Topological fault-tolerance in cluster state quantum computation
Open accessAbstract
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivalence transformations for these boundary conditions that can be used to simplify fault-tolerant circuits and to derive circuit identities in a topological manner. The spatial dimensionality of the scheme can be reduced to two by converting one spatial axis of the cluster into time. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors. The operational overhead is poly-logarithmic in the circuit size.
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Three-dimensional cluster states are sufficient for measurement-based fault-tolerant quantum computing.
“three-dimensional cluster states are sufficient for measurement-based fault-tolerant quantum computing28,29”
From Quantum computational advantage with a programmable photonic processor (2022) · cites this paper as [29]
Error-correction is directly built into the 3D cluster lattice and yields a threshold of 6.7 × 10^-3 for a model with probabilistic gate errors, including imperfect preparation of the cluster state.
“Error-correction is directly built into the cluster lattice and yields a threshold of 6 . 7 × 10 -3 75 , for a model with probabilistic gate errors, including imperfect preparation of the cluster state.”
From Measurement-based quantum computation (2009) · cites this paper as [75]
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- Authors
- Raussendorf, R., Harrington, J., & Goyal, K.
- Affiliations
- Perimeter Institute (CA)
- California Institute of Technology (US)
- ORCID
- Raussendorf, R
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2007-06-29
- Volume
- 9
- Issue
- 6
- Pages
- 199-199
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2119388976
- Cited by
- 617
- References
- 37
- Citations by year
- 2026: 28 · 2025: 35 · 2024: 43 · 2023: 38 · 2022: 29 · 2021: 31 · 2020: 33 · 2019: 28 · 2018: 36 · 2017: 35 · 2016: 32 · 2015: 33 · 2014: 35 · 2013: 37 · 2012: 37
- FWCI
- 29.03
- 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)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (FG0392ER40701)
- Government of Canada
- Natural Sciences and Engineering Research Council of Canada
- 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
- cluster states, one-way quantum computation, boundary conditions, equivalence transformations, error threshold, time-to-space conversion
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