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Fault-tolerant gates via homological product codes

Jochym-O'Connor, Tomas (2019) Fault-tolerant gates via homological product codes. Quantum, 3 . Art. No. 120. ISSN 2521-327X. doi:10.22331/q-2019-02-04-120.

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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.

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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).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
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Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Record Number:CaltechAUTHORS:20190212-154658098
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92856
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:37
Last Modified:16 Nov 2021 16:54

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