Publication: Twins percolation for qubit losses in topological color codes
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2018-08-06
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IoP publishing ltd
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Abstract
In this Letter, we establish and explore a new connection between quantum information theory and classical statistical mechanics by studying the problem of qubit losses in 2D topological color codes. We introduce a protocol to cope with qubit losses, which is based on the identification and removal of a twin qubit from the code, and which guarantees the recovery of a valid three-colorable and trivalent reconstructed color code. Moreover, we show that determining the corresponding qubit loss error threshold is equivalent to a new generalized classical percolation problem. We numerically compute the associated qubit loss thresholds for two families of 2D color code and find that with p = 0.461 ± 0.005 these are close to satisfying the fundamental limit of 50% as imposed by the no-cloning theorem. Our findings reveal a new connection between topological color codes and percolation theory, show high robustness of color codes against qubit loss, and are directly relevant for implementations of topological quantum error correction in various physical platforms.
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© 2018 American Physical Society. D. V. thanks M. Gutiérrez for fruitful discussions. We acknowledge support by U.S. A.R.O. through Grant No. W911NF-14-1-010. The research is also based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the U.S. Army Research Office Grant No. W911NF-16-1-0070. M. A. M. D. acknowledges support from Spanish MINECO Grant No. FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. We acknowledge the resources and support of High Performance Computing Wales, where most of the simulations were performed, as well as the HPC-Université de Strasbourg. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the view of the U.S. Army Research Office.