Percolation, Renormalization, and Quantum Computing with Nondeterministic Gates
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We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.
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By exploiting percolation, scalable quantum computation with non-deterministic gates is possible even with simple non-switching optical circuits.
“However, by exploiting a phenomenon known as percolation, scalable quantum computation with non-deterministic gates is possible even with simple non-switching optical circuits 41 .”
From Measurement-based quantum computation (2009) · cites this paper as [41]
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- Authors
- Kieling, K., Rudolph, T., & Eisert, J.
- Affiliations
- Imperial College London (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-09-25
- Volume
- 99
- Issue
- 13
- Pages
- 130501-130501
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2152434138
- Cited by
- 121
- References
- 24
- Citations by year
- 2026: 6 · 2025: 10 · 2024: 8 · 2023: 6 · 2022: 4 · 2021: 6 · 2020: 4 · 2019: 5 · 2018: 6 · 2017: 5 · 2016: 3 · 2015: 3 · 2014: 7 · 2013: 4 · 2012: 3
- FWCI
- 13.02
- 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)
- Funders
- Engineering and Physical Sciences Research Council (GR/S51226/01)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- percolation theory, entangled states, optical quantum computing, ultracold atoms in optical lattices, hole defects, single-qubit measurement, resource scaling
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