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On the role of entanglement in quantum-computational speed-up
Open accessAbstract
For any quantum algorithm operating on pure states, we prove that the presence of multi‐partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the quantum algorithm is to offer an exponential speed‐up over classical computation. Furthermore, we prove that the algorithm can be efficiently simulated classically to within a prescribed tolerance η even if a suitably small amount of global entanglement is present. We explicitly identify the occurrence of increasing multi‐partite entanglement in Shor's algorithm. Our results do not apply to quantum algorithms operating on mixed states in general and we discuss the suggestion that an exponential computational speed‐up might be possible with mixed states in the total absence of entanglement. Finally, despite the essential role of entanglement for pure‐state algorithms, we argue that it is nevertheless misleading to view entanglement as a key resource for quantum‐computational power.
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“It has been demonstrated that if the 'quantum entanglement phenomenon' is not used in the quantum algorithm, then the same algorithm can be worked with classical 0 and 1 bits computer systems without any remarkable change in computational speed.”
From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [22]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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“The 'quantum entanglement phenomenon' is the cornerstone of quantum calculation speed and pieces of literature are available [21, 22].”
From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [22]
Experimental — accuracy not yet measuredIn the citing paper
“The existence of entanglement is fundamental for useful quantum computation.”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [45]
In the citing paper
“It has been proved that any quantum algorithm that does not employ entanglement can be enacted in a classical computer with no significant difference in speed [44,45].”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [45]
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Metadata
- Authors
- Jozsa, R., & Linden, N.
- Affiliations
- University of Bristol (GB)
- ORCID
- Jozsa, Richard
- Venue
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2003-08-08
- Volume
- 459
- Issue
- 2036
- Pages
- 2011-2032
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- OpenAlex
- W2163036762
- Cited by
- 839
- References
- 18
- Citations by year
- 2026: 30 · 2025: 71 · 2024: 55 · 2023: 61 · 2022: 56 · 2021: 48 · 2020: 46 · 2019: 33 · 2018: 40 · 2017: 33 · 2016: 33 · 2015: 40 · 2014: 36 · 2013: 45 · 2012: 20
- FWCI
- 20.16
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Explore Bristol Research (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Cambridge University Engineering Department Publications Database (submittedVersion)
- Bristol Research (University of Bristol) (submittedVersion)
- arXiv (Cornell University)
- 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 Mechanics and Applications
- Keywords
- quantum entanglement, multipartite entanglement, global entanglement, Shor's algorithm, classical simulation of quantum algorithms, exponential speedup, mixed states
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