.1103/physreva.76.052315 · Cited by 236 · see citing works
Completeness of the Classical 2D Ising Model and Universal Quantum Computation
Van den Nest, M., Dür, W., & Briegel, H. J. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.110501 · Cited by 63 · see citing works
Self-citationBrowne, D., & Briegel, H. (2016) · Quantum Information · doi:10.1002/9783527805785.ch21 · Cited by 29 · see citing works
Self-citation
- Authors
- Nest, M. V. D., Dür, W., Miyake, A., & Briegel, H. J.
- Affiliations
- Austrian Academy of Sciences (AT)
- ORCID
- Dür, W
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2007-06-29
- Volume
- 9
- Issue
- 6
- Pages
- 204-204
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2149760285
- Cited by
- 97
- References
- 106
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 4 · 2023: 3 · 2022: 3 · 2021: 1 · 2020: 2 · 2019: 1 · 2018: 4 · 2017: 2 · 2016: 2 · 2015: 1 · 2014: 5 · 2013: 4 · 2012: 3
- FWCI
- 18.15
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Commission
- Österreichischen Akademie der Wissenschaften
- Austrian Science Fund
- Japan Society for the Promotion of Science
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- one-way quantum computation, measurement-based quantum computation, universality, entanglement measures, cluster states, GHZ states, W state, graph states, local operations, entanglement scaling
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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