Classical simulation versus universality in measurement-based quantum computation
Open accessAbstract
We investigate for which resource states an efficient classical simulation of measurement-based quantum computation is possible. We show that the Schmidt-rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidt-rank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement-based quantum computation is possible for all states with logarithmically bounded Schmidt-rank width (with respect to the system size). For graph states where the Schmidt-rank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory.
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The entanglement measure 'entanglement width' can be used to identify efficiently simulatable states.
“for example, the entanglement measure 'entanglement width' can be used to identify efficiently simulatable states 91,94 .”
From Measurement-based quantum computation (2009) · cites this paper as [94]
The efficient classical simulation of MQC on stabilizer states with bounded tree-width yields a novel classical algorithm to efficiently calculate the partition function on (inhomogeneous) q-state spin models on tree-like graphs with or without magnetic fields.
“In turn, the efficient classical simulation of MQC on stabilizer states with bounded tree-width 94 , as demonstrated in 91 , yields a novel classical algorithm to efficiently calculate the partition function on (inhomogenous) q -state spin models on tree-like-graphs with or without magnetic fields 95,96 .”
From Measurement-based quantum computation (2009) · cites this paper as [94]
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References 16 · Cited by 95
Research works printed but not linked: 1
- [28]S. Aaronson and D. Gottesman, quant-ph/0406196; S. Anders and H.-J. Briegel, Phys. Rev. A 73 , 022334 (2006). · arXiv
- Authors
- Van den Nest, M., Dür, W., Vidal, G., & Briegel, H. J.
- Affiliations
- Austrian Academy of Sciences (AT)
- The University of Queensland (AU)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-01-31
- Volume
- 75
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1994508806
- Cited by
- 95
- References
- 16
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 5 · 2023: 5 · 2022: 3 · 2021: 5 · 2020: 6 · 2019: 3 · 2018: 4 · 2017: 3 · 2016: 2 · 2015: 3 · 2014: 8 · 2013: 5 · 2012: 5
- FWCI
- 5.51
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- measurement-based quantum computation, classical simulation, resource states, universality, tree tensor networks, graph states
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