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Freiburg 2019 – scientific programme

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FM: Fall Meeting

FM 60: Quantum Computation: Fault Tolerance & Error Correction

FM 60.2: Talk

Wednesday, September 25, 2019, 14:30–14:45, 3044

Twins Percolation for Qubit Losses in Topological Color CodesDavide Vodola1, •David Amaro1, Miguel Angel Martin-Delgado2, and Markus Müller11Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom — 2Departamento de Fisica Teorica I, Universidad Complutense, 28040 Madrid, Spain

In our work [1] 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.

[1] D. Vodola, D. Amaro, M. A. Martin-Delgado, and M. Müller, Phys. Rev. Lett. 121, 060501 (2018)

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