2014/03/11 by Jonas T. Anderson, Guillaume Duclos-Cianci, David Poulin · 2 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.113.080501
published as Phys. Rev. Lett. 113, 080501 (2014) · 6 pages
arxiv created 2014/03/11 · arxiv updated 2014/08/27
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 generate 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.