2018/02/28 by D. Vodola, Davide Vodola, David Amaro +5
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Computer science #Connection (principal bundle) #Geometry #Mathematics #Percolation (cognitive psychology) #Percolation theory #Percolation threshold #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Qubit #Robustness (evolution) #Statistical physics #Topology (electrical circuits) #Toric code #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevlett.121.060501
published as Phys. Rev. Lett. 121, 060501 (2018) · 6+7 pages, 3+7 figures
arxiv created 2018/03/07 · openalex publication_date 2018/08/06 · arxiv updated 2018/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.