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Code conversion with the quantum Golay code for a universal transversal gate set

Journal Article · · Physical Review A

The [[7,1,3]] Steane code and [[23,1,7]] quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. These two codes have transversal implementations of all Clifford gates but require some other scheme for fault-tolerant T gates. Using magic states, Clifford operations, and measurements is one common scheme, but magic-state distillation can have a large overhead. Code conversion is one avenue for implementing a universal gate set fault tolerantly without the use of magic-state distillation. Analogously to how the [[7,1,3]] Steane code can be fault tolerantly converted to and from the [[15,1,3]] Reed-Muller code which has a transversal T gate, the [[23,1,7]] Golay code can be converted to a [[95,1,7]] triorthogonal code with a transversal T gate. Further, a crucial ingredient of this procedure is the [[49,1,5]] triorthogonal code, which can itself be seen as being related to the self-dual [[17,1,5]] two-dimensional color code. Additionally, a method for code conversion based on a transversal CNOT between the codes, rather than stabilizer measurements, is described.

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0012704
OSTI ID:
2340738
Alternate ID(s):
OSTI ID: 2473780
Report Number(s):
BNL--225539-2024-JAAM
Journal Information:
Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 109; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (5)


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