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Morphing Quantum Codes
Open accessAbstract
We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes.In particular, we morph the 15-qubit Reed-Muller code to obtain a [[10,1,2]] code that is the smallest-known stabilizer code with a fault-tolerant logical T gate.In addition, we construct a family of hybrid color-toric codes by morphing the color code.Our code family inherits the fault-tolerant gates of the original color code, implemented via constant-depth local unitaries.As a special case of this construction, we obtain toric codes with fault-tolerant multiqubit control-Z gates.We also provide an efficient decoding algorithm for hybrid color-toric codes in two dimensions and numerically benchmark its performance for phase-flip noise.We expect that morphing may also be a useful technique for modifying other code families such as triorthogonal codes.
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Small 3D [[8,3,2]] codes encode three logicals per block, feature d = 2 (d = 4) in the Z basis (X basis), implying error-detection (error-correction) capabilities for Z (X) errors, and can realize a transversal CNOT between blocks.
“We focus on small 3D [[8,3,2]] codes16,17,26,27 (Fig. 5a), which have various appealing features. They encode three logicals per block, feature d = 2 (d = 4) in the Z basis (X basis), implying error-detection (error-correction) capabilities for Z (X) errors and can realize a transversal CNOT between blocks.”
From Logical quantum processor based on reconfigurable atom arrays (2024) · cites this paper as [17]
The Ball codes section identifies the 3D hyperoctahedron code as [[8,3,2]], and Additional information states that ball codes have Z-distance two. Our copy establishes only that their X-distance is at least two; it does not establish X-distance four or describe a transversal CNOT between [[8,3,2]] blocks. (LLM, conf=0.86)
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Sorted by citations
Logical quantum processor based on reconfigurable atom arrays
Bluvstein, D., Evered, S. J., Geim, A. A., Li, S. H., Zhou, H., Manovitz, T., Ebadi, S., Cain, M., Kalinowski, M., Hangleiter, D., et al. (2024) · Nature · doi:10.1038/s41586-023-06927-3 · Cited by 1,119
High-fidelity teleportation of a logical qubit using transversal gates and lattice surgery
Ryan-Anderson, C., Brown, N. C., Baldwin, C. H., Dreiling, J. M., Foltz, C., Gaebler, J. P., Gatterman, T. M., Hewitt, N., Holliman, C., Horst, C. V., et al. (2024) · Science · doi:10.1126/science.adp6016 · Cited by 52
Metadata
- Authors
- Vasmer, M., & Kubica, A.
- Affiliations
- University of Waterloo (CA)
- California Institute of Technology (US)
- Venue
- PRX Quantum
- Publisher
- American Physical Society (APS)
- Published
- 2022-08-08
- Volume
- 3
- Issue
- 3
- ISSN
- 2691-3399 (ISSN-L)
- OpenAlex
- W3217663389
- Cited by
- 39
- References
- 11
- Citations by year
- 2026: 7 · 2025: 16 · 2024: 5 · 2023: 5 · 2022: 6
- FWCI
- 2.14
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PRX Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Government of Canada
- Innovation, Science and Economic Development Canada
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum error-correcting codes, stabilizer codes, color codes, toric code, decoding algorithms, phase-flip noise
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