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Limitations on Transversal Gates for Hypergraph Product Codes

Authors :
Simon Burton
Dan E. Browne
Source :
IEEE Transactions on Information Theory. 68:1772-1781
Publication Year :
2022
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2022.

Abstract

We analyze the structure of the logical operators from a class of quantum codes that generalizes the surface codes. These are the hypergraph product codes, restricted to the vertical sector. By generalizing an argument of Bravyi and K\"onig, we find that transversal gates for these codes must be restricted to the Clifford group.

Subjects

Subjects :
Surface (mathematics)
Discrete mathematics
Class (set theory)
Hypergraph
Group (mathematics)
Structure (category theory)
Quantum codes
020206 networking & telecommunications
02 engineering and technology
Library and Information Sciences
Computer Science Applications
Product (mathematics)
Transversal (combinatorics)
0202 electrical engineering, electronic engineering, information engineering
Information Systems
Mathematics

Details

ISSN :
15579654 and 00189448
Volume :
68
Database :
OpenAIRE
Journal :
IEEE Transactions on Information Theory
Accession number :
edsair.doi...........a74557df8c659859a82330a643b6a70e

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