Twins Percolation for Qubit Losses in Topological Color Codes

Abstract

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 lattice. Moreover, we show that determining the corresponding qubit loss error threshold is equivalent to a new generalized classical percolation process. We numerically compute the associated qubit loss thresholds for two families of 2D color code and find that these are close to satisfying the fundamental limit $p_{\text{fund}}=0.461\pm 0.005$ close to the 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 relevant for implementations of quantum error correction in various physical platforms.

arXiv comment6+7 pages, 3+7 figures

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• Analytical percolation theory for topological color codes under qubit loss
• Efficient percolation simulations for lossy photonic fusion networks
• Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture
• Fundamental thresholds for computational and erasure errors via the coherent information
• On the Local Equivalence of 2D Color Codes and Surface Codes with Applications