Fault-tolerant quantum computation with few qubits
Open accessAbstract
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. Here, we study the 15-qubit Hamming code, which protects seven encoded qubits to distance three. We give fault-tolerant procedures for applying arbitrary Clifford operations on these encoded qubits, using only two extra qubits, 17 in total. In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 in total. The procedures could enable testing more sophisticated protected circuits in small-scale quantum devices. Our main technique is to use gadgets to protect gates against correlated faults. We also take advantage of special code symmetries, and use pieceable fault tolerance.
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If several layers of encoding are implemented, the qubit overhead multiplies and up to thousands of physical qubits might be needed to encode one logical qubit.
“Moreover, if several layers of encoding are implemented, the qubit overhead multiplies and up to thousands of physical qubits might be needed to encode one logical qubit [61].”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [61]
Cites
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Realization of Real-Time Fault-Tolerant Quantum Error Correction
Ryan-Anderson, C., Bohnet, J. G., Lee, K., Gresh, D., Hankin, A., Gaebler, J. P., Francois, D., Chernoguzov, A., Lucchetti, D., Brown, N. C., et al. (2021) · Physical Review X · doi:10.1103/physrevx.11.041058 · Cited by 306 · see citing works
Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits
Chamberland, C., Zhu, G., Yoder, T. J., Hertzberg, J. B., & Cross, A. W. (2020) · Physical Review X · doi:10.1103/physrevx.10.011022 · Cited by 223 · see citing works
Neutral atom quantum computing hardware: performance and end-user perspective
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Protecting expressive circuits with a quantum error detection code
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- Authors
- Chao, R., & Reichardt, B. W.
- Affiliations
- University of Southern California (US)
- Corresponding author
- Chao, Rui
- Venue
- npj Quantum Information
- Published
- 2018-09-12
- Volume
- 4
- Issue
- 1
- ISSN
- 2056-6387 (ISSN-L)
- OpenAlex
- W2616847007
- Cited by
- 137
- References
- 4
- Citations by year
- 2026: 10 · 2025: 20 · 2024: 14 · 2023: 17 · 2022: 18 · 2021: 16 · 2020: 25 · 2019: 11 · 2018: 5 · 2017: 1
- FWCI
- 8.02
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- npj Quantum Information (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (CCF-1254119)
- DOD | Army Research Office (W911NF-12-1-0541)
- 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
- fault-tolerant quantum computing, Hamming codes, encoded qubits, Clifford operations
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