Published February 4, 2019
| Version Submitted + Published
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Fault-tolerant gates via homological product codes
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Abstract
A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.
Additional Information
© 2019. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Published: 2019-02-04. We thank Benjamin J. Brown, and Sam Roberts for insightful discussions on intermediary correction of errors during the fault-tolerant operations. We also thank Christopher Chamberland and John Preskill for comments during the development of this work and Sergey Bravyi for feedback on the initial manuscript. We acknowledge the support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY- 1733907).Attached Files
Published - q-2019-02-04-120.pdf
Submitted - 1807.09783v1.pdf
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1807.09783v1.pdf
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Additional details
Identifiers
- Eprint ID
- 92856
- Resolver ID
- CaltechAUTHORS:20190212-154658098
Related works
- Describes
- http://arxiv.org/abs/1807.09783 (URL)
Funding
- Walter Burke Institute for Theoretical Physics, Caltech
- Sherman Fairchild Foundation
- Institute for Quantum Information and Matter (IQIM)
- NSF
- PHY-1733907
Dates
- Created
-
2019-02-15Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field