Fault-tolerant conversion between the Steane and Reed-Muller quantum codes

Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant T an...

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Bibliographic Details
Published in:Physical review letters 2014-08, Vol.113 (8), p.080501-080501, Article 080501
Main Authors: Anderson, Jonas T, Duclos-Cianci, Guillaume, Poulin, David
Format: Article
Language:English
Subjects:
Computation
Conversion
Error correction
Fault tolerance
Gages
Gates
Gauges
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Summary:Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant T and control-control-Z gates. Combined with the Clifford group, either of these two gates generates a universal set. Here, we combine these two features by demonstrating how to fault-tolerantly convert between these two codes, providing a new method to realize universal fault-tolerant quantum computation. One interpretation of our result is that both codes correspond to the same subsystem code in different gauges. Our scheme extends to the entire family of quantum Reed-Muller codes.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.113.080501