Universal Resources for Measurement-Based Quantum Computation
Open accessAbstract
We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other universal resource. We obtain a powerful criterion to assess the universality of graph states by introducing an entanglement measure which necessarily grows unboundedly with the system size for all universal resource states. Furthermore, we prove that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and obtain the first example of a universal nongraph state.
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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 [80]
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 [80]
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Geometric Entanglement of Symmetric States and the Majorana Representation
Aulbach, M., Markham, D., & Murao, M. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-18073-6_12 · Cited by 18 · see citing works
Direct evaluation of pure graph state entanglement
Hajdušek, M., & Murao, M. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/1/013039 · Cited by 18 · see citing works
Spin lattices with two-body Hamiltonians for which the ground state encodes a cluster state
Griffin, T., & Bartlett, S. D. (2008) · Physical Review A · doi:10.1103/physreva.78.062306 · Cited by 18 · see citing works
Measurement-Based Quantum Computation and Undecidable Logic
Van den Nest, M., & Briegel, H. J. (2008) · Foundations of Physics · doi:10.1007/s10701-008-9212-6 · Cited by 17 · see citing works
Self-citation
- Authors
- Van den Nest, M., Miyake, A., Dür, W., & Briegel, H. J.
- Affiliations
- Universität Innsbruck (AT)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-10-13
- Volume
- 97
- Issue
- 15
- Pages
- 150504-150504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2125945272
- Cited by
- 238
- References
- 20
- Citations by year
- 2026: 6 · 2025: 15 · 2024: 9 · 2023: 10 · 2022: 8 · 2021: 12 · 2020: 6 · 2019: 8 · 2018: 5 · 2017: 5 · 2016: 8 · 2015: 7 · 2014: 14 · 2013: 16 · 2012: 15
- FWCI
- 23.98
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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
- measurement-based quantum computation, universal quantum computation, entanglement resource, cluster states, graph states, entanglement measures, single-qubit operations, hexagonal lattice, triangular lattice
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